help-0

[kind jasper]

oh its 2/3

[abstract fractal]

Yes

[kind jasper]

shit, its too late for me

then im doing it correctly lmao

my bad

thanks for the help ❤️

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[tough dawn]

I need help with this assignment. I'm not sure how I would go about solving this

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[tough dawn]

<@&286206848099549185>

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[slender marten]

F(s) = (As + B)/(s^2 + 1) + (Cs + D)/(s^2 + 16).

[near saffron]

As+B and Cs+D are one degree less than their denominators

[smoky cloud]

there is no such need to memorizing its common understanding or u can say some logical stuff

[slender marten]

Part 2:

[slender marten]

Part 1:

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[alpine sable]

Can someone please confirm if this is fully simplified.

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[alpine sable]

<@&286206848099549185>

[slender marten]

On the right fraction I'd probably write it as 9(m^2 + 1)/[6(m^2 + 1)^(5/2)] to then combine the fractions.

Oh. It's a 5/3 not a 5/2.

[alpine sable]

i dont understand

oh nvm i get it I think

[alpine sable]

I got more question, how does

Turn into

<@&286206848099549185>

also same for this end

im not sure how this works or if there is a rule im missing

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[abstract fractal]

Write as a fraction and get common denominators

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[lavish ether]

If I have a map $H:V\to W$ between 2 vector spaces that is bijective and linear, does that guarentee $H^{-1}:W\to V$ is also linear?

[ocean seal]

Beous

[lavish ether]

wait i think i figured it out

let $u,v\in W$ and $\tilde{u},\tilde{v}\in V$ such that $H(\tilde{u})=u$ and $H(\tilde{v})=v$. then $H^{-1}(u)+H^{-1}(v)=\tilde{u}+\tilde{v}=H^{-1}(H(\tilde{u}+\tilde{v}))=H^{-1}(H(\tilde{u})+H(\tilde{v}))=H^{-1}(u+v)$

[ocean seal]

Beous

[lavish ether]

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[vague iris]

I just wanna ask if the angle I got is correct. We're doing vectors. I'm not sure if I did the right solution.

[vague iris]

It would look like this. The angle is between the y axis and the black line

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[quick nimbus]

how would you approch this question?

[proud pike]

figure out what (A ∖ B) is, then figure out what (A ∖ B) ∩ C is.

(A ∖ B) is all the elements in A not in B, and (A ∖ B) ∩ C are all of those elements that are also in C

[quick nimbus]

so basically what A and C have in common that B does not

[vale wigeon]

could say that yes

[quick nimbus]

how do you calculate A\B?

[vale wigeon]

you can draw a number line

[quick nimbus]

like this right?

so the difference is 0 onwards

[vale wigeon]

wdym by "0 onwards"

can you write the difference as an interval?

[quick nimbus]

uhhh

ill try

[vale wigeon]

i can assure you it is in fact an interval

[quick nimbus]

[0, +infinity)

[vale wigeon]

also that number line looks a bit shoddy

what's o?

[quick nimbus]

sorry its not supposed to send transparrently

[vale wigeon]

so you think that (-7.5, 3) \ (0, +infty) = [0, +infty)?

[quick nimbus]

red line is b

ohhh hold on i see my mistake

[vale wigeon]

the red line is B...? then why is it going off to the left and not to the right

[quick nimbus]

i thought b was -infinity

apologies

the difference is (-infinity, 0]

[vale wigeon]

are you sure

[quick nimbus]

red is b

[vale wigeon]

so you think that (-7.5, 3) \ (0, +infty) = (-infty, 0]?

[quick nimbus]

b is 0 to infinity

and C is all intergers

[vale wigeon]

so you think that (-7.5, 3) \ (0, +infty) = (-infty, 0]?

[quick nimbus]

so the difference between a is that it goes beyod 0 to the left up till -7.5

mmm maybe

[vale wigeon]

i don't appreciate how my question kept getting unanswered

[quick nimbus]

[-7.5, 0]?

not -infinity

but -7.5

[vale wigeon]

well you said this here...

but also are you sure you didn't screw up by a point

[quick nimbus]

your question opened my eyes 😅

[quick nimbus]

wdym?

[vale wigeon]

[-7.5, 0]?

[quick nimbus]

mmm well B also has 0

so what would we say is the other value besides -7.5?

like do we just sai -0.1?

[vale wigeon]

did you not see the part i specifically bolded to draw your attention to it

[quick nimbus]

sorry bare with me this is my first time doing proofs 😅

[vale wigeon]

literally don't care

when someone tries to draw your attention to something it is probably a good idea to pay attention to it

anyway

why did you put an inclusive bracket at the -7.5 end?

