help-13

[sick ruin]

Also can you please be a little more gracious?

[cedar kiln]

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[trim axle]

why is $e^{x^{2}}=/e^{2x}$?

[wraith dagger]

Synthetic

[trim axle]

that is meant to be not equal but idk how to do it here

[livid hound]

\neq

[trim axle]

cool

[buoyant zodiac]

It's e to the power of x^2

$x^2 \neq 2x$

[trim axle]

but i thought when you have indices to the power of other numbers you multiply them

[wraith dagger]

ViB

[livid hound]

$e^{x^2}$ represents $e^{(x^2)}$ which is different to \
$(e^x)^2 = e^{2x}$

[trim axle]

like $2^{2^{3}}=2^{6}$

[wraith dagger]

ℝamonov

Synthetic

[buoyant zodiac]

it has to have parentheses

[trim axle]

ahh

[buoyant zodiac]

2^3 is 8

[trim axle]

ok that makes sense

[buoyant zodiac]

you do the highest exponents first

[trim axle]

lol thank you guys

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[trim axle]

what wrong with my working here?

tried doing it by parts but got a different answer than my workbook

they got $\frac{1}{3}(sin3x+\frac{1}{3}cos3x)+c$

[wraith dagger]

Synthetic

[strong lantern]

it will be sin3x

first step

[trim axle]

what happens to the x there?

[strong lantern]

"xsin3x/3"

[trim axle]

but the x in xsin3x isnt in the answer

:/

[strong lantern]

In first part of first step im saying

wait

[trim axle]

yeah just that sticky x

[trim axle]

yeah

[strong lantern]

ye

[trim axle]

but i still have the x in there

before sin3x

[strong lantern]

wait

there is x

[trim axle]

you think its an issue with the book?

[strong lantern]

i think answer here is slightly wrong

[trim axle]

ah cool

[strong lantern]

yes imma getting x too

[trim axle]

well thanks mate

ill probably have another question in a min

going over the questions i got wrong

[strong lantern]

nice

[trim axle]

to get the integral of (x-2)^-1 i multiply the derivative of what is inside the parenthesis by ln x-2 right?

[strong lantern]

check your first step again

check the splitting

[trim axle]

ah easy fix

🙂

[cedar kiln]

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[cedar kiln]

@scenic pasture Has your question been resolved?

[cedar kiln]

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[vague perch]

rearrange into y=mx+c

m is ur gradient

[cedar kiln]

@halcyon wasp Has your question been resolved?

[vague perch]

? wdym im wrong

u use the coordinates (0,3) by subbing it into ur equation to get C

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[rigid spoke]

This is what I’ve done so far and I’m not sure where to go from here

[cedar kiln]

@rigid spoke Has your question been resolved?

[gray condor]

all potential energy is converted to kinetic energy

dw

I’ve done this

let x be the extension

mg(0.1+x) = 0.5kx^2

right?

solve the quadratic

and find out x

using quad formula

@rigid spoke

[gray condor]

DO NOT USE FORCES METHOD

if you do

[dense wing]

Obviously they aren't going to use forces

It explicitly says to use energy

[gray condor]

yeah, it’s much nicer

[dense wing]

Duh.

[gray condor]

When they tried to find tension and stuff, I thought they were trying to do it using forces

[rigid spoke]

Yeah I got it

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[dense wing]

that is in fact a derivative

[limpid grail]

When the x has a power do you always multiply by the derivative

[dense wing]

You apply chain rule when chain rule is applicable

3^(x^2) is a composition, so you use chain rule

[limpid grail]

I see

ty

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[gloomy minnow]

we need to solve for x

[cedar kiln]

@gloomy minnow Has your question been resolved?

[cedar kiln]

@gloomy minnow Has your question been resolved?

[gloomy minnow]

damn I thought it wouldn't help

but it did

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[crimson sedge]

cos θ = √3/2
sin θ = 1/2

How can I find θ?

[green belfry]

Sintheta/costheta
=tantheta

[gaunt hamlet]

Unit circle

[gloomy minnow]

no that doesn't work

[livid hound]

information is lost when you do division like that

[green belfry]

Oh yeh

[crimson sedge]

like when i get this i want to know what is theta

I know here that it is 30° or π/6

[gloomy minnow]

think about which quadrant theta would lie in

[gaunt hamlet]

It's not 30 degrees

[green belfry]

Can u just multiply them together and then by 2

And solve for sin 2thet

A

[crimson sedge]

It's 1/2 i misspelled

[gaunt hamlet]

The easiest way would be to just remember your unit circle. Picture what angle gives a sin of 1/2 and a cos of √3/2

[crimson sedge]

Is there another way like equation or something for this problem?

