help-38

[dry copper]

Thank you!

[wind python]

.close

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[trim jolt]

@solar shoal Has your question been resolved?

[zinc ginkgo]

Why are you subtracting 0.5

I'm not saying you're wrong, just seems kinda randomly placed

Just calculate expected winnings and show it's negative. Then the "house edge" is the amount you're losing divided by the amount you're betting

If I understand your definition of house edge correctly

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[stuck cove]

Ok i need some advice on how to understand basic probalitys .

Following task :
We got an urn that contains 6 blue , 5 black and 4 red balls .
The probalitys are
3/7 , 4/6 , 2/5 .
2 balls are withdrawn from the urn without laying them back .

Now what is ( omega,P) ( P specifically)

What is the probalitz that 2 balls have the same collor .

This is not laplace as the probalitys are not the same so i canot use the 4 formulas like n^k and so on . is this correct?

[trail ingot]

The probalitys are
3/7 , 4/6 , 2/5 .

[stuck cove]

3/7 to draw a blue , 4/7 black and so on

[trail ingot]

!original

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[trail ingot]

shouldn't those numbers be 6/15, 5/15, and 4/15

[stuck cove]

Wrote it down as it was given

[trail ingot]

!original

[trim jolt]

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.

[trail ingot]

was the original problem in english?

[stuck cove]

It was in german

But got this just from other people , values might have been different .

[bright junco]

im just gonna leave this here, maybe it helps

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[stuck cove]

Ah well im gona look into it myself some more then .close

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[foggy spindle]

10) Compare the variation in heights to the variation in weights of thirteen-year old girls.
The heights (in inches) and weights (in pounds) of nine randomly selected
thirteen-year old girls are listed below.
Heights (inches): 58.7 61.4 62.1 64.7 60.1 58.3 64.6 63.7 66.1
Weights 97 93 119 96 90 123 98 139

How do we get 123.33 as the mean/average? IIrc that is what the x with a horzoneline above it means

We I try to find the mean I get 559.7/9 = 62.19

[lament reef]

well 123.33 is definitely not correct, since the average can't be greater than all of the heights listed

your answer seems correct to me

[outer kiln]

x with the dash might be another type of average because even the second average is weirdly high

[foggy spindle]

where does 123.33 come from? There no audio explain it.

In the end im suppose to find the coefficient of variation, but im lost at the first step

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[twin storm]

what does the ' mean

[thorn zephyr]

the difference

[twin storm]

now like

what does y'^2 mean

[thorn zephyr]

it is high skill paper

[twin storm]

does it mean derivative

[thorn zephyr]

it is power 2

yes

[thorn zephyr]

sorry if my eng;ish bad btw

english

[twin storm]

wht i have circled

what does y' mean

does it mean y-x

[thorn zephyr]

y(x)

it is derivative

[twin storm]

so derivative of y with respect to ?

[thorn zephyr]

yes

.

is there a proplem?

[ember violet]

They're asking you what the derivative of y is respect to, the question mark was meant to be a "fill it in" kind of thing

[thorn zephyr]

i im not good at english which is confusing me

y it is like f(x)

dy/dx

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[wraith hinge]

is the attitude of a right angled triangle to its hypotenuse always <= 1/2 (hypotenuse)?

[wraith hinge]

which would imply that if AD > 1/2(BC), then the triangle is not right angled

is this true?

[wraith hinge]

considering BC as the largest side

[ionic pendant]

yes, the length of the altitude is the geometric mean of the two line segments it creates, whereas half of the hypotenuse is the arithmetic mean

so it follows by AM-GM

[wraith hinge]

yes

so is my hypothesis correct

[trim jolt]

@wraith hinge Has your question been resolved?

[wraith hinge]

<@&286206848099549185>

[cursive cliff]

Helloo

@wraith hinge

[wraith hinge]

hi

[cursive cliff]

what doubt?

[wraith hinge]

..

[cursive cliff]

Yes

because in a right angled triangle AD is always = 1/2(BC)

@wraith hinge

@wraith hinge https://mathematicsbhilai.blogspot.com/2015/12/median-to-hypotenuse-of-right-triangle.html

Check this article

[wraith hinge]

ohh

thank u

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[agile rampart]

I have a statistics question. Our teacher reviewed the answers in class, so all my questions up to the last part are correct. However, In part D my error is in putting (z <= z*) = .9 when the teacher put (z<= z*) .05. I have no idea how you get to .05 for it.

[agile rampart]

BTW, pardon the confusion. The image shows .5 next to the arrows, but it has to be .05

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@agile rampart Has your question been resolved?

