help-33

[ebon schooner]

wait how are both answers wrong?

[amber ruin]

$\frac{\sin(61.9)}{\sin(83.1)}\neq\frac{7}{9} \ \frac{\sin(50.5)}{\sin(94.5)}\neq\frac{7}{9}$

[elfin berry]

ta

[amber ruin]

its just law of sines for B and C

[ebon schooner]

no its not working

because 94.5 and 83.1

are not the exact decimal numbers i think

I rounded them

[amber ruin]

that doesn't make much difference I think

[ebon schooner]

ok so why did I get 2 different answers again?

sorry I'm still a bit confused

[amber ruin]

hm I think you're right about approximation

it seems that 95 and 50 are the correct answers

[ebon schooner]

i dunno then

cause i keep getting two different things

and I cant use ambiguous case as well

[amber ruin]

maybe there is some confusion between radians and degrees

in your calculator

[ebon schooner]

its in degrees

[amber ruin]

I'm guessing that sin -1 function is very sensitive to even small approximation errors because its input is a value between -1 and 1

[ebon schooner]

okay

.close

[marsh citrus]

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[nova totem]

I'm very close to getting the moderators; stick to your channel

.close

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[sleek lake]

discord

it's in the name

we literally hack people

[nova totem]

LOL

[marsh citrus]

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[jolly apex]

Hello! I would like to get help with this one. I need to find the perimeter of this shape.

[jolly apex]

Basically Im planning to break this down

Like the rectangle, triangle, and the semi circle

I know their formulas but I just don't know how to incorporate that

[patent seal]

i assume you knoww everything beside the part with the circle

correct?

[jolly apex]

yes

[patent seal]

allrigt so you need scope of the circle. the scope is calulated with the diameter*pi

so you have 7ft+4ft+3ft+5.7fr and for the circle part (8*pi)/2 because it's only half of it 12.6ft

7ft+4ft+3ft+5.7fr+12.6ft=32.3

[jolly apex]

ohh! I get it now

[patent seal]

is it answered like that?

[jolly apex]

just a quick question how did u get 12.6ft

[jolly apex]

yes

[patent seal]

you see that the diameter of the hypotetical circle is 8

because you have 2*4fr

[jolly apex]

yeah

[patent seal]

then you calculate 8*pi

and this divided by 2

since it's a semi circle

[jolly apex]

ohh! ok

thank u so much!

[patent seal]

no problem

.close

can't close it for you

[jolly apex]

.close

[marsh citrus]

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[wise minnow]

Help!

[marsh citrus]

@wise minnow Has your question been resolved?

[wise minnow]

Helpppp

Ahhhh

[gilded smelt]

!status

[marsh citrus]

What step are you on?
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3. I got an answer but I'm told it's wrong
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6. None of the above

[gilded smelt]

also, your question

[marsh citrus]

@wise minnow Has your question been resolved?

[marsh citrus]

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[torpid owl]

is this right? (the answer choices on the right side of the equation are the same for each dropdown)

[torpid owl]

.closw

.close

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[marsh citrus]

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[azure trench]

For part b if the tank is initially full what value of h would I sub into the eqn

[glass silo]

If it's initally full then the height of the water would be 1

As the radius of the hemisphere is 1, you'd have the maximum depth of the water you could have is 1

[marsh citrus]

@azure trench Has your question been resolved?

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[marsh citrus]

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[paper herald]

help

[paper herald]

with this

how you can find y=5x etc

[late grove]

line AB will have the coordinates (0, 0) and (1, 5). from there you can just use rise-over-run to get the equation

[paper herald]

how

[late grove]

y = mx + c. the gradient (m) here is going to be $\frac{5 - 0}{1 - 0} = 5$

[elfin berry]

raonicalias

[late grove]

y = 5x + c. substitute one of the points in and c = 0

[paper herald]

what is 5-0/1/-0

[late grove]

It's how we calculate the slope of the line AB

[paper herald]

?

[late grove]

yeah! we're using that formula here

[paper herald]

Do you know integrals? why split in two areas?

[late grove]

once we get the line equations for all of the lines we can express the triangle's area in terms of the areas underneath the lines

area under the line from (0, 0) to (1, 5) + area under the line from (1, 5) to (2, 2) - the area under the line from (0, 0) to (2, 2)

[paper herald]

thx for help me !

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[versed turret]

If we add 2 to the numerator of the usual fraction, and 3 to the denominator, then the value of the fraction will not change. If we add 1 to the numerator and the 6 to denominator, then the value of the fraction will decrease by 1/6. Find this fraction

[late grove]

$\frac{x}{y} = \frac{x+2}{y+3}$ and
$\frac{x+1}{y+6} - \frac{1}{6} = \frac{x}{y}$

[elfin berry]

raonicalias

[versed turret]

do I solve this in system or?

