help-13

[wanton oak]

So should it be (Ax + B)(e^x) + C?

[gaunt hamlet]

You're introducing another t

There's no t in the problem

[wanton oak]

sorry bad habit

[gaunt hamlet]

It's fine. That should work

[wanton oak]

Also i've been having trouble understanding when to use which method

How can I determine when I should use Annihilator method, Undetermined Coefficient, or Variation of parameters?

[gaunt hamlet]

Undetermined coefficients only work for a subset of inhomogenous terms. Variation of parameters is more applicable to a wider range of inhomogenous terms, but is messier

I'm not familiar with the annihilator method, unfortunately

[wanton oak]

so would it be safe to say I can apply variation of parameters to all nonhomogeneous higher order diff eq instead of relying on the other two?

[gaunt hamlet]

If undetermined coefficients work, then variation of parameters will probably work, however it's a lot slower as opposed to undetermined coefficients

[wanton oak]

Alright

thank you

.close

[cedar kiln]

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[jovial aurora]

Someone please help

I am getting 2 answers

....

[gaunt hamlet]

Show your work

[jovial aurora]

ok

Prime factorization of 400= 2^4 x 5^2 so add one to the exponents 5 x 3 = 15, so 15x = 60 so x = 4 and minus 1 is equal to 3

x = 3

[gaunt hamlet]

Can you justify your steps? Why did you add one to the exponents? Why did you multiply them? Why did you subtract one from x at the end? I've gotta know your complete thought process

[jovial aurora]

Well, In my class I take, to find the number of factors of a certain number, we need to find the prime factorization and add one to the exponents, and then multiply to get the number of factors

@gaunt hamlet Is that better?

[gaunt hamlet]

Lemme think rq, I mightve been thinking about the problem wrong

[jovial aurora]

Ik it was confusing for me at first also

ok

[modern compass]

you shouldn't subtract 1 at the end. you've already got 2 as a factor

[jovial aurora]

ye

so is 3 correct?

[modern compass]

my bad

shouldn't

[gaunt hamlet]

You could think of it like this. The prime factorization of 400 is 2⁴*5², so what's the prime factorization of (400)*2^x?

[jovial aurora]

Hmmm

Ye u could

@gaunt hamlet so how would u tackle this problem

[gaunt hamlet]

If 400 is 2⁴*5², then (400)*2^x is (2⁴*5²)*2^x. Do you see where to go from here?

[jovial aurora]

I mean, not really

thats when I put 3 as the answer

[gaunt hamlet]

You can combine something in the last expression

[jovial aurora]

I am not really sure..

Is 3 correct?

[gaunt hamlet]

No

[jovial aurora]

oh

ok

[gaunt hamlet]

What is a^b * a^c? Remember your laws of exponents

[jovial aurora]

i Still dont understand

[gaunt hamlet]

There's a very relevant property of exponents

$a^b * a^c = a^{b + c}$

[wraith dagger]

Gamer Dio

[jovial aurora]

Ohh

ye

Ok

OHHH

I c

10^6

wai

t

no

[gaunt hamlet]

?

[jovial aurora]

that wrong

I did it wrong

Wait so what would be the answer and how would u get there

[gaunt hamlet]

I'm not going to just give you the answer

We have that $400 * 2^x = 2^4 * 5^2 * 2^x$, right?

[wraith dagger]

Gamer Dio

[jovial aurora]

yes

I got that

[gaunt hamlet]

Using the property above, how would we simplify the expression?

[jovial aurora]

4^4+x * 5^2

[gaunt hamlet]

Why?

[jovial aurora]

Because using the property above

a will stay same

and u need to add exponents

coefficient will stay same

Right?

[gaunt hamlet]

Why did the 2 become a 4, though?

[jovial aurora]

Bc 2x2

OH WAIT

u would keep 2

nvm

Im being dumb

lol

2^4+x * 5^2

[gaunt hamlet]

So now we have the prime factorization of 400 * 2^x

How do we find the number of factors?

[jovial aurora]

um

Lemme think

One sec

so would U add 1 to 4+x?

and the same to 2

?

[gaunt hamlet]

Ye

[jovial aurora]

so its 18?

[gaunt hamlet]

What's 18?

[jovial aurora]

x

[gaunt hamlet]

Show your work

[jovial aurora]

1+4+x = 5+x

2+1 = 3

5+x * 3 = 60?

[gaunt hamlet]

Your forgetting a parenthesis

The 3 isn't just multiplying the x

[jovial aurora]

oh right

x = 15?

(5+x) * (3) = 60

[gaunt hamlet]

That's what I got

[jovial aurora]

Oh ok

thanks!

for the help

!close

$close

Idk how to close these things lol

[gaunt hamlet]

.close

[jovial aurora]

oh

.close

[cedar kiln]

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[jovial aurora]

Ok

[cedar kiln]

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[blissful dove]

someone help me answer?

[blissful dove]

the deadline h o

can anyone help me?

nvm i figured it out

.close

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[naive verge]

Does anyone have any tips on how to integrate this? Maybe trig sub?