[zinc ginkgo]

do you know what "90% of their batteries to last between 20 and 40 months" means?

this is almost right. should be P(20 < x < 40) = 0.9

That implies 1 - P(20 < x < 40) = 1 - 0.9 = 0.1

Use 1 - P(20 < x < 40) = P(X < 20) + P(X > 40)

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[old zinc]

It is wrong idk why

[tall kernel]

your answer is right

you're just forgetting (0, 0)

[old zinc]

Wait if i sq the whole equation then i get another answer 1,3

Bc x-2+y=2

Bc x-2+3x=2

[tall kernel]

you cant do that

[old zinc]

Why

[tall kernel]

if you square root the whole equation

you get

$\sqrt{(x-2)^2 + y^2} = 2$

[solid kiln]

w

[old zinc]

Huh

[tall kernel]

$\sqrt{(x-2)^2 + y^2} \neq (x-2)^2 + y^2$

[solid kiln]

w

[old zinc]

Yeah but how

We could square root them tho??

[tall kernel]

well its not really useful

[tall kernel]

you wouldn;t get anything here

[tall kernel]

since this

[old zinc]

I am so confused

But math dont make sense

I put the points in the problem and it still said i was wrong

So idk man

[trim jolt]

@old zinc Has your question been resolved?

[trim jolt]

@old zinc Has your question been resolved?

[ember violet]

Your problem is that it says POINTS

There is a 2nd set of values where it intersects

[old zinc]

I did that

Lmao ik how to do paranthesis

[ember violet]

You don't have it in your working

[old zinc]

The other guy told me to do it lmao

[ember violet]

Your working shows only 1 point, which is (2/5,6/5)

[old zinc]

Bro i put both it didnt work lmao

[ember violet]

Can you please just show exactly what you put in

[old zinc]

Im not on my computer rn so

[ember violet]

Okay, well, did you remember to use decimal form and use the same format the question tells you to?

[old zinc]

Yes bruh

[ember violet]

Because the solutions are definitely right unless you didn't calculate y correctly for x = 0 which would be weird

[old zinc]

I did everything i could

Asking on discord was my last bet

[ember violet]

welp, I'm afraid this is absolutely a you problem, you've already got one of the solutions, which is (0.4,1.2) and you claim that you have the other, which is (0,0)

[old zinc]

Alright man whatever u say

[ember violet]

If you didn't input it in like that then you're just not formatting it correctly

[old zinc]

Ik i did everything i could

[ember violet]

mhm

[old zinc]

Im asking my teacher tmr

[ember violet]

You seem to like to blame others a lot when you didn't even show all your working and you left your full working in fraction form, yet you claim to have done it in decimal

[old zinc]

Bro its not that deep holy fucking shit

[ember violet]

So you're on your own, adios

[old zinc]

I did multiple attempts

[ember violet]

LMAO you've been getting angry this entire time at something that has been confirmed to be your fault

[old zinc]

Where am i blaming others lmfao?

[ember violet]

Go tell your teacher, bye!

[old zinc]

U told me to do stuff i alr did

So much for a “helper

[ember violet]

Clearly you didn't because multiple other people have confirmed the solutions, which you didn't fully show bc you were lazy

[old zinc]

Bro i am OUTSIDE right now

[ember violet]

I ain't a helper LMAO, you're so in denial, go tell your teacher and deal with it, bye!

[old zinc]

I an not next to my computer

LOL

Bro is actually pissing me off, no where was i blaming anyone 💀💀 the stuff bro said to do i alr did. Stop pretending like youre doing shit and lying abt others to feel better abt your fake “helpfulness” that is actually passive aggressiveness and condescension of pride that you cant get anywhere else because you like to “blame” others for your incompetence. Bro is mad that i alr did everything and you are not contributing. Continue to be an asshole because that’s what you are. I literally said i did everything i could, and I said I wasn’t next to my computer mutiple times. This is why i dont like asking for help and why i said discord was my last bet because there are always condescendingppl like her

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[wraith hinge]

Hello!! Can I have some help?

[wraith hinge]

(ii), (iii) and (iv)?

Please. 🙏

[faint schooner]

Distance formula

Do you know it?

[tawny kettle]

2. use distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

[wraith hinge]

No?

[solid kiln]

fish

[wraith hinge]

What’s that?

Oh..

Distance to find length?

[tawny kettle]

essentially, pythagorean theorem for points

you can think of PQ as a line connecting P and Q, so the distance would be the length

[wraith hinge]

This?

[tawny kettle]

yeah

then for 3 and 4: the gradient is $m=\frac{y_2-y_1}{x_2-x_1}$, sometimes also called slope. for 4: using the slope intercept formula for a line, just find the b value

[solid kiln]

fish

[wraith hinge]

Thank you!