[late grove]

don't try solving it in a system, just try solving the first one

you won't get any number for x or y, but you'll find y in terms of x

from there you can substitute y in the other equation to get your answer

[versed turret]

I will try that thanks

[late grove]

lmk what you get for the first equation, and then lmk your final answer

I'll tell you if you got anything wrong

[versed turret]

well, y=3x/2

[late grove]

correct!

[versed turret]

I get x negative

[late grove]

yes, x is negative

[versed turret]

-16

?

final answer is 2/3

[late grove]

$x = -\frac{7}{8}$ according to my calculator

[elfin berry]

raonicalias

[versed turret]

in the answers it is written 8/12

but 2/3 is 8/12

[late grove]

huh

$\frac{x + 1}{\frac{3x}{2} + 6} - \frac{1}{6} = \frac{x}{y}$

[elfin berry]

raonicalias

[versed turret]

u should also write x/3x/2

[late grove]

Dw was about to

$\frac{x + 1}{\frac{3x}{2} + 6} - \frac{1}{6} = \frac{x}{\frac{3x}{2}}$

[elfin berry]

raonicalias

[late grove]

$\frac{x + 1}{\frac{3x}{2} + 6} - \frac{1}{6} = \frac{2x}{3x}$

[elfin berry]

raonicalias

[late grove]

$\frac{x + 1}{\frac{3x}{2} + 6}= \frac{2}{3} + \frac{1}{6}$

[elfin berry]

raonicalias

[late grove]

try it from here

Wait you're right haha

yeah it's -16

No clue why my calculator got that

[versed turret]

npp

I dont understand why it is 8/12 in answers tho

[late grove]

what were they asking you for? x/y?

[versed turret]

the question is: what is that fraction

so yeah prolly x/y

well, I think we got it right anyways, ty for help!

.close

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[mighty shoal]

hi could someone help me with this? im not sure what the 120 degrees turn refers to and it would be really helpful

[sleek lake]

sounds really weird

[mighty shoal]

yeah im not sure in which direction the 120 is

does it like go back

[sleek lake]

this makes most sense

[mighty shoal]

ah okay i did that as well

hopefully its right

thanks!

[sleek lake]

well okay no

like it really could be 60° instead and 120 on the other side

it's just less walking so maybe he preferred that

[mighty shoal]

imma just go with this one, hopefully he likes to walk less

[sleek lake]

and it's not actually isosceles

[mighty shoal]

yep

[mighty shoal]

i think this one makes more sense

so ill go with this

thanks man

.close

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[sleek lake]

so it would be like this

[mighty shoal]

.reopen

[marsh citrus]

✅

[mighty shoal]

whoops

[mighty shoal]

so something like this?

[sleek lake]

so is it possible to draw it with 120° at all, i'm confused

no, that angle is meant ot be 60

[mighty shoal]

oh shit yeah mb

what if its like this

"which is 120 degrees to the direction he was first walking in" do u know what this could be?

[sleek lake]

okay yeah clearly you can draw it both ways

i would assume he's doing the longer path with 60°

[mighty shoal]

ah okay thank you

ill go with that then

[sleek lake]

but why

[mighty shoal]

wdym?

[sleek lake]

so messed up

i can't convince myself either one is clearly right

[mighty shoal]

same bruh like its worded so weirdly

and when i search online they have both drawings

[sleek lake]

it's like you said, the best argument is that he would walk less this way

[mighty shoal]

the 60 degrees way right?

or the 120

[sleek lake]

the 120 inner angle

[mighty shoal]

ah okay thank you

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[smoky lodge]

how did we get to (1/2)1/10

[tight furnace]

What progress have you made

[smoky lodge]

I haven't done any calculations, im trying to understand how it got into that

[tight furnace]

Do you see any ways to simplify the top equation

[smoky lodge]

I cant think of any

except for this

idk if this is correct

[tight furnace]

why did you turn ^10 into a tenth root?

[quasi minnow]

e^-k=2^-1/10
-k = ln(1/2)^1/10
k=1/10 * ln(2)

[smoky lodge]

oh ok that was incorrect lol

how to get to here : e^-k=2^-1/10

[tight furnace]

What operation do you perform to both sides to get rid of the ^10

[tight furnace]

positive 1/10

[smoky lodge]

so i raise both sides by 1/10?

[tight furnace]

Yeah

[smoky lodge]

does finding the 10th root also woork?

oh ok i see it now

[tight furnace]

Yeah

[smoky lodge]

lemme try it

I got it

thank you both!

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[marsh citrus]

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[worn field]

I wasn’t sure where to ask but what are the roots,factors and zeroes of a quadratic

[fathom ridge]

Roots of a quadratic are the values for which it equals 0, these can be real, or imaginary.
All quadratics can be factored in the form of (x - a)(x - b) where a and b are (potentially complex) roots of the quadratic, generally though, if you're asked to factor a quadratic, these would be rational numbers.
Zeros and roots are equivalent.