[quick nimbus]

becuase As value is (-7.5, 3)

so my thought process is that it would end at -7.5

[vale wigeon]

A is (-7.5, 3) yes. so does -7.5 belong to A?

[quick nimbus]

yes

[vale wigeon]

no

[quick nimbus]

how come?

[vale wigeon]

round brackets mean the endpoint itself is not in the interval.

[quick nimbus]

but in the question none of the interval used [] brackets

ohhh

i see

so its (-7.5, 0)

[vale wigeon]

no you're screwing up again

in the other direction this time

you're excluding a point that you shouldn't

[quick nimbus]

what point

o?

0*

so it should be (-7.5, 0]

[vale wigeon]

finally

ok and now we need to intersect this with Z

[quick nimbus]

so the answer would be 0,-3, and -5?

[quick nimbus]

line C correct? C is all intergers so its interval is (-infinity, infinity)

[vale wigeon]

the word "integer" only has one R in it, and no, C (aka Z) is not an interval at all

[quick nimbus]

sorry im just new to learning english 😅

[vale wigeon]

what is your native language

[quick nimbus]

arabic

[quick nimbus]

but anyway this is valid correct?

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[fleet cradle]

i need help on these 4 :cccc

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<@&286206848099549185>

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[wheat crow]

A 1.5 kg sphere is dropped into a large vat of mercury in what can be considered
laminar flow conditions. The terminal velocity of the sphere is 0.3 m/s, calculate the b
value of the sphere in these conditions.
anyone help me with this polease?

[wheat crow]

hey

i know this is a physics question

but could anyone help?

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[ornate condor]

whats a polynomial

[ornate condor]

its like a0+a1x+a2x2+...+anxn for some finite n?

so sinx in power series has infinite terms thus isnt a polynomial. is that right?

ok got it

thanks google

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[ornate condor]

is 0 a polynomial

[void maple]

i dont believe so

[worn fox]

Yes

The zero polynomial

[wise fiber]

yes

np

[ornate condor]

A polynomial expression is an expression that can be built from constants and symbols called variables or indeterminates by means of addition, multiplication and exponentiation to a non-negative integer power.

hm it says non negative int powers

[vale wigeon]

0 is the empty sum

[ornate condor]

so its a polynomial of degree 0

[vale wigeon]

not quite

[ornate condor]

so also, 1 is a polynomial

[vale wigeon]

if the 0 polynomial is given a degree at all it's usually something like -∞

[ornate condor]

wait what

[vale wigeon]

to ensure the property deg(fg) = deg(f) + deg(g) holds for example

[vale wigeon]

nonzero constants are degree 0 though yes

[ornate condor]

hm

then polynomial of degree n means

anx^n

an is non zero

right

[vale wigeon]

wording is a little stinky but yes

[ornate condor]

hm

how do i word it better

[vale wigeon]

don't know

would have suggested better wording if i knew how to fix it

[ornate condor]

:c

its ok

thanks

everyone

and myself

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[glad dock]

Yeah, I know. I got the intervals x >= -1 and x < -2, is that incorrect?

I'm not sure I follow. I've checked with Geogebra and I think my intervals make sense if you look at the graph.

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[fervent spire]

Hello, Is there an easier and faster way to solve this question? I already know its factored form but it would be a hellish to solve 1 by 1.

[mortal trellis]

well what is the factored form

[fervent spire]

((k+2)(k-2)(k+1)(k-1))/((k²(k+3)(k-3))

[mortal trellis]

ok. and now write out the first few terms of that

you'll see that some stuff will cancel

[fervent spire]

I can't see some stuff to be canceled or I missed something.

[mortal trellis]

write out the first two terms for k=4 and k=5

on the other hand, not enough stuff cancels, so I'm not really sure what to do after that

[fervent spire]

Hmmm, Okay.

I guess I have to brute force this?

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[fervent spire]

I guess I have to find some pattern.

[fervent spire]

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[surreal sky]

How do i solve this problem? I did the base case which is 1^3 = 1^2 then I said sum from k=1 to p for p^3 = sum from (k=1 to p for p)^2, how do i prove for p+1??

[lone heart]

@surreal sky Has your question been resolved?

[sonic kiln]

You want to do it by induction, right?

[surreal sky]

yup

[sonic kiln]

So by assumption you know $(\sum_{k=1}^n k)^2=\sum_{k=1}^n k^3$

[ocean seal]

Blaxapate

[surreal sky]

yes

This is what I have so far..

[sonic kiln]

Now $(\sum_{k=1}^{n+1} k)^2=(\sum_{k=1}^n k+(n+1))^2=(\sum_{k=1}^n k)^2+(n+1)^2+2(n+1)(\sum_{k=1}^n k)$

[ocean seal]

Blaxapate

[surreal sky]

oh

I think I got it

thank you

[sonic kiln]

No problem

[surreal sky]

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[vale junco]

what do u need to find

[radiant robin]

A to D

[vale junco]

the distance?

ok

[radiant robin]

how can a to b be used?