[naive verge]

i think it is even

This is apart of bigger double integration surface area problem

I can add more context in a bit let me write it up

[modern compass]

it's almost certainly a trig sub

[naive verge]

This is what I have rn

[cedar kiln]

@naive verge Has your question been resolved?

[naive verge]

I finally solved it!

you need to solve for theta in terms of y

and then you get pi as your answer

then take the integral in terms of x and get 6pi

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[simple tapir]

i chose 90* by guessing and honestly i have no clue if i'm right if i am can you explain how im right and if im wrong could you help teach me the right way to do it?

[simple tapir]

trying to learn about this since my online school has very outdated video tutorials that do a horrible job at explaining these

i'm assuming that angle A is a right angle therefore equaling 90* but i don't trust my answer

nvm

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[open swallow]

I don’t understand how to solve this problem

Can I use L’hopitals to shortcut this or something?

<@&286206848099549185>

[neat canyon]

hi there

1 and 2 can not be true

the function is discontinuous at 3

at 0 as the problem states

the function is 2x-2

you just have to do 2*0-2

= -2

so both answers are wrong

and there is no derivative where the function is discontinuous

so none of then are true

[cedar kiln]

@open swallow Has your question been resolved?

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[crimson sedge]

@quasi venture is there a simpler way to tackle this problem than finding the x and y equations?

actually you know what

I don't have to go through all the product rules

i could just plug in the terms

like this?

[glossy mist]

No

dy/dtheta is not dr/dtheta * sin(theta)

[crimson sedge]

hm?

[glossy mist]

Oh I misread

That looks correct actually

[crimson sedge]

ok so i can just memorize the formula or derive the formula on the exam and plug it in

nice

[glossy mist]

Yeah, memorising it probably isn't necessary - just write out your r, x and y and then see what you need to do to get what you want

[crimson sedge]

sounds good

are u good with finding the area of rose petals?

[glossy mist]

Sure

[crimson sedge]

so this is the theorem

I don't understand how the area of one petal can be found by integrating the fn from 0 to pi/2

[glossy mist]

When you integrate on the polar plane, you are finding the distance from the point at angle theta to the origin

[crimson sedge]

is there a way to visualize this?

[glossy mist]

So at each point, you can imagine drawing a straight line from the point to the origin, and that's what you're finding overall

Uhhh

Put your arm out in front of you and kind of bring your forearm up but your upper arm straight

Kind of like you've just done a bicep curl

Then keep your elbow in the same place and move your arm so it is parallel with your chest

The area you moved your arm through is like integrating from the origin to pi/2

So if the curve has a weird shape, as long as you integrate that distance you find what is in the curve to the origin

[crimson sedge]

umm

nope

ok hold on

so what you're saying is

this area is from 0 < theta < pi/2

like the unit circle?

this must be from pi/2 to pi

@glossy mist

[glossy mist]

Yes exactly

So from 0, the initial line

To pi / 2, which is 90 degrees

[crimson sedge]

right

[glossy mist]

Which gets the petal from this image

And to emphasise the point further, you could do 2 * the integral of pi/4 to pi/2

and get the same number!

[crimson sedge]

so in this case I would find the area of the circle from 0 to pi, then subtract the area of cardioid from the same interval, yes?

[crimson sedge]

huh touche

[crimson sedge]

so this could work if the rose function was say r = 3 cos 2thata

[glossy mist]

Yeah, you could go from 0 to pi/2 and then double it for one petal

[glossy mist]

No, not quite*

You need to start integrating the smaller one from the point of intersection to the other point of intersection

Otherwise you subtract a little extra that lies outside the circle

[crimson sedge]

not if I set the boundary from 0 to pi

no?

im looking at this like a radar

[spring solar]

can anyone help with trig?

[crimson sedge]

@glossy misthello?

[bold hinge]

No.

You have to find the points of intersection.

Does that make sense to you?

[crimson sedge]

nope

im trying to wrap my head around it

[glossy mist]

0 to pi

Inclues the bit between the intiial line and the red circle of the blue thing

Which if you subtract, isn't in the red circle

So you're subtracting extra

[bold hinge]

Ok. Let me use an example

[crimson sedge]

you mean this part?

[bold hinge]

Let's say you want to find the points of intersection of the functions:
y=x^2
y=x

How would you do that?

Think.

[crimson sedge]

equate the two

[bold hinge]

Yes!

[crimson sedge]

Is that a dead sea scroll btw?

[bold hinge]

So let's say you want to find the points of intersection of:
r = 2+2sinθ
r = 6sinθ

[bold hinge]

Υes

[spring solar]

trig help plz

im dyin over here

[bold hinge]

#❓how-to-get-help

[crimson sedge]

ok then I get 2 - 4 sin theta = r

but so what?

[bold hinge]

Nope

Why do you have an r there?

[crimson sedge]

because i set the two equations equal

[bold hinge]

No you didn't

r = 2 + 2sint
r = 6sint
2+2sint = 6sint, because r=r

Just using t for theta here because I don't feel like typing greek

[crimson sedge]

ok

then umm

2-4 sin t = 0

[bold hinge]

2 = 4sint

2/4 = sint

1/2 = sin(t)

[crimson sedge]

right

and that's umm

pi/6?

so the intersection pt is at pi/6?