[worn field]

so if a quadratic was factored like this then would the roots be 3 and 4
(x-3)(x-4)=0

[desert socket]

roots and zeroes are the same thing
These are those are values of x for which the quadratic equation has a value of zero
Factors of a quadratic are two terms into which a quadratic can be factorised into
Example take the quadratic x^2+3x+2
It can be factored to (x+1)(x+2)
So (x+1) and (x+2) are two distinct factors of the quadratic equation
Value of x when these factors are set to 0 are the roots
So (x+1)=0 and (x+2)=0
x=-1,-2
These values are roots/zeroes of the quadratic

[worn field]

ohhh thanks

[marsh citrus]

@worn field Has your question been resolved?

[fathom ridge]

Yeah and (x - 3) and (x - 4) are called the factors of that quadratic

[marsh citrus]

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[marsh citrus]

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[marble glacier]

bro

No im here to ask you why you created 2 accounts

to post the exact same question

https://gyazo.com/fc2bd0a807696099c0f207102a3450e5

oh

so you both joined the server today

[proud ice]

This counts as occupying multiple channels and is not allowed.

If you need help, then..

!status

[marsh citrus]

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

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

[marble glacier]

if you'd bother to read your other channel

i told you what to do

I've laready

told you what to do

look in the other channel

bro

Yea ok

BRO

THE CHANNELS R PUBLIC

bro take a chill pill

how did u get this?

AHh ok

Well first things first

have u finished of the probabilty tree?

you've said my name more than anyone this week

calm down

in total how many balls are in bag B

hint: look at the denom

bro

Naw

Have fun bro

You see maybe if the joke was funny i wouldve let you off

but its like 12 yr old jokes

Yea

ok

Fill in the rest of the tree diagram hint: no matter what you get out the first bag will NOT affect the 2nd bag

[hollow loom]

Um according to #rules he shouldn't be in this server

[marble glacier]

yea

hes 16 he just got held back 4 years

[hollow loom]

You act childish

[main idol]

Don't encourage people to avoid the rules

[marble glacier]

Ok now fil in the TREE the probability cannot change for bag B no matter what you pull out of bag A

so it'll be all the same

2/5 for red and 3/5 for blue

[hollow loom]

Same probability for red and blue no matter what you pull out of bag A

[marble glacier]

ive told you what to do

either take my advice or dont

stick to your 221/100 if you like

[hollow loom]

Ok step by step

What is the probability of pulling a red out of bag B

It's given

Also wrong

For bag B

Look at the tree diagram

Straightforward

Yess

Now what is the probability of blue from bag B

Okay now those are the same probability for all the rest of bag B probability

It is independent to bag A

Doesn't matter what you get from bag A you will have same probability for bag B

No

Um also no

Um

How did you get to that answer

What did your brain do

What's the thought process

Was it a guess.....

Ah

Um

Red for what

Red ball from bag A

Or bag B

Or do you mean P(red red)

[delicate prairie]

.close

[marsh citrus]

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[main idol]

Ty rocketman

[marsh citrus]

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[heavy sonnet]

how is the correct method to solve this

[eternal tundra]

xcox?

[heavy sonnet]

cos, srry

[eternal tundra]

ahhh

[crisp mantle]

Cos (1/x) is a real number between -1 and 1

And this real number is multiplied by x, x tends to zero

[eternal tundra]

we have f*g where f goes to 0 and g does not diverge to infinity

[crisp mantle]

So substitute x=0, its a real number multiplied by 0

Which is 0

[heavy sonnet]

is it called a bounded function no?

[eternal tundra]

yes i assume so

at least i would translate it like that

[heavy sonnet]

in spanish is "acotada" which is the translation

so, everytime that a bounded function appears, it acts like a natural number no?

or like a "k"

[high ledge]

Is it $\lim_{x \to 0^{-}} (x \cos(\frac{1}{x}))$?

[elfin berry]

Rub05

[heavy sonnet]

yeah

[steel sapphire]

Yeah it was kinda confusing lol

[high ledge]

In this cases, you only have to rewrite the expression and then use L'Hopital

$xcos(\frac{1}{x}) = \frac{cos(\frac{1}{x})}{\frac{1}{x}}$

[heavy sonnet]

but they told me that is not that difficult

[elfin berry]

Rub05

[heavy sonnet]

i only have to take into account that the cos function is bounded and it is multiplied by zero

so the result is 0

[high ledge]

You just have to do this every time you see a product like this one

[high ledge]

That's right too

But it's not multiplied by zero, it's multiplied by numbers that are ≈ 0

[heavy sonnet]

ok, thanks

.close

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[clever forge]

Would it probably be something like n = n

[high pine]

expression not equation

[clever forge]

oh

well would it mean n + n

[high pine]

but n + n doesn't work

for n = 3 it gives 3 + 3 = 6, not 12

[clever forge]

oh

let me try

n + n^2

i guess its also equation

[high pine]

still not, for n = 2 we have 2 + (2)^2 = 2 + 4 = 6, should be 9

[clever forge]

then im close to it

[high pine]

Do you see the pattern or you're just guessing

[clever forge]

but its asking for the total of squares

not shaded

[high pine]

yes

ik

[clever forge]

oh

3n + n

[high pine]

close but no

for n = 2 it gives 3(2) + 2 = 6 + 2 = 8

3n + 3 works

[clever forge]

2*6 + 3 isnt it?

what am i asking

nvm

oooohhh

3*2 + 3 = 9 so therefore would it be expanding until undefined moment?