Something I can do on paper

[eternal comet]

You can draw the unit circle

on paper

the paper being optional

[crimson sedge]

Thank you guys I I appreciate it

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[lapis spindle]

i got theta=pi/6 which isnt allowed so idk what to do

[dense wing]

just find the angle in the 2nd quadrant...?

use unit circle

[lapis spindle]

oh i forgot about the whole quadrant thing srry im not used to pi

like this?

[dense wing]

that angle isn't 5pi/6 as labelled but yes

[lapis spindle]

why isnt it 5pi/6?

[dense wing]

cause 5pi/6 is obtuse

and you clearly labelled an acute angle

[lapis spindle]

the drawing was rlly quick

isnt it pi-pi/6?

[dense wing]

yes

which is from the arm to +x

[leaden snow]

In the 2nd quadrant, sin(x) > 0 and cos(x) < 0. tan(x) = sin(x) / cos(x) < 0. Knowing the unit circle and how trig functions relate to it can narrow down the options immediately

[lapis spindle]

ye ik that from "all students take calculus"

except the part where tan(x)=sin(x) rlly?

oh nvm

didnt see the sin(x)/cos(x)

but ye i know these

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[upper abyss]

Know how to find a maximum value of a curve in general?

https://www.mathsisfun.com/calculus/maxima-minima.html

[lapis spindle]

alr let me see

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[granite island]

hey fellas. i have no idea how to do (-1,1) or (-2,1) cause it comes out undefined

[granite island]

this is the example

if u reply pls ping

cause i will be doing the other pts in the meantime

[leaden snow]

@granite island Substitute each point into your differential equation. That will give you the slope

[granite island]

the problem i'm having though is that -1, 1 is undef

unless i'm substituting wrong?

[leaden snow]

If you look at the limit

[granite island]

oh right

limits

[leaden snow]

$\lim_{(x,y) \to (-1,1)} -\frac{x^2}{y-1} = -\infty$ right?

[wraith dagger]

Navix

[granite island]

oh shit that's how you do latex

uh

let me make sure

yeah

lol im making sure

ur def better at this than i am

but yeah

so it's just straight down?

[leaden snow]

but it depends on if you approach y=1 from below or from above

[granite island]

fuck

[leaden snow]

its either +infinity or -infinity

but that shouldnt change the graph

its should be vertical in either case

[granite island]

either vertical?

ok

and

that would b same

for -2,1 right

[leaden snow]

yea

[granite island]

alr

thanks a lot

oh

shit

this was wrong

[leaden snow]

lemme check

[granite island]

so

4/1

-4

[leaden snow]

at (-1,2)

shouldnt that be going to the right?

[granite island]

isnt it

hold on

1/

[leaden snow]

the pink knob is to the left

[granite island]

1/1 * -1

wouldnt that be -1 *1

[leaden snow]

slope is -1

[granite island]

yeah

OH

[leaden snow]

so 1 unit in the +x-direction

[granite island]

right

[leaden snow]

means 1 down

[granite island]

yeah down

god this is gonna take ages

well

thanks

im gonna wait a moment

before closing

[leaden snow]

haha maybe this is the only error

[granite island]

cause i accidentally exited the tab

and i lost the progress

so i have to keep the pic

[leaden snow]

lol rip

[granite island]

alr

it was right

cool

thanks so much

[leaden snow]

np

[granite island]

.close

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[broken escarp]

I’m on stuck on this question

[dusty hazel]

See

Well your work?

[broken escarp]

I need to Find the length of the segment indicated

[dusty hazel]

Which segment is x?

[broken escarp]

The steps on how to answer the question

[dusty hazel]

The small horizontal one or the vertical one?

[kindred storm]

@broken escarp Do you know about the unit circle?

[broken escarp]

I don’t know I was given this problem

[kindred storm]

@dusty hazel The one it's halfway along.

[dusty hazel]

I still don't follow. Is it the other half of the chord?
Or it's the small portion of the diameter?

[kindred storm]

Is it halfway along the other half of the chord?

[broken escarp]

Uhhh I did use the Pythagorean theorem for three problems then use

[dusty hazel]

Now that's new.

I'm aware.

[kindred storm]

@broken escarp Draw a line from the center of the circle to where the 11 long line hits the circle.

Then, that line will be a radius since it goes from the center to the edge of the circle.

[dusty hazel]

Same, I'll exit too.

[broken escarp]

K

[kindred storm]

So, since the line you just drew goes from the center of the circle to the edge, it's a radius, so it's the same length as the 14.4 length radius.

Does that make sense?

[broken escarp]

K

Yea I understand

[kindred storm]

OK, now you can use the Pythagorean theorem to get the other side of the right triangle you just created.

[broken escarp]

K

[kindred storm]

What do you get for the other side?