[bold hinge]

Look at the graph. How many points of intersection do the curves have

[crimson sedge]

2

[bold hinge]

So we have pi/6 and?

[crimson sedge]

oh the umm

2nd quadrant variant

so pi/6 + pi/2

no

[bold hinge]

No

[crimson sedge]

[bold hinge]

Hint:

sin(30)=sin(150)

[crimson sedge]

isn't that pi/6 + pi/2?

oh no

ok umm pi - pi/6

there we go

[bold hinge]

Yes

Which is?

[crimson sedge]

5pi/6

[bold hinge]

Right!

Now we have the bounds for the integral

[crimson sedge]

ok but what exactly do these points have to do in finding the area of the integral

[bold hinge]

We have the bounds

[crimson sedge]

ok

[crimson sedge]

what do I do with the 2 functions?

do I find the area of the circle than subtract smaller one from it?

[bold hinge]

Yes, but do it like this

$A = \int_a^b \frac{1}{2}(6\sin(t))^2 dt - \int_a^b \frac{1}{2}(2+2\sin(t))^2 dt$

[wraith dagger]

EndTimes

[bold hinge]

Where a and b are the values we found earlier

[crimson sedge]

ok

tysm!

btw which part of the dead sea scrolls is that

[bold hinge]

The based part

[crimson sedge]

wut

[bold hinge]

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[little wolf]

Can anyone tell me where do they get the equation from?

[cedar kiln]

@little wolf Has your question been resolved?

[little wolf]

.close

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[south dawn]

@knotty shell

[thick bison]

HI

i need help

with an activity

like 13 items

its about quadrilaterals

does anyone know about this?

given LO=48 LJ=73, FIND OJ

hello?

[south dawn]

you have to post your question that is open. It is easier if you figure out what is not in A and what intersects in both set. In other word, numbers that are in both sets. 1, 3, 4, 5 in both A and B so, it is in the venn diagram intersection. Is that make sense?

[thick bison]

someone help me i dont know how to solve quadrilaterals

[south dawn]

You have to go to open channel. Help-6 is open

[thick bison]

ok

[south dawn]

Which number is common in B and C? that is your intersection

You're welcome. B and C, only 5 is in there.

You know, complement of B means things in A that is not in B but it is in A. is 2 is the only one? I am slow because I have to go back and forth with your picture. I am going to just write it out on my paper sorry.

What is that symbol between A complement and AUB?

It seems that AUB is exact same set as A

Your textbook doesn't say?

If sets are equal, complement is empty

[crimson sedge]

it could be symmetric difference

[south dawn]

don't be sad. Let me put it another way. A Complement means something is not in A. continues

number 6 thru 9 is not in A, but in U.

[crimson sedge]

@south dawn haha we almost have the same name

[south dawn]

Maybe I am not explaining the way you can understand. sorry. Let me think about how to say it better

[south dawn]

I know. Nice name. 🙂 Do you have a better way to explain? I think a Vann diagram is a best way to go.

[crimson sedge]

which part?

[south dawn]

How do you create vann diagram here? I will try to create via paint.

[crimson sedge]

personally I would just compute the sets

[south dawn]

It is asking for vann diagram

OK, this is what I got. 5 is in all set A, B, C

b complement-that is not in B but in A is 2. so far so good

which one?

I believe it is 6,7,8,9. from the U. I wish I know what that \ means. I don't have your textbook

@crimson sedge agree with that assessment?

[crimson sedge]

\ should mean set minus

or set difference whatever

[crimson sedge]

I think 2 should also be there?

[south dawn]

60-65, A complement is 2

[south dawn]

let me relook

[south dawn]

why? aren't we not listing things that are in U but not in A \B'?

[crimson sedge]

yea

2 is in B' so 2 cannot be in A \B'

[south dawn]

See, the symbol \ is need to be defined. I wish there is a website tell you what that is

[crimson sedge]

https://mathworld.wolfram.com/SetDifference.html it's a pretty standard symbol, enough that it doesn't need to be defined every time that it's used

[south dawn]

A - B is A-B = { x: x∈A and x∉B}

[crimson sedge]

but it should have been in the person's book or notes or whatever

I usually use \ and lots of people do 😛

[south dawn]

I take your word for it. \ means minus. Well if you look at the definition of A - B is A-B = { x: x∈A and x∉B} it does not include 2

[crimson sedge]

what doesn't include 2?

[south dawn]

60-65 A complement looks empty because they are exact same set.
A or B is 1 - 5 and A = 1- 5. It is not 6,7,8,9 and I am going to assume symbol is like adding

Did we loose Ikay0813? lol

[crimson sedge]

I think so 😆

[south dawn]

🙂 luckily I opened the pic on other tab. so 60-65 is universal set?

[south dawn]

I feel bad about that student. I have been there.

[crimson sedge]

I haven't done it yet

it doesn't seem like everything would be in there though

are you assuming the circle with cross is symmetric difference?

[south dawn]

honestly I don't know what that mean. However, questioner needs to provide that info.

[crimson sedge]

we might have some trouble obtaining that info 😆

[south dawn]

Do we need to cry or what? 😭

[crimson sedge]

yes

[south dawn]

So the venn diagram I drew via paint looks good?