3n + 3

[high pine]

wdym by undefined moment, it works for every finite n

[clever forge]

thats what i was asking just different words used sorry to confuse you

Thanks for helping!

.close

[marsh citrus]

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[coarse ruin]

Hi please could anyone help me rearrange this

It is trigonometric functions

Thank you

<@&286206848099549185>

[marsh citrus]

@coarse ruin Has your question been resolved?

[coarse ruin]

<@&286206848099549185>

Hey how would i rearrange this equation

.close

[marsh citrus]

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[bleak chasm]

<@&286206848099549185>

[marsh citrus]

@bleak chasm Has your question been resolved?

[bleak chasm]

.close

[marsh citrus]

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[marsh citrus]

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[tribal pivot]

can i say x^0 is 1 or is it 0^0?

[pliant maple]

0^0 still equals 1

[tribal pivot]

isn't it undefined?

[pliant maple]

nope

[tribal pivot]

alright thanks

.close

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[rocky pilot]

can someone plz help I dont know where to start on this prblm

[feral crypt]

From the image provided, it is not possible to tell what is being asked for.

Find what of the following?

[rocky pilot]

The prblm is asking to find f'(2) g'(6) and h'(2)

Im quite confused on how to start

<@&286206848099549185> ?

[spark siren]

if F = f + g, what is F' then?

[rocky pilot]

F'= f'(x) + g'(x)

G'= f'(x) + g'(x)

H'= 3f'(x) + 2g'(x)

I know that much

at least I think so

[spark siren]

so you need just f' and g' which can easily be seen in teh graph

[rocky pilot]

9 and 4?

[spark siren]

no, f an g are linear,, you need the slope of f and g.

[rocky pilot]

y-y1=m(x-x1) yes?

[spark siren]

yes

[rocky pilot]

ok and do I plug in f(x); (9,9) and g(x); (4,0) into that?

Dont know what I should plug in there

[spark siren]

no. for f:
P1(0/9) and P2(9/0)

for g is would suggest (0/4) and (4/6)

[rocky pilot]

how did u get 4/6

[rocky pilot]

why that point specifically?

[spark siren]

just choose a point you like.

[rocky pilot]

So then I plug in these into y-y1=m(x-x1)
P1(0/9) and P2(9/0)
(0/4) and (4/6)

still a lil confused

[spark siren]

if a function is linear, you need only two points to determine the slope. which one does not matter. you can takt this one i suggested, you can take other ones. it doesnot matter.

[solemn plover]

Or you could use y=mx+c

To find m

Then you easily have f'(x)

And g'(x)

[rocky pilot]

how do I use that

[solemn plover]

C is the point at which the line touches y axis

[rocky pilot]

ok

[solemn plover]

Can you do it?

[rocky pilot]

yea c is basically 9 for f(x) and 4 is for g(x)

[solemn plover]

Yes

Then apply y=mx+c

[rocky pilot]

y=m(0)+9 for f(x) I assume
y=m(4)+6 for g(x) I assume

[solemn plover]

And what about y

[rocky pilot]

9=m(0)+9
6=m(4)+6

correct?

[solemn plover]

I'd say use a point where x≠0

Because you need to find m

[spark siren]

that is just the same what you had earlier. but its your decision.

[solemn plover]

for f(x) why don't you use (1,8)

[rocky pilot]

this point fine?

[rocky pilot]

oh alr

[solemn plover]

Any point that lies on the line would work

[rocky pilot]

8=m(1)+8
6=m(4)+6

correct?

[solemn plover]

What is the c for f(x)?

[rocky pilot]

9?

[solemn plover]

And what have you input?

[rocky pilot]

oh I see

8=m(1)+9 for f(x)
6=m(4)+4 for g(x)

[solemn plover]

Y=mx+c

What is the c for g(x)

[rocky pilot]

4

[solemn plover]

Check again

[rocky pilot]

its not 4?

[solemn plover]

It's 4

Cheeky boi

[rocky pilot]

oh ok

[solemn plover]

You put 6

[rocky pilot]

miss input trust

8=m(1)+9 for f(x)
6=m(4)+4 for g(x)

[solemn plover]

M is the slope

There fore the derivative at any point

[rocky pilot]

slope for f(x) is -1
slope for g(x) is 1/2
correct?