[broken escarp]

Wait something like this

[kindred storm]

Yes, but don't call it x, because that letter is already being used for another line segment.

You can call it a or y or something.

[broken escarp]

K

So y= 9.29?

[kindred storm]

Yes, that's right.

Then, the 9.29 and the x together make a radius.

That whole segment with those two segments put together goes from the center to the edge.

So, we know that it's the same length as the other radiuses, so it's 14.4.

Does that make sense?

[broken escarp]

Yea

It makes sense

[kindred storm]

OK, so do you know how to get x from that?

[broken escarp]

No

[kindred storm]

OK, so the length of the radius going rightwards from the center is 9.29 + x, right?

[broken escarp]

Ok

[kindred storm]

So, you can say that 9.29 + x = 14.4, since it's a radius and the other radius is 14.4 long.

Does that make sense?

[broken escarp]

Yea

It makes sense

[kindred storm]

So, what do you get for x?

[broken escarp]

11?

[kindred storm]

Why do you say 11?

[broken escarp]

Wait do I use the Pythagorean theorem?

[kindred storm]

Nope, we did it to get the 9.29.

So, label the bottom of the right triangle 9.29.

[broken escarp]

K

Now what

[kindred storm]

Is your triangle like that?

[broken escarp]

Yea

[kindred storm]

OK, so see the line segment that has the 9.29 part and the x part?

[broken escarp]

Yea

[kindred storm]

If you put those together, you get a line segment that's 9.29 + x long, right?

[broken escarp]

Yea

[kindred storm]

And that bigger line segment goes from the center to the edge of the circle, right?

[broken escarp]

Yes

[kindred storm]

Any line segment that goes from the center to the edge of a circle is a radius of the circle.

So, that line segment will also be 14.4 long because the other radiuses are 14.4 long.

Does that make sense?

[broken escarp]

Yea

[kindred storm]

OK, so we can say that that bigger line segment is 9.29 + x long and also that it's 14.4 long, right?

[broken escarp]

Yea

[kindred storm]

So, since the length of the bigger line segment is both of them, those are equal to each other.

So, 9.29 + x = 14.4.

Do you understand why?

[broken escarp]

Yea I understand

[kindred storm]

OK, so now we have an algebra problem.

9.29 + x = 14.4.

Solve it for x.

What do you get?

[broken escarp]

5.11?

[kindred storm]

Yes, that's right.

[broken escarp]

Thanks

[kindred storm]

You're welcome.

[broken escarp]

.close

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[crimson sedge]

I am slightly confused on how I should be plugging this

[kindred storm]

Well, you can do it this way.

f(g(x))
= f(10ˣ)

Does that step make sense? We're just substitutitng g(x) for what it equals.

[crimson sedge]

yes I had this done

but it went all confusing

[kindred storm]

Oh, how far did you get?

[crimson sedge]

ok so according to the answer I am supposed to somehow plug log10

I am just confused how did this happen

[kindred storm]

Oh, OK, let's go over that.

f(x) = x + x²

Let's use that.

So, if we have f(x), it's easy to see that it's x + x².

What if we have something other than x inside the f, though?

Well, for that, we replaced the x on the left side of the equal sign with something, so we do the replacement on the right side, too.

f(x) = x + x²
f(107x²) = (107x²) + (107x²)²

Do you see how I replaced x on both sides with 107x²?

[crimson sedge]

yes.

[kindred storm]

And a good trick to keep from mistakes is to surround the replacements with parentheses.

[crimson sedge]

noted'

[kindred storm]

So, we have:

f(x) = log₁₀(x)
f(10ˣ) = log₁₀((10ˣ))

I replaced x on both sides with 10ˣ to see what f(10ˣ) would be.

Does that make sense?

[crimson sedge]

yes'

[kindred storm]

So, that's how they got f(g(x)) = log₁₀(10ˣ).

[crimson sedge]

MAKES SENSE

thank you

[kindred storm]

You're welcome.

[crimson sedge]

.close

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[visual nymph]

Cars pass through the automated car wash at the Shell on Carling Avenue at a rate of 6 cars per
hour. The rate at which they pass through the car wash follows a Poisson distribution. You must
define a new random variable as appropriate throughout this question.

[visual nymph]

Assuming that the automated car wash at the gas station is open 18 hours a day, what is the
expected number of cars that pass through the car wash in a given day? What is the standard
deviation for this 18 hour day?

so its possion

so to get the mean would it be 6 x 18=108?

then use the formula

square root of 108, 10.39?

<@&286206848099549185>

and for this question which is part of it

would it be covernt the 6 to minutes 6/60 then x 12= 1.2

would x be 0 since its says x>1

what i did

[cedar kiln]

@visual nymph Has your question been resolved?

[visual nymph]

anyone?