[vale junco]

mark the center of circle as O

and connect line AO

then use the law of cosines to find angle OBA

[radiant robin]

thanks!!

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[west bluff]

helloooo can someone help me get the right answers for this question using quadratic and perfect square trinomial thank youuu

[runic trench]

There r like 8 qns

[west bluff]

yes

just question number 6 yes :>

[runic trench]

a=3 b=11 c=8

[runic trench]

Put them inside the quadratic formula

[west bluff]

yes

and then

[runic trench]

And solve

[west bluff]

ohh okay thank you so much!

[runic trench]

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[west bluff]

.close

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[fickle adder]

What are they doing here? How do they eliminate the pap -zaz out of the integral?

[fickle adder]

they're setting a_z to 0 but why's that?

full solution

<@&286206848099549185>

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[shut parcel]

Can someone help me with question 14? I have provided a table, which is part of question 14

[shut parcel]

Note: 50% of capital gains is taxed in Canada

How I tried solving question 14 a): 0.50(2,000) = 1,000. Now, 1,000(0.26) bc of the tax bracket = 260. From here, Idk what to do. Do I have to find out the total income? If so, how would I do that😢

[solemn wedge]

Progressive Tag System is a System where the tax increases with increase in income.

use another channel please!

[shut parcel]

@dusky tulip This is already occupied

[dusky tulip]

Ogi

Mb

[solemn wedge]

You must have been provided with a table or sorts

[shut parcel]

@dusky tulip Please delete your question

[dusky tulip]

U don’t gotta be a bch about relax

[solemn wedge]

Are you 100% sure the Table from Q12 applies to Q14 as well?

[shut parcel]

Not sure if this solution from a different question helps in any way lol

I think so

[south mantle]

bruh its been like 5 hours

[shut parcel]

Or do I use the table from the textbook?

[solemn wedge]

Because according to the table, your income is over $100,392 , but not more than $155,625

(26% tax)

[shut parcel]

Oh darn

I’m now unsure which table to use

[solemn wedge]

wait im confused too

[shut parcel]

There’s this table from the textbook, which says the Federal Income Tax Rates and Brackets for Individuals (2020)

Let’s say we use the same table from question 12

What would be my total income

<@&286206848099549185>

@solemn wedge

[solemn wedge]

It's tough to tell

It can be anything between $100,392 to $155,625

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@shut parcel Has your question been resolved?

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[alpine sable]

What would my equation be?

[vale wigeon]

well, what are you asked to find?

in words, of course

[alpine sable]

the area of the region the helicopter can see

[vale wigeon]

right.

and what shape is the region visible to the helicopter?

[alpine sable]

circle

[vale wigeon]

right.

so we want to find the area of a circle.

do you know how to do that?

[alpine sable]

can you refresh my memory please?

[vale wigeon]

ok, let me keep jogging your memory then

what measurement of a circle is the most important for determining how big or small it is?

[alpine sable]

the area?

[vale wigeon]

well... sure... but the area's what we want to find. and it's not really obvious what we could get the area from.

perhaps it's the length of something that we want to get a grip on.

after all, most areas are computed from lengths of some kind.

[alpine sable]

oh alright

so the length

[vale wigeon]

well what length?

what words do you know that relate to circles and signify some kind of length or distance?

[alpine sable]

radius?

[vale wigeon]

great

before we proceed, can you remind yourself of what we call the radius of a circle?

[alpine sable]

in the problem or?

[vale wigeon]

no, we're still doing some general thinking/memory-jogging.

we'll get to the problem in due time.

[alpine sable]

ok ok

um

diameter?

No

[vale wigeon]

can you remind yourself of what we call the radius of a circle?

[alpine sable]

im sorry this makes no sense

[vale wigeon]

what makes no sense?

are you saying you do not know what the word "radius" means?

[alpine sable]

i guess idk the book meaning

[vale wigeon]

"book meaning" as opposed to what other meaning?

[alpine sable]

i guess you could say its a circular area?

[vale wigeon]

so what you're saying is, "The radius of a circle is a circular area."

how quaint.

[wind yoke]

How do you not know what radius and you are given a problem to solve and find area in a graph ?

[alpine sable]

yeah thats what im saying

didnt say it was right

[vale wigeon]

well, ok, so the conclusion is that in fact you do not know what the word "radius" refers to. i would've liked it better if we came to that conclusion with less runaround.

but alright.

the radius of a circle is, by definition, the distance from the center of the circle to a point on the circle.