[whole coral]

(as a minor point, extend your square roots to cover all terms - some people can be more picky than others )

[wraith hinge]

Ok!!! Cool! I’ll keep that in mind.

Now what should I do for (iv)?

[tawny kettle]

the slope intercept form of a line is $y=mx+b$, then use the information given to find the value of b (parallel lines have the same slope)

[solid kiln]

fish

[wraith hinge]

What’s “b”?

Do I go with any ‘y’ value and ‘x’ as 2?

And input the gradient value?

What’s the “b” mean?

[faint schooner]

You will solve for that

When x is 2 and y is 0

Since it says parallel the gradient will be the same

[wraith hinge]

What will that look like?

Wait, hm.

[faint schooner]

Or just use point slope

[wraith hinge]

How can I rearrange it to isolate b?

Hey?

[faint schooner]

You’ve got this

[wraith hinge]

I am not sure what to do though.

Haha, can I have some help please?

[faint schooner]

Subtract both sides by 2/7

[wraith hinge]

It equals -2/7?

[faint schooner]

Yes

[wraith hinge]

The equation is y = 1/7x - 2/7

[faint schooner]

Yes

[wraith hinge]

Thank you!

So, I’m not sure how to factorise these.

I tried to for the first wrong but it was WAY off.

Hello? Help please! 🙏

[faint schooner]

Factor a 3 out

Then, difference of squares

[faint schooner]

What

[wraith hinge]

I am so lost.

How do I do this?

[faint schooner]

You are close

[faint schooner]

Difference of square from this

So 3 will be a coefficient

[austere cedar]

Make sure you have the "difference of squares" formula in front of you

[wraith hinge]

Oh, I don’t have that.

I don’t quite get it.

Hello?

[zinc ginkgo]

this is right yes

but might help to factor out a 3 from the starting expression first

like 3 * [9y^2 - 1]. then apply the a^2-b^2 formula to the stuff in []

[wraith hinge]

Hmm..

Ok I’ll try it.

If ‘3’ is ‘a’, ‘9’ is ‘b’ then what’s the ‘-1’?

Still incorrect and I’m not sure what I should do.

Could I have some help?

Question (a) and (b).

Please 🙏.

<@&286206848099549185>

[soft rapids]

hi

it is a smooth curve

not a line

so you need to take the derivative and evaluate it at x=1

[wraith hinge]

What is derivative?

[somber token]

...

[wraith hinge]

I just searched it up.

I’m still confused.

How do I do that?

[somber token]

do yk the rule for powers?

the derivative for for such x^n+c = nx^n-1

the constant becomes 0

iirc

hs was a long time ago and i dont take calc anymore

i.e. suppose i have x^4+80 for f(x) thus f'(x) follow the power rule is 4x^3

iirc

again high school was a long time ago

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[wraith hinge]

2y=x+8 so I have to divide everything by 2 in this equation but what would x/2 give me ?

[zinc ginkgo]

!original

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[wraith hinge]

-x+2y=8

[zinc ginkgo]

That's just an equation. What's the instructions

[wraith hinge]

I have to isolate the variable so I can use it in the equation below

wouldn't x/2 give me 1/2x cause its techniqually 1x/2 ?

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[opaque eagle]

can i send a dm to any helper? i just need my work to be rechecked before i submit it

[tribal pond]

sus sounds like an exam

[river willow]

sus

[opaque eagle]

it's not an exam lol

[tribal pond]

uh huh

[river willow]

just send it here

[opaque eagle]

aight

[bright quarry]

sus

[tribal pond]

unimaginely sus

[opaque eagle]

i'd like to ask if my final answer is actually correct

[tribal pond]

but var, function looks good

[stray temple]

looks like an exam to me

[bright quarry]

points

[tribal pond]

what's the diff between solution and answer

[opaque eagle]

bro it's not an exam omg 😭

[tribal pond]

eh to be fair, they list points on my hw

[stray temple]

never had that lol

[opaque eagle]

the answer is the final thingy

[tribal pond]

is solution the work to get to the answer

[opaque eagle]

i think our teacher wants it to be separated for clarification

[opaque eagle]

yeah

[tribal pond]

well F(6) = 60,000

F(x) is not necessarily that

[opaque eagle]

is the 0<x<12 correct?

[opaque eagle]

alr

[tribal pond]

why do you need to the list the domain

for a specific value

[tribal pond]

show us the header

[opaque eagle]

okay

it's not an exam i swear

we can't use gadgets during exams lol

[tribal pond]

EVEN MORE SUS

[opaque eagle]

WHAT??? 😭

[bright quarry]

gadgets

[tribal pond]

who says gadgets

[opaque eagle]

bruh that's a homework why is it sus for y'all

[tribal pond]

I'm j messing now

okay

it should be good with the changes

[opaque eagle]

last question is this one

[tribal pond]

there shouldn't be a domain

for a specific x

[opaque eagle]

wdym

[stray temple]

theres no need for it

[opaque eagle]

oh alright thank you!