[cedar kiln]

@visual nymph Has your question been resolved?

[visual nymph]

?

[visual nymph]

?

well i got a diff question

After you select 10 candies, you win $50 for each blue candy and lose $30 for each
non-blue candy. Let Y represent the total winnings.

What is the probability that you win at least $200?

still a bit confused on how ud do this small n is 10

Consider a box of 30 candies (5 blue, 10 red and 15 green). A sample of 10 candies is randomly
selected (without replacement) from the box. Let X be the number of blue candies in the sample.

[cedar kiln]

@visual nymph Has your question been resolved?

[visual nymph]

<@&286206848099549185>

[wicked fiber]

well the money earned is

Y = 50 * X - (10-X)*30

now find the distribution of X

and then make a transformation

[visual nymph]

and wed just find x which is 200 right?

[visual nymph]

why is it sub but not adding?

[cedar kiln]

@visual nymph Has your question been resolved?

[cedar kiln]

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[jade latch]

quick question. x divided by x cancels out right?

[jade latch]

wait shit i meant to ask
does 16x - 6x cancel out into 10

[candid vortex]

close, 16x - 6x = 10x; not just 10

[jade latch]

gotcha!

.close

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[visual sundial]

I got this for solving the first inequality which was question 1

I somehow proved that B is a subset of A and not the other way around

I've tried using calculators and graphing and such but just can't figure out how A is a subset of B

[cedar kiln]

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[crimson sedge]

x^4 - 125x2 + 484
decompose by multiplicative factors

[crimson sedge]

<@&286206848099549185>

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[solid quarry]

what angle

do you know vectors

if you know the incident ray direction and the normal of the mirror/plane you can get the reflected ray direction

what information DO you have about the situation?

its best done with vectors tbh

but if you insist to use angles..

no

a vector represents a direction and length

yeah id think so

maybe learn a little bit about vectors before learning the reflection formula

depends what theta is here

but i can show you how to do it with angles

well

basically you can just consider the problem when the mirror is horizontal

you can transform the problem into the same thing by subtracting the angle of the mirror from the incoming ray, solving the problem and then adding the angle back at the end

https://cdn.discordapp.com/attachments/903430334681608232/955375601517232228/KDVhyrVRMyIPRi2FSPAc_ole1.png

hold up fam i think ur jumping to conclusions

what does an angle of 0 represent in ur program

if an object has an angle of 0 what does that mean

ah desmos

can u show me

umm

ok so

this is fucked up

but anyway

i can tell u how to get the reflected slope based on the incident slope

youre getting the angle from slope anyway right?

atan(slope) = angle

[cedar kiln]

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[oblique brook]

I would like help knowing where I should partition these matrices, I can do the calculation parts.

[cedar kiln]

@oblique brook Has your question been resolved?

[oblique brook]

<@&286206848099549185>

[unique bramble]

partition them in blocks of 2x2 and 1x2, 2x2 and 2x1 respectivly

then multiplication rules apply

this is an example

then

same multiplication applies

as normal number

but now with subdevided matrices

@oblique brook

[oblique brook]

can you draw the partition lines on my specific example?

I’ve tried different combinations but I seem to end up with blocks that I can’t multiply

[unique bramble]

well its not possible by the dim ive given

havent noticed the dimentions are different

[oblique brook]

So what should I do

[unique bramble]

this is a way

partitioned in 2

so a valid solution

[oblique brook]

Oh wow didn’t know you could do that

Thanks

[unique bramble]

np

[oblique brook]

It asks for two ways can you think of another one?

[cedar kiln]

@oblique brook Has your question been resolved?

[unique bramble]

try to puzzle a bit yourself too

im sure you will find one

[oblique brook]

Alright thanks for the help

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[crimson sedge]

Can someone please tell me how do you integrate and differentiate a term when there is e to the power of something (like e^xy²)

[cedar kiln]

Please don't occupy multiple help channels.

[dense wing]

chain rule and like usual...?

also depends on how the exponential is actually written, and wrt what vraiable

@crimson sedge

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[zenith python]

Can anyone of you who can solve all of this? don't worry cause I already have my answers to be fair, I just want to make sure if it's all correct or maybe I have a mistake that I don't know thank youuu

[zenith python]

These are my answers pls check it thankss ☺️

1. a.0.4968, b. 0.4656, c. 0.3186, d. 0.4656

2. a.0.4798, b. 0.5011, c. 0.4987, and I dont know the letter d because the z-score is -48.5 I dont know this oneee

Our topic is CLT ( Central Limit Theorem)

[cedar kiln]

@zenith python Has your question been resolved?