[south dawn]

I googled for that symbols and I couldn't find it. I don't know.

[crimson sedge]

why aren't 3 and 4 in the space shared by A and B?

[crimson sedge]

https://en.wikipedia.org/wiki/Symmetric_difference I would guess it's this but only because I have no other guesses

and I'm not confident that's what it is

[south dawn]

I think I need to go to bed. OMG

[south dawn]

Oh, thanks. I was told by my teacher, never to assume.

[crimson sedge]

that looks fine to me but I would still just compute the sets

[south dawn]

How do you answer the question if you don't know all the detail. I asked and she did not know so what can I do. I

[crimson sedge]

what details are missing other than what the oplus means?

[south dawn]

\ and cross inside the circle

[crimson sedge]

\ is a standard symbol though

[south dawn]

If you say so.

It looks like a division to me

[crimson sedge]

it really is 😂

division is written with a /

[south dawn]

what about other one. do you know?

[crimson sedge]

$\oplus$?

[wraith dagger]

yume ♡

[south dawn]

what's that? I found this. https://www.rapidtables.com/math/symbols/Set_Symbols.html

[crimson sedge]

as an aside, the \ for set difference really is standard notation

[crimson sedge]

it doesn't have any standard meaning as an operation on sets, but it does in other places

https://en.wikipedia.org/wiki/Direct_sum like this

[south dawn]

Look at that. A\B we have a name. relative complement is equivalent to A-B objects that belong to A and not to B https://www.rapidtables.com/math/symbols/Set_Symbols.html same place

[crimson sedge]

yea

[south dawn]

I still can't find cross inside the circle and its definition

[crimson sedge]

see here for some places it has a standard meaning

it doesn't really have a definition

it's just a symbol used for an operation

[south dawn]

Everything has names and definition. I must

symbol to do what?

[crimson sedge]

often to take two algebraic structures and "add" them to get another one

but it really depends on the context

[south dawn]

You know you're right. You have to know the context. I still searching. I even searched set operation symbols.

[crimson sedge]

this was the weirdest help session I've taken part in

the person who asked the question... got banned for asking help on an exam maybe?

but then we still talked about the problems for like an hour

[south dawn]

I know right? 🤣 Because we are nerds? haha. i have learn much by just helping people. I get so upset that I can find the definition for the symbol though. I probably dream about it. Can I add you as my friend? thank you for sticking with me. You're a trooper. 🙂

[crimson sedge]

haha sure 😊

[south dawn]

Thank you. I give up searching for that symbol today. I need to get some sleep. You take care now.

[crimson sedge]

you too, sleep well

[south dawn]

.close

[cedar kiln]

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[cedar kiln]

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[proven sapphire]

What is the mean difference between the potential infinity and the actual infinity? Can someone give me an example of both of them?

[proven sapphire]

I have read many articles on the internet but still don’t get it.

[cedar kiln]

@proven sapphire Has your question been resolved?

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@proven sapphire Has your question been resolved?

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[sudden nimbus]

How do I do a.

[dense hornet]

what have you tried?

[sudden nimbus]

Like this?

[dense hornet]

yeah sure, looks good,

[sudden nimbus]

Cheers

Also got this bugger

Wtf is b 😅

Never heard of it

[dense hornet]

eh not sure what it means by the percentage change in l there, ill leave this to someone else

[sudden nimbus]

All good bro

<@&286206848099549185>

[cedar kiln]

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[livid mica]

f(x)= k+h(x-2)^2

[livid mica]

f(x) goes through the origin and the maximum value of f(x) is 8, find f(x)

i understand the origin part and from that i got k+4h=0

[glass blade]

Yes

[livid mica]

but how do u get max value

i mean how do u use it

[glass blade]

Now for the maximum part
Put f'(x) =0

[livid mica]

yeah

wait sorry why is it =0

[glass blade]

I was actually using maxima minima concept here

[livid mica]

my teacher gave the answers but i dont understand it

[glass blade]

f'(x) = 0 gives critical points

[glass blade]

Share the part where you don't understand

[livid mica]

He wrote: max value= 8 so when x=2, f(x)=8

[glass blade]

f'(x) = 2h(x-2) = 0
=> x=2 @livid mica

[livid mica]

why did it become 2h

[glass blade]

I just did the derivative

f'(x) = d(f(x))/dx

[livid mica]

sorry i still dont get it

where did the k go

[glass blade]

k is constant
Whenever you try to find the derivative of a constant part
It becomes 0

[livid mica]

looks like i need to work on functions

wait hol up

the function is h(x-2)^2 +k

so the vertex of it is x=2

does that also work

[glass blade]

Yes it's the critical point

Now the maxima of your function lies at 8

[livid mica]

so by the maximum value did they mean the vertex or what

[glass blade]

depends

if your h>0 then vertex is the minimum

If h<0 then vertex is maximum

[livid mica]

yeah

okay thanks

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[sharp kettle]

I have $V\in \mathbb{K}$ Vectorspace $U_{1}, U_{2} \subseteq V$ with $V=U_{1} \oplus U_{2}$
I have to construct a Projection $\pi : V\rightarrow V$ on $U_1$ along $U_2$. Then I have to prove it's unique.