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[viscid mirage]

I look back on past lectures and cant find any examples. Trig btw

[blazing geode]

It is bigger than 3

The top is bigger than 3

The value of sqrt3 is approximately to 1.732

[bright junco]

sine and cosine cant just have any value, they are bounded by -1 and 1. namely, -1<= sinθ <= 1

so having sinθ equal 1.154 is impossible

[bright quarry]

george washington’s birthday

[blazing geode]

Bill is right

[viscid mirage]

Thanks for all that, and so quickly!

.close

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[blazing geode]

God, I did not know that

[bright quarry]

now you do

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[echo jasper]

sf?

round to the 4 sf?

[vagrant marsh]

did you mean to do (2.998*10^8)/(105.5*10^6)?

[echo jasper]

it for this

oh

i have to put the parantheses

[vagrant marsh]

yes

otherwise it gets interpreted from left to right

[echo jasper]

Ohhh ok

[vagrant marsh]

but yes, 4sf because your smallest amount of sigfigs in the quotient is 4

[echo jasper]

hi

so 2.842 is good?

or just 2.84

since is the same as 2.840

so the answer would be 2.84 m

then we do 2.84x10^-6

meter to micro

i think at least

actually

2.84x10^6

i think positive

by accident

h

i mean ur doing good

U have great future

[zinc ginkgo]

Oh are you 10 years old yet

[ionic pendant]

it looks like you are using a TI 84 calculator. you shold use "EE" (2nd -> ,). this both saves on key strokes and ensures that the number is interpreted as one thing (e.g. 1/105.5E6 would be interpreted correctly)

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[zinc raft]

How do you tell if it’s “and” or “or”?

[trail ingot]

|x| > a translates to x > a or x < -a

'and' wouldn't really make sense because there aren't any numbers that are > 11 and < -11

[zinc raft]

Ohh yeah

Okay thank you

What would it look like if it was and?

[dense breach]

|2x+3| < -11?

[trail ingot]

lmao

|2x+3| < 11 would translate to 2x+3 < 11 and 2x+3 > -11

but this one is kinda awkward

it might help if you can draw pictures.

green numbers x satisfy |x| < 11, and are less than 11 and greater than -11

red numbers x satisfy |x| > 11, and are greater than 11 or less than -11

that's kinda what i draw in my mind to figure out what translates to what

[wraith hinge]

I have a chain of every integer

in my mind

[trim jolt]

@zinc raft Has your question been resolved?

[zinc raft]

Wait what does the a stand for here

[trail ingot]

anything you want

[zinc raft]

How can x < -a if the x was in absolute value? Wouldn’t it be positive making it greater than the negative a?

[trim jolt]

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[trail ingot]

.reopen

[trim jolt]

✅

[lusty delta]

[trail ingot]

well let's just take |x| > 11 for example

[lilac flame]

x can be negative

[trail ingot]

if x = -100, then |x| > 11

because |x| = 100

[lilac flame]

100 > 11

89 > 0

[trail ingot]

deep

[lilac flame]

1 > 0

[lusty delta]

same

[trim jolt]

@zinc raft Has your question been resolved?

[wraith hinge]

because 1=1² and 1²>0 because a²>0 for all real a

[lilac flame]

valid and real

[trail ingot]

that's..... not even true

[trim jolt]

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[marsh forum]

problem (a)

[marsh forum]

so by defn . the first limit states that $|x-a| < \delta \implies f(x) >M$

[trail ingot]

this isn't a very clear statement

[solid kiln]

Veni, vidi, perii is not f(wai)

[marsh forum]

And the second limit that $|x-a| < \delta_2 \implies |g(x)- c| < \varepsilon$

[solid kiln]

Veni, vidi, perii is not f(wai)

[trail ingot]

there should really be some there existss and for alls here

or some fix variables (or let variable...s)

[marsh forum]

we now take min ( \delta, \delta_2$

[marsh forum]

I've skipped that for now

[trail ingot]

it will make it really hard to say "yes that sounds good" then

[sudden mist]

Why?