[solemn plover]

Idk about calculations

Yeah

Correct

[rocky pilot]

Well it seems right

[solemn plover]

You can proceed further by your own

[rocky pilot]

Yea

I checked the answer key and I got it right

thanks HillBill

[solemn plover]

Anytime mate

[rocky pilot]

.close

[marsh citrus]

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[marsh citrus]

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[torpid owl]

the length of side c?

huh??

is this khan academy?

how many attempts do you have?

what math are you taking?

oh this is definitely out of my range

when is it due?

I would suggest just opening a help-forum query and when someone more educated (lol) views it they can help you better,

Unless this is due tonight

mm...

just open a query on the help-forum

all the smart guys are sleeping right now

[still temple]

I forgot how to solve

Does it equal to 180 in

Do yk if the whole shape is equaivalent to 180 in.

A is 30 b is 30 and c is 30

That’s 90

(I don’t know what I’m talking abt)

So therefore

6+ 4 is 10

(I’m clueless)

[marsh citrus]

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[still temple]

Welcome

[marsh citrus]

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[clever raven]

how do i classify the series, if the general term is (n/n+1)^n

[clever raven]

I can only use cauchy and d'alembert

d'alembert and cauchy's limit converges to 1 - , so it doesn't classify

Maybe u can point me in the right direction

[sweet pawn]

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

You can expand this using the binomial theorem

Assuming n is integer

[clever raven]

Yes it is natural

[sweet pawn]

Great

Then you get a double sum

[clever raven]

split and then

[sweet pawn]

$$\sum_{n=0}^{\infty} \left( \sum_{k=0}^n \binom{n}{k} (-1)^k (n+1)^{-k} \right)$$

[elfin berry]

Mr. Gamer

[clever raven]

shitt i don't undersand binomial

guess i'll have to dig on that for a while

Thanks!

Wait

[sweet pawn]

WHAT

[clever raven]

(1 - 1/(n+1))^n this looks very similar to e

[clever raven]

srry don't mean to annoy u

[sweet pawn]

$\lim_{n \to \infty} (1-\frac{1}{n+1})^n = \frac{1}{e}$

[elfin berry]

Mr. Gamer

[sweet pawn]

So that means you know the series doesn't converge

Because the terms don't even go to 0

[clever raven]

Then i don't need to do the binomial expansion

I got super scared

Thank u!

[sweet pawn]

LOL

[marsh citrus]

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[tribal wing]

Help me

[dry prawn]

!status

[marsh citrus]

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

[tribal wing]

2 3 6

[dry prawn]

show your work

[tribal wing]

I kinda don’t know how to do it

[dry prawn]

ok so 5 of the 15 cookies are chocolate chip

which means the probability of selecting a chocolate chip cookie is what?

[tribal wing]

5/15

[dry prawn]

reduce the fraction please

[tribal wing]

I think like 1/3

[dry prawn]

indeed

so which of those 4 options is equivalent to 1/3?

[tribal wing]

B

[dry prawn]

B it is

[tribal wing]

Thank u

[sharp harness]

slightly irrelevant but what does ``$\frac{2}{3}1$" (from option D) even mean?

[elfin berry]

bee

[dry prawn]

either a typo or a horribly written mixed fraction i guess

[glass silo]

[ wouldn't be surprised if it were a $\frac231$ type thing]

[elfin berry]

@glass silo

[glass silo]

rather than e.g. \frac{2}{31} etc

[marsh citrus]

@tribal wing Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[mint iris]

If i have imaginary poles do I still need to use routh table to find Wc

[mint iris]

for root locus

[marsh citrus]

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[marsh citrus]

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[sturdy haven]

I need a walkthrouhg

[marsh citrus]

@sturdy haven Has your question been resolved?

[main idol]

!show

[marsh citrus]

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

[sturdy haven]

i dont know how to start

wow impressive help

[main idol]

chill your sarcasm, there's like 30 open channels

go pay for a tutor if you can't wait

[sturdy haven]

i didnt say anything about the wait.

actually its 22 not 30

also considering the fact that i waited 20+ minutes while other new channels get automatic help.

very good

.close

[marsh citrus]

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[main idol]

have a better attitude next time

[marsh citrus]

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[sturdy haven]

the fact bro came back just to insult me.

[sturdy haven]

.close

[marsh citrus]

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[main idol]

i didn't insult you. didn't call you a name or anything

just gave you good advice

[sturdy haven]

oh now your responing faster

at least you can show that u can improve in something

[main idol]

.

[sturdy haven]

👏

[main idol]

feel free to pay for a tutor if you don't like the free help

[sturdy haven]

I thought there was 30+ channel maybe it would be better to help those people instead of coming back to talkback

[rugged cobalt]

do you still need help

[marsh citrus]

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[marsh citrus]

@mild quartz Has your question been resolved?

[mild quartz]

<@&286206848099549185> Please?