[wraith dagger]

Simplex

[sharp kettle]

<@&286206848099549185>

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[cedar kiln]

Please don't occupy multiple help channels.

[somber mason]

<@&286206848099549185>

y= (-4x+3)(x+3)
y= -4x² -9x+9
y’= -8x-9
0=-8x-9
8x=-9
x=-9/8
y= (-4(-9/8)+3) ((-9/8)+3)

this is what i got so far

im stuck on how to do the rest

[cedar kiln]

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[gleaming jasper]

Only the top part

[bold vine]

This part is wrong

Think about where these angles are

And what angle(s) you're looking for

[bold vine]

Careful with π and 2π, look at your original interval

[gleaming jasper]

it said less than 2 pi so these solutions are right? because its less than less 2 pi

[bold vine]

You have 2π as a solution

[gleaming jasper]

oh.. oops didn't see it

is that the only mistake?

i uhh.. had the same answer but without 2 pi as a solution and is still wrong

[bold vine]

What other solution are you missing?

[gleaming jasper]

idk. I entered 1.74, 4.54, pi

i got 7.5/10 = missing one answer

[bold vine]

check your current solutions again - it's small

[gleaming jasper]

im sure they are 100% correct for cos(t) = -1/6

but is sin(t) = 0 correct?

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[harsh nova]

This is a calculus question where we want to evaluate the limit. I understand everything except the thing I marked in red. Where does the “x” come from when we divide (lne^-x + 1)?

[bold vine]

@harsh nova Everything was divded by x

[livid hound]

the structure is horrid

by mashing everything together it isn't immediately clear which part was done first

it'd probably be a bit clearer in

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[frigid canyon]

what;'s the problem?

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[half willow]

i dont know how to solve

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[dusk flower]

I need some help with fractional powers

[kindred storm]

@dusk flower One of the rules is to post the question you need help with and what you've tried.

Or to ask something about how they work in general.

[dusk flower]

It's not really a specific question , it's just the concept of how to solve it that I'm having trouble with

[kindred storm]

What's an example of something you want to know how to solve?

[dusk flower]

81 To the power of -3/4

[kindred storm]

OK, so negative means reciprocal, the numerator works like a normal power, and the denominator works like a root.

[wraith dagger]

Chai T. Rex

[kindred storm]

Does that make sense?

[dusk flower]

Yes, thx

[kindred storm]

No problem.

[dusk flower]

I can get it from there

.close

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[cedar kiln]

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[gloomy nacelle]

Do you know simultaneous equations

[hollow vortex]

kinda

[gloomy nacelle]

You are given 2 points on the equation which are (3, 9) and (4, 10)

So you should substitute them into the equation and get 2 equations

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[burnt shard]

What are the primary steps to solve optimization word problems?

[tepid lion]

Not sure there is a one-size-fits-all, but all the ones I have ended up doing generally ask you to write a system of equations that describe the scenario, solve for a variable, substitute it in, then take the derivative of your substituted equation and solve for your variable. You can then check whether your solution is a min/max by taking the second derivative and plugging your variable in.

It’s probably better to ask general questions in the topical channels though, especially if you are having trouble with the concept in general.

[burnt shard]

Yea, I know how to solve and all. My main issue is coming up with the 2 equations. I currently have a question I'm trying to solve as well

[tepid lion]

I can see if I can help. I took calc 1 recently, so no promises. I remember being pretty good with optimization though.

[burnt shard]

“A printer needs to make a poster that will have a total of 500 cm2 that will have 3 cm margins on the sides and 2 cm margins on the top and bottom. What dimensions of the poser will give the largest printed area?”

[tepid lion]

Okay. So your total area is 500.

[burnt shard]

yea

[tepid lion]

We can also write the formula for area in terms of x and y.

Normally, the area would be equal to xy, but you have to consider the margins as well.

[burnt shard]

yea so 500 = 2x + 2y

?

[tepid lion]

Not quite. Have you drawn a picture?

[burnt shard]

a rectangle

top and bottom labelled 2cm

sides labelled 3cm

[burnt shard]

arent u going to label them as well?

x is 2 and y is 3

[tepid lion]

x should be the dimension of the poster. 3 is the margin horizontally, and you have two of them.

If area is the product of the two lengths, then can you write the equation for area in terms of x and y seeing this?

[burnt shard]

right

[tepid lion]

Did you get an equation?

[burnt shard]

500 = xy

is the first one

[tepid lion]

That would be okay if we knew the area of the poster, but we don’t. We only know the area of the poster PLUS it’s margins.

[burnt shard]

true

[tepid lion]

To consider the margins, we should write one length as:

,,x + 3 + 3

[wraith dagger]

Lidoh

[tepid lion]

x is the length of our poster space, and there is a 3cm margin on each side.

[burnt shard]

I have an equation: A(printed) = (x-6)(y-4)

[tepid lion]

That is really close. The area of the whole thing is equal to 500, so we should write our equation using the area of the whole poster.