[marsh forum]

We want a common $\delta$ for both limits

[solid kiln]

Veni, vidi, perii is not f(wai)

[sudden mist]

I would recommend first seeing what you can do with f(x) + g(x) before thinking about any delta

[marsh forum]

wdym

$|f(x)+g(x)| \leq |f(x)|+|g(x)|$

oops

[solid kiln]

Veni, vidi, perii is not f(wai)

[marsh forum]

Hope I don't make this same mistake in an hour

[marsh forum]

why though

I mean $f(x)>M and g(x)> c - \varpepsilon$

I can add them. now

[sudden mist]

I mean, why start with a delta when it’s not clear what choice will let you show that f(x) + g(x) > epsilon

[solid kiln]

Veni, vidi, perii is not f(wai)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[marsh forum]

That's why I took the min

so $f(x)+g(x)> M+ c - \varepsilon$

[solid kiln]

Veni, vidi, perii is not f(wai)

[marsh forum]

which is still more than M

so this tends to $\infty$

[solid kiln]

Veni, vidi, perii is not f(wai)

[marsh forum]

thanks

.close

[trim jolt]

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[main sigil]

what? Why?

what if epsilon > c

You should really do what layla suggested here

write it with all the foralls and exists

and prove it with all the foralls and exists

[marsh forum]

hmm

How would that help

.reopen

[trim jolt]

✅

[marsh forum]

$\froall \varepsilon > 0 \exists \delta >) st |x-a| < \delta \implies |f(x)-L|< \varepsilon$

[solid kiln]

Veni, vidi, perii is not f(wai)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[marsh forum]

Like this?

$\forall \varepsilon > 0 \exists \delta >0 st |x-a| < \delta \implies |f(x)-L|< \varepsilon$

[solid kiln]

Veni, vidi, perii is not f(wai)

[marsh forum]

like this?

and $\forall M>0 , \exists \delta >0 st x>M \implies g(x)>L$

[solid kiln]

Veni, vidi, perii is not f(wai)

[trim jolt]

@marsh forum Has your question been resolved?

[main sigil]

Even if this was true, you cant imply that M + c - epsilon > M

[marsh forum]

I know

[marsh forum]

Is this wrong?

[main sigil]

Yeah, i think so

it doesnt even use delta

[marsh forum]

oh shit

made the same mistajke again

Thought I was finding the limit at infty

Yeah, I know

[main sigil]

wait that was actually wrong

[marsh forum]

just used the wrong defn because of my stress

[main sigil]

i did the same mistake as you lol

[main sigil]

There is no need to be stressed about this, is there?

[marsh forum]

$\forall M>0 \exists \delta >0 st 0<|x-a|< \delta \implies f(x)>M$

[solid kiln]

Veni, vidi, perii is not f(wai)

[marsh forum]

Yeah, just want that A grade

[main sigil]

This looks fine 👍

Let's also interpret the goal

[solid kiln]

MæthIsAlwaysRight

[main sigil]

just f(x) + g(x) instead of f(x)

[marsh forum]

yeah

[main sigil]

So essentially, for any M > 0, you need to find delta, such that 0 < |x-a| < delta -> f(x) + g(x) > M

this is probably the best way to write it

And you need to prove that such delta works

So you can start your proof by "Let M be a real number > 0".
Note that the first condition then guarantees that there is a delta, such that 0 < |x-a| < delta => f(x) > M

but we need f(x) + g(x) > M

so this delta probably wont work. Nor will minimum of this delta and delta from the 2nd limit

[marsh forum]

Ok, have my exam in 30 minutes , probably not the best time to do this

Leave it for now

[main sigil]

I see

[marsh forum]

Thanks

[main sigil]

good luck

[marsh forum]

Thanks

. close

.close

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[indigo latch]

,rotate

[indigo latch]

Did I mess up

[meager bloom]

b²-4ac = (-8)²-4(2)(-4)

=64+32

[indigo latch]

/2

I gotta use quadratic formula

[meager bloom]

-- becomes plus

Remember

[indigo latch]

Ahhh

So it’s 96/4

[meager bloom]

√96

[indigo latch]

Not a perfect square

[meager bloom]

Yep

[indigo latch]

Can I do 48 and 2

Or diff number

[meager bloom]

Better do √16x6

[indigo latch]

Yup cause 16 is 4

[meager bloom]

Yes

[indigo latch]

Now I just divide by 4

[meager bloom]

Yes

[indigo latch]

X=2+-sqrt6

[meager bloom]

Correct

[indigo latch]

So those are the answers

[meager bloom]

I hope so

[indigo latch]

@meager bloom this look good orrr

[meager bloom]

Sorry bro, I don't remember parabola and others terms and general form

[indigo latch]

Vertex is - b/2a

And then to f(that number)

Those 2 numbers would give you vertex

I got -b/2a=2

And f(2)=-12

I was right

.close

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[proud coral]

Is this really right?

Approximation of f(0,1) = 1,125333…

[trim jolt]

@proud coral Has your question been resolved?