[alpine sable]

alright

[vale wigeon]

(note that in this case we must distinguish between "circle" meaning the curve and "disk" meaning what's inside the curve, but still)

this is something you really ought to know and/or something your textbook really should've taught you.

you could even have googled it yourself.

anyway

if we know the radius of a circle, we can in fact compute its area using a handy formula:

A = π * r^2.

[alpine sable]

alright

so how do i find the radius

[vale wigeon]

well, let's go back to the problem

https://cdn.discordapp.com/attachments/490557019623915520/1019647851799793745/IMG_2214.png

you are given here two points that are directly across from each other.

you might know the word that refers to the distance between two such points.

in fact you have already said this word before, though it was in the wrong context.

[alpine sable]

diameter?

[vale wigeon]

that's right.

and do you know the relationship between the diameter and radius of a circle?

[alpine sable]

what is it?

[vale wigeon]

the diameter is exactly twice the radius.

something that should jump out at you if you draw a circle and a diameter through it.

[alpine sable]

oh alright

[vale wigeon]

to summarize, here is the roadmap for this problem:

• find the diameter of the circle by calculating the distance between the two given points
• halve the diameter to get the radius
• use the formula A = πr^2 to get the area.

[alpine sable]

ok ok

thanks

.close

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[rough bramble]

I need some help

[rough bramble]

Like my logic the price is 10 DKK

At 30

But idk what it more wants

[snow furnace]

Do you have the equation yet?

[rough bramble]

No

That’s the whole task

Do I have to determine the regulation first or

[snow furnace]

For the equation, you can use point slope form, like y-y1=m(x-x1)

Not sure what it means by regulation though, is it translated?

[rough bramble]

Yeah that’s what i’m doing

But it doesn’t make any sense

[snow furnace]

What work do you have right now

Find the slope, and pick one of the points, such as 10,110, and use those for your x1 and y1

So you get y-110= -5(x-10)

And solve from there

[cerulean abyss]

?avatar lafo

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@rough bramble Has your question been resolved?

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[valid ivy]

i have this question which i know the answer to

[valid ivy]

problem is

i dont know which option should i choose

here it is

well i was wondering which option to choose 1 or 5

[wary stream]

Does it say to round?

[valid ivy]

they asked for two digits after decimal point

[wary stream]

Is your boxed answer rounded to two digits after the decimal point?

[valid ivy]

well not

but

[wary stream]

Then you should round it

[valid ivy]

say for example u have 1.86999 wouldnt that just be 1.87?

[wary stream]

Yes

[valid ivy]

i have the same case with another exercise which is 1.246

if its the right way to answer

that would be 1.25?

[wary stream]

Yes

[valid ivy]

aight

wish its that way

thx

.close

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[rain pebble]

Hello, can anyone please tell me what this notation means?

[worn fox]

Show it in context

[rain pebble]

Integration by parts

[worn fox]

It's uv evaluated at b, minus uv evaluated at a

Like in normal definite integration

[rain pebble]

Aaah I see. I must've missed it somewhere

Thank you

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[shut sleet]

I am a little confused with this notation of matrices. So i get the i j part (that's the specific numbered row or column kinda like a coordinate system) but what does the "a" mean?

[shut sleet]

and the "b" and "c"?

[abstract fractal]

a_ij is the element of A in the ith row and jth column

That's just how it's notated

[shut sleet]

why wouldnt it be notated as A[i, j]?

like why does it have to be lowercase?

does the lowercase letter have any significance?

[abstract fractal]

It's equivalent to, say, a variable. I could calculate a_12 + a_24 if I wanted. Or I could find the trace with Σa_ii

[naive valley]

it's just the choice the author is making, he wants to call the elements something, and that is the notation he selected

some authors would say A_ij for example

[shut sleet]

oh i see

i think at least lol

thank you

[naive valley]

think of "suppose that A = [a_ij]" as meaning: "Suppose that A is a matrix whose i,j'th element is called a_ij"

[shut sleet]

got it

that makes sense

thank you once again

.close

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[violet idol]

Could someone please demonstrate to me why

[violet idol]

[lament glen]

$a^{\log_a(b)} = b$ right?

[ocean seal]

Doggo

[lament glen]

do that to both sides on this

[violet idol]

yes because that log_ab would be c just like a^c = b

wait which sides?

[lament glen]

$$a^{\log_a(b) + \log_a(c)} = a^{\log_a(b\cdot c)}$$

[ocean seal]

Doggo

[lament glen]

then you just use $a^{b + c} = a^b \cdot a^c$

[ocean seal]

Doggo

[violet idol]

wait

I didn't get it

[snow furnace]

You can change the logs to exponents yeah?