,,A = (x + 6)(y + 4)

[wraith dagger]

Lidoh

[tepid lion]

,,A = 500

[wraith dagger]

Lidoh

[burnt shard]

i think that works as well but what I did was I used the area of the whole poster 500 = xy solved for y so 500/x and plugged it in to A(printed) = (x-6)(y-4)

[tepid lion]

Oh, okay.

[burnt shard]

does that seem right?

[tepid lion]

Then that should be fine.

[burnt shard]

ok

but u can resume your method

i wanna see anyway

im getting x = 11.2

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[cedar kiln]

@burnt shard Has your question been resolved?

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[mystic void]

Q11. In dividing fractions, multiply the second fraction by the reciprocal of the first fraction.
1 point
A. True
B. False

[mystic void]

Q11. In dividing fractions, multiply the second fraction by the reciprocal of the first fraction.
1 point
A. True
B. False

[tight herald]

Do you know what a reciprocal is?

[mystic void]

no :/

[tight herald]

$\frac{a}{b} the reciprocal is \frac{b}{a}$

[wraith dagger]

Breeziboi

[mystic void]

oh

[tight herald]

It is the fraction flipped

[mystic void]

ohh

ok

[tight herald]

LCD is Least Common Denominator

Hope that helps

Do you know how to find that?

[cedar kiln]

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[calm bronze]

Hello

[calm bronze]

I have a question about this

The coordinate is (-9,-9i)

I'm not sure how to find the conjugate of an ordered pair, especially without an operation to flip?

[upper abyss]

Weird way to say this.
The number is -9 - 9i
Its conjugate is -9 + 9i

[calm bronze]

That's what I had in mind

Since -9i had the negative plus the i

[upper abyss]

t?

[calm bronze]

i

Its imaginary number i

Like root -1

that i

Anyway

Do I reflect that across x axis

since that's basically what's happening

[upper abyss]

Ye

[calm bronze]

So it should be -9, 9i

x and y in order

[upper abyss]

The conjugate is -9 + 9i, yes

[calm bronze]

So that's what I graph?

(-9, 0)

[upper abyss]

x and y?

[calm bronze]

9*

I have to graph the point

So it would be (-9, 9i) on the graph

-9 left on x and 9i upward on y

Are you following?

[upper abyss]

9i upward? How do you travel by an imaginary amount?

[calm bronze]

On the imaginary axis?

[upper abyss]

I'm being facetious, yes you put the point 9 units to the left, and 9 units up

But you are mixing notations hard

[calm bronze]

Ok

Um

Alright,

I was just clarifying, but ok.

[upper abyss]

ok.

[calm bronze]

I was explaining this, that's all

Thanks for help

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[open frost]

Im not sure how to do number 8 I don't know if im supposed to use trigonometry or Pythagorean theorem.

[queen horizon]

to find the other side?

[open frost]

Yeah

[queen horizon]

yeah you can do that

$28^{2}-19^{2}=x^{2}$

[wraith dagger]

2022 squared

[queen horizon]

then simplify the root

[open frost]

the answer is 20.6??

ty

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[calm bronze]

Hello

[calm bronze]

I'm stuck on this

It's obvi not an integer or whole number

It is a rational number bc it's a repeating decimak

But wether or not it's real is what I'm stuck on

[willow hill]

and its a real number

ok

basically

real numbers are basically

every number

[calm bronze]

Since it's unethical to plot it on anumber line

But it's still possible

Go ahead

[willow hill]

ok

well if a number is rational

its real too

if a number is irrational

its also real

[calm bronze]

Ah, good to know

[willow hill]

if you're dealing with complex numbers

where you have like 4 + 3i

those aren't very real

but that guy

[calm bronze]

imaginary

[willow hill]

46.4444....

is as real as they come

[calm bronze]

correct

and it makes sense

bc on a number line

u can still plot

46 and 4/9

or 44/99

and so on

[willow hill]

i dont really get that number line analogy

you mean like

[calm bronze]

It's something I was taguht

[willow hill]

a dog

isn't a real number

or something lol

[calm bronze]

lol

[willow hill]

but if it helps you that's good

[calm bronze]

It does

It sounds weird but it helps a lot

SO rational + real

Hold on imma write down more notes

[willow hill]

rational + irrational = real

[calm bronze]

SEc

K

Good to go

[willow hill]

🙏

[calm bronze]

Thanks for your time.

HAve a good day

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[little wolf]

Why is the k = 1.96, shouldn't it be 1.645 from the given table of critical values?

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[little wolf]

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[proven abyss]

Hello, can someone help me make a frequency distribution table for this?

[silk stream]

do you know how to make one?

[proven abyss]

No

[silk stream]

ok

frequency distribution tables are easy

so example

[proven abyss]

Btw it's ungrouped

[silk stream]

oh ok

[proven abyss]

And i don't really know how to make an ungrouped FDT

[silk stream]

sorry i was helping someone

tbh idk what the difference between grouped and ungrouped are

so

[proven abyss]

Oof

Welp, i'm gonna find someone who can help

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[runic lava]

why does this converge (what tests to use to get there)? i found that the sum of the term inside the nth exponent diverges.

[manic stratus]

I'm not sure if this is the correct answer, but I hope you will be grateful for my help.

n^2+1 will be greater than n, regardless of whether or not it is raised to the power of n. that means the values will keep on getting smaller, and when added together, will not equal infinity

A better way to do it would be to evaluate the limit

[runic lava]

would the limit of the term not equal 0 though? which means i have to use another test?