[dull temple]

,rccw

[dull temple]

might help if we knew the definition of f(x)

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[wind isle]

Im revising from a model sheet complex numbers and i dont understand where the 63i and 3i came from. I planned out my way of thinking in the screenshot as best as I can

[delicate belfry]

$(a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd$

[solid kiln]

Good

[wind isle]

I still dont understand

[delicate belfry]

What is 1 * 9

[wind isle]

9

[delicate belfry]

What is 1 * 3i

[wind isle]

3i

[delicate belfry]

What is 7i * 9

[wind isle]

Ohhhh

I see what I missed

Alr thanks

[delicate belfry]

welcome

[wind isle]

.close

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[cursive drum]

Did I do well in this expression? The book says it's -1/2 instead of 1/2

[dusty sleet]

,rotate

[dusty sleet]

$$\ln\frac{e^2}{\sqrt{\frac{1}{e^3}}}$$

[solid kiln]

Alberto Z.

[dusty sleet]

This one?

[cursive drum]

yes

how did you know

lol

[cosmic meadow]

Both are wrong?

[dusty sleet]

I just tried to decipher the photo

[cursive drum]

ohh alright

do you guys see any mistake there?

[cursive drum]

here

[dusty sleet]

A minus sign has been missed

[cursive drum]

yeah could be

but i dont see where

bruh

[dusty sleet]

What's $\ln e^{-\frac{3}{2}}$ equal to?

[cosmic meadow]

2 - (-3/2)

[solid kiln]

Alberto Z.

[cursive drum]

ohh

so it sums right

[trim jolt]

@cursive drum Has your question been resolved?

[worldly ocean]

-1.5

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[pseudo garnet]

What does ∮ mean?

[wraith hinge]

its for complex integral calculus

so basically integral calculus in the complex plane

[pseudo garnet]

Oh

Thanks!

[wraith hinge]

you welcome

u could find it online too

[livid orbit]

maybe you should check line integral on wikipedia

this circle can mean that you're integrating with respect like counterclockwise

[wraith hinge]

https://en.m.wikipedia.org/wiki/Contour_integration

[livid orbit]

following a path

[ionic pendant]

$\oint$ means a line integral along a closed path (often specifically counterclockwise)

[solid kiln]

cloud

[trim jolt]

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[acoustic bay]

im really lost in part i

i know that surjective is when you map x to at least one y

but how do i show that

[median torrent]

Surjective means that

For any object in the output space, there is some input that will achieve that object

So in other words

For any element z, of Z,

There are some (x, y) in natural.numbers/integers so f(x, y) = z

[grand drift]

let's breakdown the syntax
f : N x Z -> Z represents two variables, one natural and one integer, mapped to an integer output

f(x,y) (N,Z) = x+y (Z)

so, we'll suppose that x is the N and y is the Z, it's sum needs to be Z

map x = 0, you have the entire Z -> Z, so it's surjective

[median torrent]

Usually to prove a "for all" type of condition

You start with an arbitrary element from the "for all" set

So start with arbitrary integer

[acoustic bay]

what if you do y=0 would it still be N -> Z

what does f((x,y)) even mean like how can you input 2 variables into a function at once i havent seen that before

[grand drift]

i specifically mapped x = 0 for simplicity, the formal explanation is:

any function f has a set of solutions S that has a given size, often abstract; uncountable

f(x,y) = x+y ; which x is natural and y is integer, what is this set?

integer is a superset of naturals, this means that integers includes naturals

and by the nature of this function (not always the case!!) and by this fact, the "natural part" doesnt matter that much when we talk about the set of solutions

example: 1+3 = 4 , natural, but also an integer

1 - 10 = -9, integer

9999 - 10000 = 1, natural, also integer

so the set of solutions S in the end is Z

how do you come up with this easily, given harder 2 dimensional functions?

often, you fix a value in one spot and analyse it

0 + (any value in Z) = Z

you're right to point that we should check y

but this case is trivial

[median torrent]

it's actually a pretty short proof for surjective

[grand drift]

(any value of N) + 0 = N

Z > N

[median torrent]

Assuming you are allowed to conclude that the difference between integer and natural is also integer

[acoustic bay]

yeah ngl this is my first problem sheet from my first algerba maths lecture im kinda cooked

i dont want to do proofs man

😭

[median torrent]

Nooooo dont feel that way

It's a very different kind of work

Just gotta get used to it

[acoustic bay]

all year 1 modules are compulsary but luckily in year 2 i get more freedom to choose what i enjoy like statistics

[median torrent]

You'll get good at it with practice

[grand drift]

as a student who went from computer science to maths, i struggled a lot with proofs aswell

my teachers were very rough on me on my syntax and explaining

[acoustic bay]

how did you work on it? just practice?