[violet idol]

how did you come up with this .

[violet idol]

what do you mean?

[lament glen]

you go from $A = B$ here to $a^A = a^B$

[ocean seal]

Doggo

[violet idol]

yes

[violet idol]

why

[lone heart]

@violet idol Has your question been resolved?

[violet idol]

https://prnt.sc/ujjuu-LZ68Qw

Why is he doing $MN = b^x \cdot b^y$?

[ocean seal]

Raid

[violet idol]

Sorry <@&286206848099549185> , I really don't how to demonstrate it

[tawny condor]

Are you asking how it helps prove the equality or how he concluded that MN = b^x * b^y?

[lone heart]

@violet idol Has your question been resolved?

[violet idol]

.close

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[alpine sable]

Hello can someone help me find angle APC

Angle ABC is 125

I'm not sure if we should pretened that Triangles ABP and PBC are just one triangle combined for this

then using that we can find APC

[uneven maple]

Aren't uh

Aren't the two triangles completely upright

[alpine sable]

yeah

[uneven maple]

Like perpendicular to the horizontal triangle

[alpine sable]

on horizontal ground

i believe

[uneven maple]

So what do you mean find apc

[trim wagon]

Is this diagram in 3d?

[uneven maple]

Yeah

[trim wagon]

Hmm okay

[uneven maple]

Oh wait okay

[alpine sable]

I wasn't sure if maybe I should just calculate APB and CPB then add them

[alpine sable]

You know angle APB

[trim wagon]

You can’t do like that

[alpine sable]

yeah

[alpine sable]

ah, then how would you recommend i do it

[trim wagon]

It’s in 3d so APB+CPB is not APC

[alpine sable]

i'm confused about APC

what is a 3D angle

[trim wagon]

Hmm lemme think

[alpine sable]

i've only seen angles in 2d before

[minor needle]

you haven't more information, how do you know ABC is 125?

[alpine sable]

it's another piece of information given

[minor needle]

so give it to us if you can

or it's only ABC

[alpine sable]

this is all

and this, but it's visible on the diagram

[trim wagon]

Hmm okay

I’m leaning towards vectors

Because ABC is Projection of APC

[alpine sable]

oh

I see

[alpine sable]

Do you mean ABC angle is the same as APC ?

[trim wagon]

No I don’t

[alpine sable]

I don't know vectors

[trim wagon]

Hmm well vectors might not be required

[alpine sable]

I didn't mess with 3D before only 2D

.close

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[paper hawk]

hi

[paper hawk]

one mo

x^2+6x+20

factorise

and

y=2x^2-8x+5

and

when b=25 a=40 find the value of a when b=36

[subtle delta]

Is there any context to this

[paper hawk]

inversely prop

i think

[wintry sage]

$a = \frac{k}{b}$

[ocean seal]

Mezza

[subtle delta]

use this

[wintry sage]

Sub in your first set to find k

[paper hawk]

ok

so 40x25

then

that would equal to k

like k=1000

ye maybe not

[wintry sage]

Yes k would be 1000

[paper hawk]

i have to pay to find out what it is💀

aight thanks for ure help

.close

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[queen canopy]

find the complex solutions of the equation... you can see what i tried doing, but it seems im wayyy off

[worn fox]

if you're trying to use the quadratic formula, there shouldn't be any z's in it. a=1, b=i, c=1

[queen canopy]

😭😭 i am stupid. thank you

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[alpine sable]

hi i need help with this

[alpine sable]

unable to derive and find a sub for n(t)

[lone heart]

@alpine sable Has your question been resolved?

[limpid spade]

well basically

K/(1+((K/n0)-1)) is a constant

so ur only interested in 1/(e^(-rt)

or e^(rt)

so take derivative of that

then multiply by cvonstant

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[wooden maple]

I understand how to determine range, zeroes and y intercept. I don't know how to obtain the Range though. For example in the question f(x)=1+root(x+2) I know the domain to be [-2,infinity) because the value in the bracket cannot be less than 0. What am I supposed to do now that I have this information? Or is solving for the range independent or knowing the domain?

[solemn juniper]

You mean you know how to determine domain, right?

[wooden maple]

Sorry, yes I know how to solve for domain.

Range is the issue - the explanation in the textbook is too proof-like and I'm not grasping it. Want to start with something a little less confusing.

For context:

[solemn juniper]

If you're not super comfortable with this more rigid way, another possible solution is to remember the range of the parent function and apply the same transformations to it as you do to the new function

To use your example: what is the range of y=sqrt(x)?

[wooden maple]

(0,infinity)

[solemn juniper]

Now 1+sqrt(x+2) shifts the graph of sqrt(x) 2 units left and 1 unit up

What does that "1 unit up" shift do to the range?