For more information, why I wrote "Now stuck with this". Second time asking for help with Substitution. First time was in "help-17" at 15:37. So you do this Integral with substitution.
And I don't know if my u is wrong or if the calculation itself was just wrong

[mild quartz]

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[hardy locust]

This is the question im stuck on, I know I need to use probability using combinations but don't know where to start. Can someone help?

[crisp mantle]

So we need to find the probability that 10 chosen people are not spies

There is only one possible case of this; where 4 particular people are not chosen (spies) and the other ten are

Thus numerator is 1

Denominator is the total number of ways of choosing 10 people out of 14

[crisp mantle]

Do you know how to find this using combinations?

[hardy locust]

14C10? idk the actual formula but I don't think I need it for the level im at right now

[crisp mantle]

Yep 14c10

[proper zodiac]

<@&268886789983436800>

[crisp mantle]

So its 1/14c10

[weary ibex]

Yes?

[hardy locust]

why is the numerator one again? because theres only 1 way to get all ten people not being spies?

[crisp mantle]

Yepp

[hardy locust]

so its 1/1001

[gritty pagoda]

There was an embed

[hardy locust]

I put it into the calculator

[crisp mantle]

Ah I haven’t calculated the answer

Tbh the formula for combinations is easy, 14c10 = 14!/(10!)(4!)

By ! I mean factorial

And the 4 in the denominator is because 14-10=4

[hardy locust]

yeah i saw that but my teacher said we dont need to know that atm

[crisp mantle]

Okay then

[hardy locust]

but thats just one example so can I try another one and oyu help if i go wrong?

[crisp mantle]

Okay

[hardy locust]

Ill try this one

so heads up exactly 6 times means the numerator is 6

i think

[crisp mantle]

Ah maybe actually I would solve this in a different manner

[hardy locust]

ok let me think for a sec

[crisp mantle]

Sure

[hardy locust]

is it 10Csomething?

[crisp mantle]

The numerator, yes

[hardy locust]

the numerator is 10c6

[crisp mantle]

Yepp

[hardy locust]

how do i know which part is the numerator and the denominator

[crisp mantle]

Numerator is the no of times the given even occurs, ie you toss a coin 10 times, how many cases exist where 6 heads appear

[hardy locust]

yep

[crisp mantle]

So like one case would be first 6 tosses are heads, another would be first 5 and 7th tosses being heads etc

The denominator is the total number of outcomes

[crisp mantle]

So one random outcome could be first 5 heads and 5 tails or all tails etc

[hardy locust]

sure

[crisp mantle]

Have you calculated the denominator?

[hardy locust]

no but its the total number of outcomes from flipping 10 coins

[crisp mantle]

Yep

[hardy locust]

so 2^10 ?

[crisp mantle]

Exactly

[hardy locust]

so its 10c6/1024

[crisp mantle]

Yes

[hardy locust]

which is 210/1024 which can be reduced to 105/512

[crisp mantle]

Yeah thats right

[hardy locust]

thank you very much. To summarize, the numerator is the number of times the event could occur which I can use my calculator for and the denominator is the total number of possible outcomes

[crisp mantle]

No problem, yep

[hardy locust]

♥️ thank you again

[crisp mantle]

Anytime!

[hardy locust]

.close

[marsh citrus]

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[cunning elk]

let f,g : N --> N. such that f(n) = g(2n) . prove that if f is Surjective then g is not Injective

[cunning elk]

pls help guys

i dont know how to start

[scenic depot]

Do you understand what surjective and injective mean?

There is no technique to this proof, you just have to understand what those mean and the cardinality of the set of the natural numbers

[cunning elk]

i do undertand but i need a proof ....

[scenic depot]

I mean I won't give you the answer, how is it gonna help you learn

[cunning elk]

i starterd like this : f is Surjective -- > for every y in N there exist x in N such the f(x) =y . f(x) = y -- > g(2x) =y

idk how to continue

[scenic depot]

I will give you a huge hint, basically the whole proof. Think about a surjective function from Even numbers to N

[cunning elk]

nvm

thx

.close

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[dire yew]

This correct

[marsh citrus]

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[spark lintel]

Hello

[spark lintel]

I have to prove this series with comparison, can we assume this is true?

Or are there cases when this isn’t

[smoky plover]

It’s the opposite I think

[proper zodiac]

$\sqrt{a} < a \iff a > 1$

[smoky plover]

Well for 1 they are qual

[elfin berry]

ΣAC

[smoky plover]

Yea and n+4>n^2+4 when 0<n<1

[marsh citrus]

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[green panther]

So this is what's going on and well, sequencing... and I am stuck essentially at this pretty basic part here and I don't know how to progress further

[green panther]

I've tried to go further by trying to square root it, but that jumbles up the 6

[marsh citrus]

@green panther Has your question been resolved?

[marsh citrus]

@green panther Has your question been resolved?

[marsh citrus]

@green panther Has your question been resolved?