[manic stratus]

it equals 0

I think at least

[runic lava]

yeah, and i think that makes the divergence test inconclusive meaning it could still diverge or converge

[manic stratus]

well the a convergent function has a limit as x approaches infinity

i.e. its limit as x approaches infinity exists

[runic lava]

so what test do i use then?

[crimson sedge]

you could use the root test

it takes care of the n exponent and then you would evalute the whole thing as n (or x if convention) approaches infinity

[runic lava]

Ok that was much easier than I thought lol

And since the result of that limit is less than 1, it is absolutely convergent?

[crimson sedge]

precisely

[runic lava]

sweet thanks <3

[crimson sedge]

remember to point out if this is homework that it converges absolutely

since the root test determines absolute convergence

[runic lava]

got it

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[crimson sedge]

👍

[cedar kiln]

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[little wolf]

Here is the question, Need help with part (iii)

[little wolf]

Why is the distribution graph's rejection region after biased is larger than before?

This is the answer key, why are we starting from P(X>= 4) suddenly?

[cedar kiln]

@little wolf Has your question been resolved?

[manic stratus]

think of how biases and power changes the p-value and the decision on whether to reject/fail to reject null

[little wolf]

hmmm the bias changed the p-value of the mean from 0.1 to 0.5?

[manic stratus]

lets see

[little wolf]

Its not shifting it, the graph with 0.5 as the mean, shouldn't it be completely unrelated with the previous graph which mean is 0.1

[manic stratus]

I'm not exactly sure but I remember hearing something about effect size and power changing the accuracy of the decision to reject or fail to reject Ho

Yeah an alternative p value will change the power based on an increase/decrease in distance from the Ho

further from Ho = more power

[little wolf]

what do you meant by the term "power"?

[manic stratus]

1-(typeII)

basically reject Ho and Ha is true, so its a good decision

[little wolf]

But I still dont get how they relate the graph before bias to the graph after bias

[manic stratus]

I'm a little bit confused on that too but I'll try and see what I remember

I believe it is something to do with z-score

[little wolf]

https://www.youtube.com/watch?v=-2Tu7LuC1jI
This is the video explaining the question, No 7 Part iii, but still dont get the explanation

[manic stratus]

He didn't write that both regions were 1% in the vid, but that is important to understanding the problem

[little wolf]

But the question did state that SL of both the graph before and after were tested at 1%

[manic stratus]

I'm not quite sure what SL is

[little wolf]

Signifcant Level

[manic stratus]

Ahhh

I always call it alpha

[little wolf]

As in the rejection region

[manic stratus]

Yeah

[little wolf]

Right?

Oh ok thought i got it wrong

[manic stratus]

Well if it is less than the significance level then it is statistically significant and you reject null hypothesis so you are correct

Ohhhhh wait a second

So in the first graph Ho is .1 and in the second its .5

[little wolf]

Wasn't less than significance level meaning Ho is true, but since you reject it, its an error, type 1 right?

[manic stratus]

Tbh I always mix up type I and type II haha

[little wolf]

Here, i got you, same, got mixed up always

[manic stratus]

but anyways the z-score is changed by the Ho being bigger. For the same value, a bigger µ would mean a smaller z-score. This means that, in order to have the same 1% rejection area, you would need to have a different standard deviation

this means the distance from the µ to the rejection zone is shifted

[little wolf]

Z = (x - µ)/σ, When µ increases, Z is lower

OHHHH that makes sense

[manic stratus]

🥳

That is a very complex problem

[little wolf]

So the sigma increases to retain that 1%

Genius

[manic stratus]

An elegant solution

[little wolf]

Ok thanks, i will try to research more on type errors

[manic stratus]

I might look into them more as well, they seem very interesting

[little wolf]

Thanks again

.close

[cedar kiln]

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[languid turtle]

can you solve q9

<@&286206848099549185>

[umbral jackal]

1st thing

pls don't ping helpers just a minute in

even when I'm in a serious emergency like cramming for tests

I wait for like at least 5-10 minutes

[languid turtle]

its not test

just say iT yoU caNt soLvE iT

[manic stratus]

are you ok

[umbral jackal]

I am

[manic stratus]

I was talking to the other guy

😅

[cedar kiln]

@languid turtle Has your question been resolved?

[cedar kiln]

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[shy garnet]

Volume of a pyramid with an equilateral triangle base where every edge of the pyramid is side a

[shy garnet]

divide the base side of the equilateral triangle by 2 to get the height of the equilateral triangle

$(a/2)^2 + h^2 = a^2\
\frac {a^{2}}{4} + h^{2} = a^{2}\
h^{2} = a^{2} - \frac {a^{2}}{4} = \frac {4a^{2}}{4} - \frac {a^{2}}{4} = \frac {3}{4}a^{2}$

[wraith dagger]

Plumbum

[shy garnet]

$h = \sqrt {\frac {3}{4}a²} = \frac {\sqrt {3}}{2}a$

[wraith dagger]

Plumbum

[shy garnet]

so that's the height of the equilateral triangle

[glass blade]

Yes you are correct

[shy garnet]

now the volume of a pyramid is 1/3Bh

where h is the height of the pyramid not the equilateral triangle

and B is the surface area of the base shape

[glass blade]

Yes

[shy garnet]

which equals to

$B = \frac {a}{2} × \frac {\sqrt{3}}{2}a = \frac {\sqrt{3}}{4}a^{2}$

[languid turtle]

no

[wraith dagger]

Plumbum

[shy garnet]

so that's the Base surface area

now HOW IN THE LIVING HELL DO I GET THE HEIGHT OF THE PYRAMID

my answer sheet said that the height of the pyramid always cuts 2/3 of the height of the equilateral triangular base

I'm like ?????