[zenith python]

Can anyone??? maybe the letter B and D of number 2 only plsss

[ocean viper]

1a seems wrong

So I would recheck everything

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[vernal pike]

What's the real and imaginary part of these?

a) Re z = 5
Im z = 2

b) Re z = 1
Im z = -1

c) Re z = 3/5
Im z = 2/5

d) Re z = 1/√2
Im z = i/√2

[elfin hemlock]

Yes

[vernal pike]

I'm unsure about d)

[elfin hemlock]

d) is wrong

Is there any term that doesn’t have i in it in d)

If not then Re(z)=0

For im look at coefficient in front of i

[vernal pike]

In d, it's the denominator that doesn't have i in it

So √2

Is that the answer?

[elfin hemlock]

For what?

[vernal pike]

For Re z

[elfin hemlock]

A term is seperated by a + or -

So how many terms are there?

[vernal pike]

One

[elfin hemlock]

Okay so still think Re z is sqrt(2)?

(Does it help if I say i/sqrt(2)=1/sqrt(2) * i?)

[vernal pike]

Yeah

d) Re z = 1/√2

I wrote this, is it wrong?

[elfin hemlock]

Yes

[elfin hemlock]

.

[vernal pike]

(Does it help if I say i/sqrt(2)=1/sqrt(2) * i?)
So which one here is Im(z), and Re(z)?

[livid hound]

recall the definitions of the real and imaginary part of a complex number

[elfin hemlock]

There is a coefficient in front of i

[vernal pike]

Oh true

[elfin hemlock]

Just like in a), b) and c)

[vernal pike]

Re(z) = 0

[elfin hemlock]

You knew how to do those, what is the difference here?

[vernal pike]

Well they're one unit, like you said they're not separated by + or -

Re(z) = 1?

[elfin hemlock]

No

[elfin hemlock]

.

0+1/sqrt(2) * i

Does that help?

[vernal pike]

Yeah

[elfin hemlock]

Its exactly the same as your question

[vernal pike]

Thanks

Makes sense now

Re(z) + Im(z) = a+bi

Right?

[elfin hemlock]

Re(z) is a and Im(z) is b

[vernal pike]

Ok

Thanks

.close

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[vernal pike]

.

[vernal pike]

z_1 = 3+2i

z_2 = 7

z_3 = -5+3i

z_4 = -6i

z_5 = 1+7i

z_6 = -2-2i

Are these correct?

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[void pecan]

Any tips on where to start with this because I have literally no idea what to do

[void pecan]

<@&286206848099549185>

[cedar kiln]

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[crimson sedge]

How can I determine g(x) in tan (x)~g(x) as x approaches pi/2 ?

[crimson sedge]

I tried to write tan as sin/cos

But the cos will give out a 0 at the end

[supple panther]

just to confirm, the problem is the limit as tan(x) approaches pi/2?

[crimson sedge]

Not really

Wait a sec

[supple panther]

What

What class?

[crimson sedge]

hmm I’m French so

let’s say

after graduation

[supple panther]

Ok nvm I cannot help here lmao

[crimson sedge]

Np

[vagrant breach]

have you seen a plot of tan before?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

A plot ?

A graph ?

Yes I have

[elfin hemlock]

What? Are you sure this isn’t limit as x approaches pi/2 of tan(x)?
If not explain what your notation means.

[cedar kiln]

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[woven escarp]

.close

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[trim axle]

this thing keeps saying my answer is wrong but i dont see how it can be

force = spring constant x extension

30 = k x (9.15 - 8.6)

k = 30/(9.15 - 8.6)
k = 54 (2 sf)#

[astral bay]

what's the answer before rounding it to 2 sf?

[eternal comet]

,w 30/(9.15 - 8.6)

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Remavas#3737

[eternal comet]

there you go

[trim axle]

yep

ty

[astral bay]

54.54, rounded to 2 sf

[trim axle]

55

uh

oof i was stuck on that for like 10 mins straight 😅

always the simple stuff that catches me out

ty guys

[eternal comet]

Be sure to round correctly heh

[trim axle]

.close

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[timber vine]

hey can anyone help me with vector calculating ?

[crimson sedge]

just paste teh question

then people will decide

[timber vine]

A balloon starts at point A (2/5/0). It moves in a straight line at constant speed and is in point B(4/8/1). At the launch of the balloon, an air plane is at point C(10/15/1) and flying in a straight line with 90 km/h in the direction vector u = (6 8 0)

• check if the balloon and plane would collide

[crimson sedge]

not enough information

we do not know the speed of the baloon

as the coordinates do not have units

if we had units, it'd be solveable

[timber vine]

I think its just about if they could collide

but tbh our teacher could have also made a mistake there

[crimson sedge]

if we get lucky their trajectories do not cross

but I have a feeling they do

so for now you can check whether they intersect

do you know how to do that?