[grand drift]

i got the hang of it watching other proofs online

https://proofwiki.org/wiki/Main_Page

this site helped me a lot

go see some concepts that you know, like area of a circle

[acoustic bay]

thank you i will check it out🙏

[grand drift]

and see the proof

it's really good

[acoustic bay]

will do appreacite the help guys

[median torrent]

Yw feel free to dm me if you feel lost i can help you with part i at least

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@acoustic bay Has your question been resolved?

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[twin yoke]

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[twin yoke]

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[maiden zinc]

Plug in infinite to e^whatever that is

Basically is it positive or negative infinite

[twin yoke]

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[maiden zinc]

Ye just write out the lim

And evaluate

basically what is e^-infinity

[twin yoke]

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[maiden zinc]

0

Rember

1/e^infinity

Is gonna be 0

[twin yoke]

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[maiden zinc]

Because 1/something huge

Is 0

[twin yoke]

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[maiden zinc]

Uh

It’s just an exponent rule

x^-n

=

1/x^n

if your denominator is super big

1/something big=0

[twin yoke]

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[maiden zinc]

But you still have

The other part

600/(20+10(0))

Which is what

[twin yoke]

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[maiden zinc]

?

You only use the 3rd equation

Because t>12

[twin yoke]

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[maiden zinc]

Ye evaluate this as it goes to infinity

[twin yoke]

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[maiden zinc]

I got this wrong on my calc test lmfao

I remeber this exact problem

i forogt to move it the bottom

So I got e^0

So my denominator was 20+10 instead of just 20

[twin yoke]

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[maiden zinc]

Nothing

Don’t worry about it

I said e^-infnity was the same as e^0

but that’s just wrong

[twin yoke]

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[maiden zinc]

Ye

[twin yoke]

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[maiden zinc]

So you see

How it’s just gonna be

600/20

[twin yoke]

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[maiden zinc]

Ye

[twin yoke]

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[maiden zinc]

So as t approaches infinity the mass of the yeast culture approaches 30 milligrams

[twin yoke]

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[maiden zinc]

No

e^the whatever was 0

Remember

[twin yoke]

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[maiden zinc]

Uh

Not +0

Because 600/(20+10e^-inf))

is the same as

600/20+10(0)

Which is just 600/20

[twin yoke]

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[maiden zinc]

Then you just have to put that 30 in context

[twin yoke]

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[maiden zinc]

No I just had the first part

And then it went into an ivt problem

[twin yoke]

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[maiden zinc]

Oh ye I had the third part

Not the 2nd

[twin yoke]

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[maiden zinc]

lim x —> c= f(c)

Limit on left and right side

[twin yoke]

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[maiden zinc]

Is equal to f(c)

[twin yoke]

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[maiden zinc]

So it simplies pretty easily

Because if you plug in 12

To the bottom

[twin yoke]

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[maiden zinc]

Which is

[twin yoke]

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[maiden zinc]

any number to the power of 0

Is what

[twin yoke]

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[maiden zinc]

Ye

[twin yoke]

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[maiden zinc]

So you have

[twin yoke]

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[maiden zinc]

600/20+10(1)

Which is what

[twin yoke]

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[maiden zinc]

Ye

So

Is it continuous

!?

[twin yoke]

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[maiden zinc]

Ok then justify it

[maiden zinc]

This

[twin yoke]

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[maiden zinc]

Not f

[twin yoke]

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[maiden zinc]

lim t—>12 Y(t)= Y(12)

I’ve gotten like at least 10 points off all year on quizzes and tests bc I use f instead of the function actually given

[twin yoke]

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[maiden zinc]

Oh ye

[twin yoke]

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[maiden zinc]

You got this man

Let’s gooo

[twin yoke]

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[placid valve]

hi, not too sure how to start this problem

[dry copper]

read this: http://tutorial-math.wip.lamar.edu/Classes/DE/IoV.aspx

only the 1st theorem and the 1st example with its solution

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[unique harness]

your equation does not represent the correct y-int

so what you have written,

the y-int is at (0, 1.5)

instead of (0,1)

so that's your mistake

[fickle sky]

you subsituted 1 for x when it's f(0)

????

[indigo latch]

Ur wrong

[unique harness]

wdym

[unique harness]

then what is this

[indigo latch]

Nah

Ur wrong

Bro

[unique harness]

i see

well good luck then

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[vale abyss]

I am kind of confused on what they mean by k

[vale abyss]

should I just treat k as a constant and then parametrize gamma and solve the integral as normal

not sure what "you will start with k = 2" is though

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[zinc ginkgo]

They tell you to set k=2

Just substitute and forget k

[vale abyss]

hmm they arent looking for a general solution?