So i need an explanation

$H : \text {height of the pyramid} | V = \frac {BH}{3}\
B = \frac {S_{b}h}{2} = \frac {\sqrt {3}}{4}a^{2}\
h = \frac {\sqrt {3}}{2}a\
S_b = a\
H = \frac {1}{3}h^{2} = \frac {1}{3}(\frac {\sqrt{3}}{2}a)(\frac {\sqrt{3}}{2}a)$

[wraith dagger]

Plumbum

[shy garnet]

$\frac {6}{12}a^{2}$

[wraith dagger]

Plumbum

[shy garnet]

$V_{p} = \frac {\sqrt {3}}{4}a^{2} \frac {6}{12}a^{2}\frac{1}{3}$

[wraith dagger]

Plumbum

[shy garnet]

$\frac {\sqrt {3}}{4}\frac {1}{6}a^{4}$

[wraith dagger]

Plumbum

[shy garnet]

$\frac {\sqrt{3}}{24}a^{4}$

[wraith dagger]

Plumbum

[shy garnet]

which is clearly not the correct answer

so i need help

<@&286206848099549185>

$H = \frac {1}{3}h^{2} = \frac {1}{3}(\frac {\sqrt{3}}{2}a)(\frac {\sqrt{3}}{2}a)\
\frac {3}{12}a^{2}$

[wraith dagger]

Plumbum

[shy garnet]

$V_{p} = \frac {\sqrt{3}}{4}a^{2} \frac {3}{12}a^{2} \frac {1}{3}$

[wraith dagger]

Plumbum

[shy garnet]

$\frac {3 \sqrt {3}}{48}a^{4}$

[wraith dagger]

Plumbum

[shy garnet]

i give up i need help

[cedar kiln]

@shy garnet Has your question been resolved?

[shy garnet]

N o

B i t c h

[cedar kiln]

@shy garnet Has your question been resolved?

[shy garnet]

.close

[cedar kiln]

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[stuck stream]

can someone help me explain this

[stuck stream]

i understand the whole problem, but i do not understand the second part

if you let v = 0

you get $\frac{20x-x^3}{2}$

[wraith dagger]

robic

[stuck stream]

how it it become $x\left(\sqrt{20}-x\right)\left(\sqrt{20}+x\right)$

[wraith dagger]

robic

[stuck stream]

if you multiply that you get the numerator

but why remove 2

[cedar kiln]

@stuck stream Has your question been resolved?

[stuck stream]

<@&286206848099549185>

[flint plinth]

i agree, it's a mistake, they dropped the 2 in the denominator. it doesn't really matter, since they're setting the result equal to zero (could just multiply by 2 to get rid of it)

[sand ether]

sup

[stuck stream]

can we add 2 to the x here @flint plinth

it will still be zero

[flint plinth]

add? or multiply?

[stuck stream]

$2x\left(\sqrt{20}-x\right)\left(\sqrt{20}+x\right)$

[wraith dagger]

robic

[flint plinth]

as long as you're setting it equal to zero, you can multiply it by any number and the solution will still be the same

namely, x=0 or x = sqrt(20) or x = -sqrt(20)

[stuck stream]

ok ty

[cedar kiln]

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[stuck stream]

.close

[cedar kiln]

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[upbeat whale]

what is this formula called

[upbeat whale]

finding the 3 points

i dont get it

i tried to grapgh it

and i got the bottom one aiming down

but how do i get the top one

do i mirror it?

[cedar kiln]

@upbeat whale Has your question been resolved?

[upbeat whale]

nvm i got it 👍

.close

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[cedar kiln]

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[sharp crystal]

a+b <= 10
b+c <= 10
I can subtract both and get:
a-c<=0 --> (a<=c)??

[sharp crystal]

a,b,c are natural numbers

[wicked brook]

well let's see if b = 1, a = 8, c = 1

does everything hold?

(the first two equations)

[sharp crystal]

Yes

[wicked brook]

is a > c?

[sharp crystal]

Y

[wicked brook]

so can you do what you did?

[sharp crystal]

maybe there is another example who doesnt work

[wicked brook]

this one doesnt work

you said a <= c, here a > c

[sharp crystal]

Oh wait

so thats not true🥲

[wicked brook]

yea sadly

[sharp crystal]

!close

😅

.close

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[gusty kraken]

hello

[gusty kraken]

pls help

[cedar kiln]

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[haughty yoke]

-15+2 is - 13 right cus i legit forogr