[marsh citrus]

@green panther Has your question been resolved?

[marsh citrus]

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[untold umbra]

Is this a mistake?

[stiff tusk]

No?

Why would it be a mistake?

[whole sleet]

Why u/u?

Derivative of u is 1
So integral of 1 is u

[marsh citrus]

@untold umbra Has your question been resolved?

[marsh citrus]

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[hybrid eagle]

The ratio of Anne's mass to Collin's mass was 3:5. If Anne's mass increased by 10kg and Collin's mass decreased by 4kg, they would have the same mass. What was Anne's original mass?

[still temple]

@hybrid eagle

[fathom ridge]

I can't hit you with 2 nosols in a row

[hybrid eagle]

.close

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[misty marten]

Roman II

[misty marten]

Ive solved most of it but i think i messed up the end

.close

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[copper drum]

We have x = 2 (mod 3), why does this imply that x = 2 or 8 (mod 9)

[devout mauve]

it doesnt

do you have more information you are ignoring?

[copper drum]

No

[devout mauve]

well what is D'_2m+1

[copper drum]

For this context it doesn’t matter like at all

[devout mauve]

so you say

[copper drum]

Does it imply 3x = 2 or 8 mod 9?

[devout mauve]

no

3x=6 mod 9

[copper drum]

That’s what I thought

[devout mauve]

ok from a quick check it does seem like a mistake

[copper drum]

Is the statement x = 2 (mod 3) implies x = 2, 5 or 8 (mod 9) correct?

[devout mauve]

yes

[copper drum]

Okay nice

[copper drum]

Do you have any idea how to show D'_2m+1 is congruent to 2 (mod 3)

[devout mauve]

no

[marsh citrus]

@copper drum Has your question been resolved?

[marsh citrus]

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[worthy stream]

need help with solving

[cobalt spindle]

split the expression into two fractions

so 3x/(x2+1) and 1/(x2+1)

the integration of second is arctanx

as for the first take 3 out of the integration and multiply and divide the entire expression by 2
and take the 2 in the denominator out of the expression

so youre left with this

then just apply substitution to this

[worthy stream]

like this?

[cobalt spindle]

yes

[marsh citrus]

@worthy stream Has your question been resolved?

[worthy stream]

can you provide how to solve⌠1/(x²+1) dx?

[cobalt spindle]

u have to remember it

its arctanx

[worthy stream]

what should I be looking "Derivative of arctan"?

[marsh citrus]

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[marsh citrus]

Please don't occupy multiple help channels.

[vital oriole]

.close

[marsh citrus]

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[marsh citrus]

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[unique hound]

I'm quite confused by this.

What is the question even asking?

[tender mantle]

It is asking the value of it

[jovial spire]

use base change theorem

[ivory gull]

this

[jovial spire]

??

[marsh citrus]

@tender mantle Has your question been resolved?

[marsh citrus]

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[marsh peak]

They would be the same if it was 10x instead of 12x

What's the original problem?

[mild quartz]

It's in German. But we had f(x) and had to find the "extreme points" (local max. / low. point on the graph)

Therefore I tried to form the first and then the second deviation

[marsh peak]

The first line of f''
Are you sure it should be 2x - 8 there?

[mild quartz]

Sorry, didnt the your first line

[marsh peak]

Or should I be looking at the green notes?

[mild quartz]

Yes, the green notes

I realised, while working on the black one, that I made a mistake. The green notes are the newer ones. And at "Ableitungen" I wanted to summarize the f(x), f'(x) and f''(x)

[marsh peak]

Wouldn't it be easier to factor the (2x - 2)
Anyway, the coefficients of x do not add up to 12 there

They are 2x + 4x - (-8x + 4x)

Or 6x - (-4x) and 10x

[mild quartz]

Oh crap. Yes, that would have made it easier.

[mild quartz]

oh man, thanks a lot. Can't deal with those - and ().
Thanks a lot! Hero for the evening!

.close

[marsh citrus]

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[frank oriole]

Why did we split it up like that

[sweet pawn]

That's wrong

[sour relic]

i thi k so too

[sweet pawn]

It should be C/(s-1)

[sour relic]

and Bx+c AT 1/s²

[frank oriole]

Yeah but I don’t understand the thing as a whole

[sour relic]

look up partial fraction decompisition in google

[frank oriole]

Ik

[marsh peak]

What they wrote works as well

[sweet pawn]

No that part is fine, (As+B)/s² = A/s + B/s²

[frank oriole]

It’s just this form doesn’t make any sense to me

[sweet pawn]

Ok then let me put it this way

Lets avoid using variables at all for a sec

How do you add fractions?

What is 1/2 + 1/7?