[solemn juniper]

[0, infinity) to be more accurate

[wooden maple]

Right sorry, should be inclusive.

[solemn juniper]

Np

[wooden maple]

It would move the Range up one as well to be [1,infinity)

[solemn juniper]

Indeed

[wooden maple]

So that makes sense when the graph is 'easy' or a polynomial. but what if the graph is something like g(x)=root(7/x-5). That becomes far more complicated to try and transpose in my head.

[solemn juniper]

That's partially why they propose that more rigid method, the algebra tends to have a less steep difficulty increase than mental visualization

[wooden maple]

If I were to extrapolate from the same in the text with the equation that I wrote above, would I just say that the root cannot be negative and therefore 0=root(7/(x-5)) must also be >=0?

Is it just about knowing what can be in a root/denominator/etc...?

[solemn juniper]

Yeah if you can extract the parent function then it's just a matter of using previously established transformation rules

Like here, sqrt(1/x) is something of a weird function, but it's not too bad

The range is (0, infinity), and there are no vertical transformations so the range is unaffected

[wooden maple]

I have to go but thanks for the help!

.close

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[swift cipher]

we need to solve for di

why did my teacher make a common denominator?
also what happend to the 1? cuz he subtracted it on 1 side doesnt he need to do it on the other side

[lone heart]

@swift cipher Has your question been resolved?

[long axle]

Is this lenses and mirrors

They made a common denominator so that they could take the reciprocal of the left side

That’s what was needed to be done in order to solve for d_i

And where did he subtract a 1?

@swift cipher

[swift cipher]

its the last step

im talking abt the 1 above di

@long axle

[long axle]

This?

[swift cipher]

yes

[long axle]

He’s not subtracting 1 here, he’s raising both sides to the power of -1 in order to get their reciprocals

[swift cipher]

so how does he get rid of the power of -1

[long axle]

He flips the fractions upside down

(Or takes the reciprocal)

[swift cipher]

oh so when u put a power u can get rid of it by flipping it

[long axle]

Well, it’s specifically for negative exponents that u can flip

And only for -1 does the exponent go away after a flip

For example

2^-1= 1/2

But 2^(-2) = 1/[(2)^2]

[swift cipher]

also last question if the di was on the top then we wouldnt need to find a common denomonator right

[swift cipher]

so it wouldnt work here cuz its a -2

[long axle]

Unless ur teacher specified to, then yea u wouldn’t need to

[long axle]

It flips, but there the 2 is squared after the flip

[swift cipher]

yea ik to actually get the value u would need to do it

[long axle]

Yep

Cuz that’s how the focal length formula is

[swift cipher]

ok thank you

[long axle]

Np

[swift cipher]

how do i close the room?

[long axle]

.close

[swift cipher]

thanks

.close

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[alpine sable]

my setup is ((1/6) * (21/36))/21/36

[prime badge]

you kinda have to manually count P(A & B)

3 2, 3 4, 4 2, three out of 36

[alpine sable]

how did you get that?

[prime badge]

i counted, did you not get P(B) by counting?

[alpine sable]

my friend helped me with the prior parts :/

[prime badge]

(3/36) / (21/36) = 1/7

[alpine sable]

i see ,thank you

[alpine sable]

how come 4 3 is excluded?

[prime badge]

second number is not even

oh you mean from the red, it's not

i just failed to draw it

[alpine sable]

oh

is AND P(A) * P(B) out side of this problem?

[prime badge]

no

it's when the events are independent

it could be either

[alpine sable]

ok thank you for the help

do you know a good stats book by chance?

.close

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[idle ocean]

I got the upper bound of 19 by plugging in a for x, radius is y + 3 (because of the y axis being -3) and height is the function in terms of y

[idle ocean]

I dont need help solving the integral I only need help setting up the integral to clarify

nvm solved it, it was two integrals I had to solve

.close

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[gilded vessel]

why are $-2+i$ and $2-i$ invalid solutions to $\sqrt{3+4i}$, in the process of solving by setting $3+4i$ equal to some complex number $(a+bi)^2$ you find that $b= \pm 1$ and then substitute this value to find $a = \pm 2$, but the final solution is stated as $\pm (2+i)$ why is this the case, why are these solutions invalid?

[ocean seal]

dog.

[gray isle]

when b=-1, a = -2 only
when b=1, a = 2 only

[gilded vessel]

thanks

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[proper sable]

in a venn diagram situation: what is A union not A

[proper sable]

assuming A = {2, 3, 4, 5, 6}

[prime badge]

"everythinh" is spelled U

[proper sable]

?