[vale abyss]

.close

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[earnest nymph]

is there a way to find what values of k create two distinct points in this eq?

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[earnest nymph]

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[wraith hinge]

How do I show the equivalence between $z(xy' +x'y)$ and $xy+xz+yz$ algebraically? I.e, [
\9{\8[\big]{z(xy'+x'y)} \oplus \8[\big]{xy+xz+yz}}' = 1
]

[wraith hinge]

i know i can just set up a truth table, but thats the long way

i just cannot see that simplification thats supposed to be here

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[vagrant marsh]

im assuming xy is x AND y and x+y is x OR y and x' is NOT x?

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[gentle sleet]

arent they finding the mgf for Y bar here?

instead of

because why is all of that being divided by n here?

wth now im even more confused why is e raised to t instead of t/n

could this be a typo?

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[topaz pagoda]

3. Mr. Alvarez is pushing a
   schoolbag from the school gate
   to the kindergarten room. The
   schoolbag has a mass of 15kg. If
   the coefficient of kinetic friction
   between the schoolbag and the
   floor is 0.36, how much force does
   Mr. Alvarez exert on the schoolbag?

[topaz pagoda]

can anyone help me

[frozen plover]

Have you written down the net force on the bag?

[topaz pagoda]

not yet

is this correct for that problem

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[rough sierra]

How do I find equation from a table?

[dull temple]

5x^2 is the correct first term, good job

you can use the y-intercept to find the constant term

and then use any other point to find the linear (x) term

[rough sierra]

so when x is 0, y is two and in mx + b, the b is y

but isnt when x is zero y is C?

idk i dont understand

[dull temple]

yea -- we use different names for the different terms for various reasons

but the idea is that the constant term (whether that's b or c) is the y-intercept

so if y = mx + b, then at 0 that's y = m(0) + b = b

but if y = ax^2 + bx + c, then at 0 that's y = a(0)^2 + b(0) + c = c

later on you might start to write equations like that as \ $y = a_0 + a_1x + a_2x^2 + a_3x^3 + \cdots$

[solid kiln]

hayley is not layla

[dull temple]

and then it's consistent, but that can get annoying with all the subscripts

[rough sierra]

but then how do i find b?

[dull temple]

once you've found a and c

you can just pick any other point

so right now you have $y = 5x^2 + bx + 2$ right

[solid kiln]

hayley is not layla

[rough sierra]

yes

[dull temple]

so let's use the point (x=2, y=4) from your chart

we know that that point has to be satisfied by that equation

so if we plug in those values of x and y

we can solve for b

[rough sierra]

ohh okay

if i have b(2) does that turn to 2b?

so is it y=5x^2-9x+2?

[dull temple]

yes

[dull temple]

probably, you can check by testing another point

for example (x=3, y=20)

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[rough sierra]

thank you

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[vestal plaza]

I don't have issues with finding the answer to part (b) only part (c) where I am confused as to what should the substitution be?

[dapper swift]

c is a classic example of conditional probability

P(score = 3 | die rolled twice)

= $\frac{P(score = 3 \cap die rolled twice)}{P(die rolled twice)}$

[solid kiln]

higher's secret twin brother

[vestal plaza]

Yes I understand that

the marking scheme also says that but

[dapper swift]

oh can you send the marking scheme then?

[vestal plaza]

will it help you

[dapper swift]

yes

[vestal plaza]

Seems pretty unhelpful to me

[dapper swift]

oh okay I can at least check what the answer should be

[vestal plaza]

Why is the dice rolled twice half it should be the all the combinations where the dice is rolled twice

[dapper swift]

ah so if X = 3, then the game is over
you roll 1 time and that's the final score

the probability that the game is not over on the first roll is hence 1 - 1/2 = 1/2

and then for the second roll you can have any number

1/2 * 1 = 1/2

[vestal plaza]

like die rolled twice happens when random variable X is not equal to 3

so the combinations we can get to that would be
1 1
2 1
1 2
0 3

Got it this next info which I am saying can be used for the intersection

How do we find the intersection

[dapper swift]

so that would be 0, 3 or 1, 2 or 2, 1

[vestal plaza]

My tutor just told multiply P(X=3) with 1/2

[dapper swift]

so just 1/6 * 1/2 + 1/6 * 1/6 + 1/6 * 1/6

[vestal plaza]

but I said that is only for independent events right

[dapper swift]

wtf that's wrong

they're not independent exactly

[vestal plaza]

And they don't say its independent

[dapper swift]

,w 1/6 * 1/2 + 1/6 * 1/6 + 1/6 * 1/6

[solid kiln]

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Requested by sooouth.

[vestal plaza]

Is this from the probability combinations which I gave

[dapper swift]

no