[timber vine]

I think so

but i`m not sure how to involve the 90 km/h

[crimson sedge]

the question actually asks if they exist at the same time at the same place

not only at the same place

that's why we need balloon speed

that's why it's not enough info

[timber vine]

oh, I see

[crimson sedge]

because question does not specify coordinate units

[timber vine]

yeah, than it´s my teachers fault, thank you

[crimson sedge]

welcome

you can try to solve it for any units : )))

so for speed s

of the balloon

[timber vine]

thankss 🙂

will do

.close

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[sharp patio]

i need help 😦 how do I solve question number 1?

[magic cosmos]

Do i ask for help here?

[sharp patio]

the answers are 2,-1 and -4 but i don't know why

[sharp patio]

i can try to help you if you help me

[magic cosmos]

idk if i can even help

got into high school late

Now i have a test soon

So i am kinda in a bad situation

[sharp patio]

whats the question clow?

[magic cosmos]

not really a question but i was trying too look for people who would teach be Algebra 1

[sharp patio]

if I were you I would google everything or search on youtube then come here when you still dont understand

also download the app "photomath" it shows you how to solve problems

[magic cosmos]

Hmm alright

but

do you know all the contents for Algebra 1?

like the things you learn in ALgebra 1

[sharp patio]

yeah shoot me a message when you need something no problem

[magic cosmos]

alr

[cedar kiln]

@sharp patio Has your question been resolved?

[mighty drift]

,rotate

[wraith dagger]

Couldn't find an attached image in the last 10 messages.

Mar 21, 2022, 9:17 PM

[mighty drift]

also that file is huge

[mighty drift]

What have you done already ?

do you know how to "try" to solve cubics the easy way ?

[dire geode]

RIP data plan

[mighty drift]

15 MB for one image. I've already sent assignments 15 pages long for a third of that

[dire geode]

but that detail when zoomed in tho. how can we solve it if we can't 10x zoom

[cedar kiln]

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[quasi anvil]

https://cdn.discordapp.com/attachments/486844875632017408/955427148536115220/unknown.png

[quasi anvil]

how do i sketch this curve

i get that you convert e^sj to cos(s) + jsin(s) but idk what to do for e*pi

[kindred storm]

eπ is just a constant, you're adding it to -eˢʲ, so the graph moves over eπ to the right.

So, the center of the circle is at (eπ, 0).

[quasi anvil]

so its at 8.54,0

[kindred storm]

,calc e * pi

[wraith dagger]

Result:

8.5397342226736

[kindred storm]

Yes, about there.

[quasi anvil]

do i just do something like this

where for -pi its at 9.54,0

[kindred storm]

Yeah, it'll be a 3/4 circle.

Radius 1.

From angle -π (straight left) counterclockwise to angle π/2 (straight up).

[quasi anvil]

and the arrow will be pointing clockwise?

[kindred storm]

Oh, wait.

It's -eˢʲ.

So, the y values are flipped in sign.

So, it'll start at straight left and go clockwise to straight down.

So, the arrow will be at the straight down end.

Pointing clockwise.

Your working needs a bit of correction.

No, maybe I'm wrong.

Let's see.

Yeah, it flips both vertically and horizontally since the real and imaginary parts are negated.

So, your working looks good.

[quasi anvil]

im a bit confused about the -pi so it starts left x axis

?

[kindred storm]

Well, usually, it's pointing leftward.

But you have a - in front of the e.

So, it flips up for down and left for right.

So, it's pointing rightward, like how you got eπ + 1.

Which is directly to the right of the center.

Then you get eπ + j, so it's up from the center.

Then you get eπ - 1, so it's directly left of center.

Then you get eπ - j, so it's directly down from center.

And you've been moving counterclockwise the whole time as you draw a circle through those points in order.

So, the arrow should point counterclockwise.

So, your work was good and the arrow(s) should point counterclockwise along the circle.

[quasi anvil]

ah ok

i think i get it now

ty

[kindred storm]

No problem.

[quasi anvil]

.close

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[crimson sedge]

how u do this

question e

[brazen basin]

in part a you already have an equation that represents the volume of the box.

set that equal to 5500

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

then what

i dont get it

[brazen basin]

solve for x

[crimson sedge]

yeah but idk how to do that

do i have to expand the eqation

[brazen basin]

you know how to FOIL?

[crimson sedge]

yeahb

[brazen basin]

(60-2x)(40-2x) can be FOILed

[crimson sedge]

yeah ik

[brazen basin]

then multiply x into it.

[crimson sedge]

where does the 5500 go

[brazen basin]

$x(60-2x)(40-2x)=5500$

[wraith dagger]

42

[crimson sedge]

yeah i get that

what do i do after that tho

[brazen basin]

have you foiled the two factors?