[frank oriole]

14 in the denominator

Then divide 14 by 2

And by 7

Add those we get the numerator

9/14

[sweet pawn]

So you're saying:
1/2 + 1/7 =
7/14 + 2/14 =
9/14

[frank oriole]

Yes

[sweet pawn]

Ok. So the whole deal behind PFD (partial fraction decomposition) is that we can go the other way

What if we START with a fraction and want to break it down into a sum of fractions?

So let's start with 9/14

9/14 = 9/(2×7) = A/2 + B/7

And we can always write any fraction with a denominator of 14 as the SUM of two fractions, one with denominator 2 and the other with denominator 7

Can you see why?

[frank oriole]

Yeah I get it

[sweet pawn]

So why don't we solve? If we have:
9/(2×7) = A/2 + B/7
Then:
9 = 7A + 2B

A = 1, B = 1, right?

[frank oriole]

Yes

[sweet pawn]

So now does that make sense as to how we can do that?

Decompose a fraction into the sum of fractions whose denominators are the factors of the original one?

[frank oriole]

Yea

[sweet pawn]

Great. Anything else?

[frank oriole]

Nope

Thank you

.close

[marsh citrus]

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[zenith bloom]

Hi. Could anyone help me solve the area of this triangle

[zenith bloom]

I used the pythagorean to solve CB which was ≈72 cm

But im not really sure what to do next

[high ledge]

Do you know some basics about trigonometry?

[proud ice]

You don't need trig

Do you know similar triangles?

[zenith bloom]

Wdym

[zenith bloom]

Im not sure honestly

[proud ice]

Do you know what similar triangles are?

[zenith bloom]

Oh yea

but how do I implement it here

thats what i didnt understand as well

[proud ice]

Try showing which angles are equal among all the triangles you see and identify which triangles are similar

Then you can use similar triangle ratio law to get the other side lengths

[zenith bloom]

1 moment

is it not like this

@proud ice

[marsh citrus]

@zenith bloom Has your question been resolved?

[marsh citrus]

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[prime mountain]

number 15

we know the identity for sin 2(theta) is

2sin(theta)cos(theta)

if tan = 3 how do we find the values of sin and cos so we can plug in the formula?

or is this not the right way to do it

[next ravine]

You know sin in terms of cos

[prime mountain]

yea?

sin^2(theta) = 1 - cos^2(theta)

this?

[next ravine]

I think so

Hmmm

[prime mountain]

but that doesnt apply here bc

we first need the value of either cos or sin

[next ravine]

Oh

tan t = 3 = sin t / cos t

sint = 3 cos t

sin^2 t + cos^2 t = 1

2 eqns, 2 unknowns

[prime mountain]

hm

wait

so whats the value of sin and cos then?

im confused

[next ravine]

You solve for them

You have 2 eqns, 2 unknowns

[prime mountain]

is there no other way

[next ravine]

Solve for them

[next ravine]

Can't think of any atm

[prime mountain]

what if i draw a right triangle and use the pythagorean therom

tan = 3/1

find r

[next ravine]

Ye, try that

[prime mountain]

= root 10

[next ravine]

#❓how-to-get-help

[marsh citrus]

@prime mountain Has your question been resolved?

[marsh citrus]

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[flat fable]

How do you do #8

[flat fable]

Ik the avg rate of change is 3/8

The first derivative is positive twice

So i reasoned that the slope since its increasing can cross the value 3/8 twice

But the answer is C (three times)

[marsh citrus]

@flat fable Has your question been resolved?

[marsh citrus]

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[tardy tangle]

for the spans R^3 part

how do you just know to decompose (a,b,c) like that

[marsh citrus]

@tardy tangle Has your question been resolved?

[marsh citrus]

@tardy tangle Has your question been resolved?

[tardy tangle]

Helpers

@tight lance

[marsh citrus]

@tardy tangle Has your question been resolved?

[marsh citrus]

@tardy tangle Has your question been resolved?

[marsh citrus]

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[marsh citrus]

@tender mantle Has your question been resolved?

[marsh citrus]

@tender mantle Has your question been resolved?

[hexed pike]

i guess the answer is 2

absolute value is the distance between the number and 0

let 2 points (0,0) and (0, (1-i)sqrt(2i))

Distance will be sqrt{[(1-i)sqrt(2i)]^2}

After all you get 2 as the final answer

[hexed pike]

distance formula FYR

[tender mantle]

How can we assume about 0,0 in exams@hexed pike ?

[hexed pike]

idk whats your exam

[tender mantle]

I got this

[hexed pike]

i^2 should be -1

[tender mantle]

Where?

Wait a minute

[hexed pike]

(1-i)^2

[tender mantle]

2i (2-2i)

I wrote it in the pic

Then i multiply it

[hexed pike]

(a-b)^2= a^2-2ab+b^2

now b=i

[tender mantle]

Yeah i added 1+1

[hexed pike]

i^2 = -1

[tender mantle]

See

[hexed pike]

em

Let me write it for you

[tender mantle]

Ohh got it

My mistake

It will be 2

[hexed pike]

Yes