[prime badge]

A union not A is everything

[proper sable]

ok so its basically saying A union to nothing

ok

[prime badge]

things outside A and things inside A

[proper sable]

oh

ohhh

thxxxx

[prime badge]

it's spelled U, I haven't seen other notation

[proper sable]

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[raven field]

Why isnt it B with (-1,1) as the o the maximum? cuz like they are in different quadrants so they should have different maximums right.

[ornate condor]

as the o the maximum?

its a local maximum i guess

[raven field]

sorry i meant to say the local maximum

im talking about the bottom question

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@raven field Has your question been resolved?

[lone heart]

@raven field Has your question been resolved?

[raven field]

I figured out why in the other question

But now I need help with something else lmao

how would I solve for C

like how would I use the equation above and all the given information to help find an answer?

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[cerulean musk]

How would I solve this problem?

[cerulean musk]

nvmnd i got it 😐

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[open roost]

using letters of the word ABSICISSA find the number of nine letter words that begin with exactly one s

[open roost]

for this it is 1 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2

/3!2!2!

but it gives15120

but the real answer is3780

[wintry sage]

It has to begin with exactly 1 s so the second letter must not be an s

[open roost]

wait but the first letter is supposed to be an s

[wintry sage]

Yes but the second can’t be

[open roost]

oh so would it be (1x8x7x6x5x4x3x2x1)/(3!2!2!)?

[open roost]

this gave me 26880 where did the formula go wrong?

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[alpine sable]

What have i done wrong here?

As the answer is not matching up with the answer key provided

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[alpine sable]

<@&286206848099549185>

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[woeful tartan]

how to find perfect product selling price?

[woeful tartan]

i have material 40,000

salary price 30,000

the spread is 25%

.close

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[alpine sable]

sigma

30
---- (3n-1)
n=2

I can't get the correct answer

[alpine sable]

Can someone give me the solution?

My lesson is about Arithmetic Series

[echo socket]

You can break the sum up

[gray isle]

$\sum_{n=2}^{30} (3n-1)?$

[ocean seal]

ℝamonov

[echo socket]

Into sum of 3n's and sum of -1's (n obviously going from 2 to 30)

[alpine sable]

oh okay

GOT IT

THX

.close

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[tepid frigate]

hi how do i solve this? can i use l'hop rule for question 14

[echo socket]

No, because cos(x) doesn't approach anything there

The squeeze theorem could help out though

[tepid frigate]

how do i squeeze it?

like -1<=cos(x)<=1?

[rigid smelt]

you could use a substitution here

try u=x-pi

but squeeze theorem is also a good alternative

[tepid frigate]

and then -1/x+pi <= cos(x)/x+pi <= 1/x+pi

?

[rigid smelt]

(tho im assuming you are familiar with the limit of cos(x)/x, if not just do squeeze theorem right away)

[tepid frigate]

is it like this?

[echo socket]

Yeah, although I'd type braces around the x + pi to avoid confusion

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[tepid frigate]

thank u

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@azure inlet Has your question been resolved?

[azure inlet]

.close

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@eternal pulsar Has your question been resolved?

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[loud siren]

.open

[vital brook]

can someone help me do this

[vital brook]

I have tried doing conditional probability

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[velvet cedar]

Hey guys

I have a relatively simple problem

But i just cant get the answer right

The complex equations one

It seems simple,you multiply the (3+i)^3

Convert the i^2 to (-1)

But i just cant get it right

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[surreal sky]

I am trying to calculate Compound Interest with Regular Contributions Formula, I found online the formula P(1+r/n)^nt + (PMT(1+r/n)^(nt) - 1)/(r/n) so I plug in P= 1000 , r = 6%, n = 12, t = 4, PMT = 200, I get 1000x1.005^48 + (200x1.005^48)/0.005 i get 52090.06, but when i plug it in an online calculator it gives 12090.06 why is my calculation so off?

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@surreal sky Has your question been resolved?

[surreal sky]

<@&286206848099549185>

i am misscalulationg? <@&286206848099549185>

hhm..

[surreal sky]

<@&286206848099549185> ??

.close

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[south mantle]

@split dagger any idea how to solve this? ;-;

[split dagger]

why me

specifically

anyway

by defintion of p, 4|p^2019+1

ie p^2019+1 = 0 (mod 4)

now just test out all the options

for option 1: it supposes that p = 1 (mod 4). Can that happen? Well if it were, then p^2019+1 = 1^2019 + 1 = 2 = 0 (mod 4)

so no

[south mantle]

Because i like how u think ;_;

[split dagger]

do the rest

[south mantle]

Makes sense

Thanks 🙏

.close

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[strange fractal]

hi can i have some help

[echo socket]

Just post the question

[strange fractal]

how do i find the mean

Wait lemme send the daya

Daya

I dont know if i did it rigjt

helo?