[crimson sedge]

yes

i got

4x^2-200x+2400

[brazen basin]

ok I admit, this is kinda of messy, do you know the cubic equation?

[crimson sedge]

no

i think i got it

nvm

i didnt get that asnwer

if you know how to do it can you just do teh question and explain it

[zenith python]

Hey hello!! sorry for the late reply so you told me that 1 a. is wrong um can you tell me why pls thanks r

[crimson sedge]

wtf is going on

.close

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[last hedge]

If I am averaging the same sample set of data for two different averages, let's call them Average-Overall and Average-Bigger for simplicity sake. Let's also say that the sample pool being averaged has exactly 200 individual numbers being tallied. Average-Overall is the total average of every one of the 200 numbers, while Average-Bigger is the average of every value over 3.

Because of this specificity, Average-Bigger has a much smaller sample size within the original pool. Let's say there are example 40 cases of values being over 3.

Is it then possible for Average-Bigger's final value to be smaller than Average-Overall's final value?

On one hand, Average-Bigger is only tallying the larger of the same numbers within Average-Overall, but on the other hand smaller numbers weigh heavier on the final average because of the smaller sample size. I've tried giving myself test cases, but my failure to prove such simply feels like I'm not creative enough to envision the proof case rather than it not being possible.

[last hedge]

For what it is or isn't worth, I'm trying to figure out if the smaller Average-Bigger means I'm doing everything incorrectly or if that is simply the natural correct answer. I am happy for any aid in figuring this out.

[dire geode]

What in the. Do you have any math in there?

[last hedge]

I mean...yeah. Averaging data is math. But on a large enough scale theory helps more than specific problems.

[dire geode]

Do you know the formula for average

[last hedge]

Like. I could type out a really, really, really long (a1+a2+a3...an)/n but learning the theory was what i was aiming for.

[dire geode]

What are you aiming for if not the average

[brazen basin]

Pretty sure worse case, Average-Bigger = Average-Overall.

[last hedge]

Some kind of confirmation that if Average-Bigger > Average-Overall, then that i means that there is definitely a math error.

Or at least theory breadcrumbs to help arrive to that conclusion. Im not looking for spoonfed answers by any means.

[brazen basin]

I think you mean Average-Bigger < Average-Overall

[dire geode]

If your data is arbitrary, I don't think you can conclude anything

[last hedge]

Yeah i did, sorry

[dire geode]

Start with assumptions and samples from distributions

[last hedge]

I am asking if its possible. If this is true, then that means it is possible for Bigger to be less than overall?

[brazen basin]

If all numbers are under 3......

[last hedge]

In my example id stated that there were at least 40 numbers within the Bigger subset.

[brazen basin]

my bad

[dire geode]

Yes it is because you haven't made any assumptions about the numbers

[last hedge]

I made the assumption that at least 40 of the 200 were greater than 3. My question was whether any further assumption could be created in which "Bigger < Overall" is true.

[brazen basin]

Assuming we are talking about real numbers, Average-Bigger >= Average-Overall. Since chopping off the number line at x = 3 is always going to push the average up.

[last hedge]

Yes, im sorry. Real numbers.

[last hedge]

Even though the smaller sample size will make small numbers weigh more?

To the Average-Bigger total.

[brazen basin]

I like to imagine a stick. Would chopping the left end of the stick always move the center of mass right?

Physical intuition says yes, even though I don't have the skills to make a formal proof.

[last hedge]

Thats a good analogy. Ive been unable to find a formal proof either. Honestly not even sure the first place to start looking.

I feel like a stick isn't necessarily weighted the same way a large data set can be though. But if this is as much as you guys know, i can close this and look elsewhere.

.close

[cedar kiln]

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[cedar kiln]

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[lunar lily]

I don't understand integral of impulse function from first step to second step

[obsidian aurora]

You integrate over a delta function.

so once you integrate the exp-function times delta(t) and the other time you integrate you exp-function over delta(t-1). Remember: how is a delta function defined?

its delta(0)=1, else its 0. Therefore if you integrate something, which is multiplied by a delta function ( f(x)*delta(t) ), you just have to plug the value into f(x) where the input of the delta function is zero

so for your first integral delta(t)=1 for t = 0, so you plug in your exp function t=0.

which makes it to one, same for the second integral d(t-1) = 1 if t = 1, so you plug t=1 in your exp function

now multiply both with 1/2 and you recive this result

hope this helps

[cedar kiln]

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[prime lily]

Let there be triangle ABC inscribed within circle O

AD is the angle bisector of BAC

construct diameter DE

point F is the intersection between AC and the circle that circumscribes AMB

BM, CM is the angle bisector of ABC and ACB respectively

prove that EF is perpendicular to AC

[cedar kiln]

@prime lily Has your question been resolved?