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[rustic crest]

can someone help me with this

[rustic crest]

How did we get the probability in this table (second picture) from the first picture?

[ancient meteor]

Ok so consider that you bet on both, "matching" and "atleast one head"

Now you have 4 possible outcomes

HH TH HT TT

So if it is a HH then you'll earn 160 as well as 240

With no other outcomes will you earn 160 and 240

So you get the probability 1/4 of earning both 160 as well as 240

[ancient meteor]

You can check for the other probabilities in this table like this too

[rustic crest]

Oh i got it now, thanks

[ancient meteor]

No problem

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[wintry sapphire]

Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $190, how many hours did the plumber work?

Write and solve an equation to determine the number of hours worked by the plumber.

50x + 35 = 190; x = 3.1 hours
50x − 35 = 190; x = 4.5 hours
35x + 50 = 190; x = 4 hours
35x − 50 = 190; x = 6.9 hours

[wintry sapphire]

hello I'm in general having issues with this problem if anyone could help thanks!

[sour breach]

suppose the number of hours worked by the plumber is x

at 50$ per hour how much would he charge for x hours?

[wintry sapphire]

4.5hours?

[sour breach]

50x

now you cant forget the solid $35 he charges for coming

what does that make the total charge

[wintry sapphire]

190

[wintry sapphire]

i think

?

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[median dirge]

Hi @wintry sapphire

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[vale tundra]

Need help

[limpid spade]

hi

[long axle]

[vale tundra]

Was changing the question to remove my school name

12C

I am ot sure what is n and what is x

[strong compass]

I can’t say for certain but that looks like the chose function for a binomial distribution question

[vale tundra]

Hmm

[strong compass]

Does that help you

[vale tundra]

Not really

[strong compass]

Also I feel like question a is wrong

[vale tundra]

Dang how

Ok lets look at A first

[strong compass]

They all die, as in 10 due

Die

You put the p(one dying)

[vale tundra]

Of 10 students 1.6 will die?

[strong compass]

Ite asking you the probability all 10 die

[vale tundra]

Ohhh

[strong compass]

I think you jusy miss read the question

[vale tundra]

Dang

I did

I am not sure how to do that now

[strong compass]

Idk how to explain this without using a simpler example

[vale tundra]

Let me check my notes

[strong compass]

Binomial is a bit overkill for this, but you can use it

[vale tundra]

Hmm

[strong compass]

Let’s say it has p(rain) = 0.4, p(me going to school) = 0.3 right, what’s the p(it raining and I go to school)?

[vale tundra]

P(rain)*P(me going to school)

[strong compass]

Good

[vale tundra]

They are independent

[strong compass]

So the p(one person dying and one person dying and one person dying...) 10 times is...

[vale tundra]

ohhh

[strong compass]

You see?

[vale tundra]

0.16^10

[strong compass]

Yep

[vale tundra]

Dnag

dang

[strong compass]

Do you see how you get that from the binomial function aswell

[vale tundra]

Makes a lot of sense

What would n be ?

[strong compass]

10

[vale tundra]

X is 1?

[strong compass]

X would be 10

[vale tundra]

p=0.16

Oh why are they both the same

[strong compass]

In this example a “success” is someone dying which is like a little sad but maths talk

[vale tundra]

;[

[strong compass]

Plugging in (10c10) * 0.16^10 *(1-0.16)^0

10c10 is just 1

Anything to the ^0 is just 1

[vale tundra]

Yep

[strong compass]

Cool

No we do b

[vale tundra]

So b is wrong too

[strong compass]

Yeh

Given what I just told you

[vale tundra]

One sec

[strong compass]

How do you think you calc b

[vale tundra]

p(1-one person dying and 1- one person dying and 1 -one person dying...)

[strong compass]

Good

[vale tundra]

0.84^10

[strong compass]

Put simply that is

Yeh good job

[vale tundra]

AYYYYYYYYYYYYYYYYY

[strong compass]

Last bur not least

2 people dying

[vale tundra]

Hmm

I am trying to see

(10c2) * 0.16^2 *(1-0.16)^8

I know this is wrong

[strong compass]

Close

Why is the last one to the power of 0

How many ppl will live if 8 die?

[vale tundra]

2

[strong compass]

My bad I just gave you the answer from my messed up wording

How many ppl live if 2 die?

[vale tundra]

8

(10c2) * 0.16^2 *(1-0.16)^8

[strong compass]

Hood so it’s to the power of 8

That’s the one

[vale tundra]

No i edited

[strong compass]

Plug that in to your calc that’ll give you your answer

[vale tundra]

Okii

[strong compass]

👍

[vale tundra]

My calc does not have C

So 10!/(10-2)!2!

[strong compass]

Yeh