[cedar kiln]

@prime lily Has your question been resolved?

[prime lily]

<@&286206848099549185>

got any ideas?

[cedar kiln]

@prime lily Has your question been resolved?

[cedar kiln]

@prime lily Has your question been resolved?

[prime lily]

nvm

[crimson sedge]

do u know what this means?

like what is the circle that circumscribes AMB?

[crimson sedge]

u should mark this

like first draw it on paper

and mark the conditions

it will be more clear to u

[prime lily]

the circumcircle of triangle AMB

[crimson sedge]

ok, what is a circumcircle?

[prime lily]

these are

[crimson sedge]

i mean, what is the definition of a circumcircle?

[prime lily]

a circle that passes through all the vertices of the polygon

[prime lily]

<@&286206848099549185>

please end my suffering

EFB isnt collinear btw

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[bold pond]

looking for help with B

[bold pond]

I am having a really hard time understanding this unit

[hard violet]

MB

[bold pond]

ay bro wtf

[hard violet]

wrong pic

here

we go

[trim sentinel]

@hard violet please go to channel thats not occupied

#❓how-to-get-help

[hard violet]

ok

[trim sentinel]

Idk why they ask to explain why the lines are parallel

I mean its just same slope different y intercept

[bold pond]

i think its just meant for us to understand and explain it

[eternal comet]

They want you to use the normal vectors

which is a little bit silly but hey, whatever

[bold pond]

yea the answer was something like since the lines are collinear, the perpendicular vectors will also be collinear and as such, the lines are parrarel

but I am looking for help with B

[eternal comet]

oh

we've already shown they are parallel

so if one of their points match

(you can probably take it from here)

[bold pond]

sorry but I dont really have a strong understand of this topic and I guess instead of asking for the answer, could you explain why in the solution page it says to insert (1,2) as the x and y saying its a common point in the first line

[eternal comet]

So, the two lines are parrallel, right

They have the same slope

[bold pond]

yes

[eternal comet]

So if we choose k so that they both have a common point

it follows that they will be coincident

[bold pond]

ok so that makes sense but where does the (1,2) come from. where was that derived from the equations given

[eternal comet]

seems like they just took x=1

computed y from the first equation

[bold pond]

is there a reason behind why they chose 1

[eternal comet]

not really

,w solve 2x - 3y + 6 = 0 when x = 100

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Remavas#3737

[eternal comet]

you could use that instead

[bold pond]

alright, thanks for explaining it

.close

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[drifting anchor]

Shouldnt it be 1/√2

[glossy mist]

No

[glossy mist]

How did you get that?

[drifting anchor]

okay so

the derivative I got is (-2x^2 + 1)/√(1-x^2)

sry

if we equate that to 0 we get

-2x^2 +1 = 0

which is ultimately x = 1/√2

right?\

[glossy mist]

Yes

[drifting anchor]

So it is 1/√2 right?

[glossy mist]

x is

You need to sub that back into the f(x)

To get the maximum y value

[drifting anchor]

nvm it says absolute max value......

sorry

Thanks

[glossy mist]

No worries, you did it all right

Got the same as my derivative 👍

[drifting anchor]

oh and

one more problem

shouldnt this be x = 0.36

cuz e^-1 is 0.36

What I got basically

[glossy mist]

Let me take a look

quickly googling this theorem

[drifting anchor]

oh wait let me send it

[eternal comet]

Let me guess, non-native english speaker huh

who learnt math in their native tongue

[glossy mist]

Nope, just not covered in A-Level Further Maths (or at least the modules I did)

Natively British!

[drifting anchor]

i meant this one

[glossy mist]

I think you have forgotten e^0 = 1?

Looking at your working briefly

[drifting anchor]

wow

yeah thanks

[glossy mist]

haha np

[drifting anchor]

but

even if i do that

thats -0.63

[glossy mist]

I got 0.46

What did you differentiate it to

[drifting anchor]

okay yeah i see the problem

thanks

how do i close this now?

[glossy mist]

no idea

i think ,close? lol

[drifting anchor]

,close

.close

[cedar kiln]

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[potent sluice]

Im very confused on this problem and would love if someone could help walk me through it and explain it to me.

[glossy mist]

The length to the midpoint is half the length to the end

Therefore

3x-2 = 0.5(5x+3)

[potent sluice]

awsome

thank you

[glossy mist]

No problem

[potent sluice]

.close

[cedar kiln]

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[tender scaffold]

human digestive system any one know?

[tender scaffold]

dm me

[dense wing]

#old-network has the biology server

[tender scaffold]

ty u

.close

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[potent sluice]

Im confused on this problem and would love for someone to help walk me through it

[glossy mist]

I think you're missing information required from the previous question