help-19

[little cedar]

yipppe

[robust wyvern]

so what does it become?

the inequality

[little cedar]

hmmmmmmmmmmm

do not know

[robust wyvern]

what i meant is what will it look like if u applied the rule

since u said its the first rule

[little cedar]

2+4u>3.2?

[robust wyvern]

Rule states x > a or x < -a

u forgot the second inequality

[little cedar]

oh

2+4u<-3.2

[robust wyvern]

its 2 - 4u btw

u mistyped it

[little cedar]

oh yea

[robust wyvern]

so now u have two inequalities 2 - 4u > 3.2 or 2 - 4u < -3.2

simply enough, solve for u in both inequalities

[little cedar]

okay thank you

oh yea lastly can you please tell me about the pfp

[robust wyvern]

uh

[little cedar]

oh damn

[robust wyvern]

anywho

[little cedar]

REAL

[robust wyvern]

js

e

u know how to find u in both inequalities yes?

[little cedar]

YES

[robust wyvern]

alr

i guess i go

[little cedar]

yes sir

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[pearl trail]

Complex numbers

Given the complex number z (see image), calculate the value of a so that z's module is equal to 1.

I've been stuck at this for longer than I should, and I think it's -2±2i but for some reason the module isn't 1 in that case :/

I learnt about complex numbers really recently so I'm struggling with it 😭😭😭

[odd edge]

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

[pearl trail]

It's in Spanish so sorry about that 😅 But the thing is, I keep revising it again and again and I still can't see where I made a mistake? But I obviously did since 1+2i's module isn't 1

[weary pelican]

where does this come from?

[pearl trail]

Cuz it's the module of the complex number

So sqrt of the real part squared plus the imaginary part squared

[weary pelican]

ok and what are the real/imaginary parts you found

[pearl trail]

ah yeah I did that apart

[weary pelican]

like what's your final z = ... + ...i

[pearl trail]

(-1-2a)/5 + ((a+8)/5)i

[weary pelican]

so if a = i for example, does that check out?

meaning did you do your job of separating real and imaginary

[pearl trail]

but why would a equal i

[weary pelican]

why not?

[pearl trail]

well one sec I'll check if it works

[weary pelican]

no but like

what I was getting at

[weary pelican]

did you really entirely do your job of separating real and imaginary parts here

if a is allowed to be any complex

[pearl trail]

OH

ok yeah that makes sense

so the real part can't have i

so ig a just doesn't have a solution then?

[weary pelican]

well it has an infinite amount of complex solutions

it's not by giving up that you'll get them

but I think the way you're getting at it is not the best way

i suggest manipulating "|z| = 1"

into something easier at least

[pearl trail]

how

[pearl trail]

I don't really get what you mean by this sorry

[weary pelican]

well first of all

i would just reduce the problem to

|3 + (a+2)i| = sqrt(5)

[pearl trail]

alright

[weary pelican]

see how that happened

[pearl trail]

yeah

ok I think I got it

thanks!

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[hybrid heart]

Did I do algebra correctly where I indicated with arrow?

[hybrid heart]

Just trying to see if -f(x) = f(-x) to see if it’s odd polynomial

[odd edge]

@hybrid heart Has your question been resolved?

[fringe bough]

Yes, factoring out the -1 like that does work, but only because (-1)^3 = -1

@hybrid heart

Like, if you had factored a 2 out of the parentheses, it would actually be 2^3, so 8

But (-1)^3 is still just -1 so it's good 👍

[hybrid heart]

Oh ok in that case I should write (-1)^3 there then

like 0.5(-1)^3 (x-3)^3 - 6 right

[fringe bough]

that would be more thorough, yeah

[hybrid heart]

ok thank you

[fringe bough]

np 👍

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[drifting pine]

Can someone verify my answers and help me with the rest, i just want to make sure I’m doing this correctly

[olive needle]

In f, where did the 7 come from? 🤔

[drifting pine]

7?

Oh

Those are y’s

[olive needle]

I just realized that. 😄

h doesn't look correct.

m doesn't look correct either.

d on page 2 is incorrect.

[drifting pine]

What did i do wrong on h

Oh, i wrote 2 inside the sqrt instead of “a”

Oh, and the 5 isn’t negative

[drifting pine]

Shoot, the a is ^2

Also, how do i do m

[drifting pine]

Oh, so sqrt(13i * 26i)

[olive needle]

-13 * -26 = 13 * 26

[drifting pine]

What about the fact that it’s a negative sqrt

Is it because you have to multiply with the signs first?

[olive needle]

It would be preferable, but is not neccesarily the only solution method.

[drifting pine]

Ok

So I’m looking for the sqrt of 438

How would I do that since it’s not a perfect sqrt

[drifting pine]

Oh i see what I did wrong

So 13 sqrt(2)

What about d on page 2

Aren’t i only supposed to get rid of the sqrt on the bottom?

So i would multiply if by sqrt(2)

Top and bottom

[olive needle]

To remove the root in the denominator, you multiply by the conjugate.

[drifting pine]

Oh

I forgot about that

And the bottom would end up being 25 * 2

Or + 2

Or - 2

It’s - 2

So it would be 20/23 - 4 sqrt(2)/23

[drifting pine]

So k on page 1 is just sqrt(3y) * sqrt(15y)?

[olive needle]

It can be simplified.

[drifting pine]

Why not sqrt(3 * y * 3 * 5 * y)

[olive needle]

You can combine them.

[drifting pine]

Wdym?

[olive needle]

You can combine them in the way that you wrote it.

[drifting pine]

Ah

[olive needle]

The idea on this server is to not give you the complete answer, but just enough hints so that you are able to figure out the answer on your own. 😉

[drifting pine]

So 3y sqrt(5) is the answer

Ik

[olive needle]

Yes.

[drifting pine]

Ima try n on page 1 and put my answer here

Is it 3x?

Since it can be rewritten as cuberoot(9 * x * 3 * x * x)?

And that would just be cuberoot(27x^3) = 3x

[olive needle]

Yes.

[drifting pine]

Epic

For a on page 2, would I just multiply the 5 sqrt(x) and the -sqrt(2) by sqrt(2x)?

[olive needle]

Yes. Distribution Property.

[drifting pine]

So that would end up as
5 sqrt(2x^2) -sqrt(4x)?

[odd edge]

@drifting pine Has your question been resolved?

[olive needle]

Yes, which you can simplify even further.

[drifting pine]

Epic

So
5x sqrt(2) -2 sqrt(x)?

[olive needle]

Yes.

[drifting pine]

Epic

[drifting pine]

For e on page two, can i just Cube root the entire thing?

Cause idk any other way for solving it

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[cosmic sentinel]

hey

[cosmic sentinel]

can anyone help me out

help pls

[pearl cargo]

,rcw

[pearl cargo]

!status

[odd edge]

What step are you on?
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[pearl cargo]

it looks good to me

it's easy to verify that 5 : x - 2 equals 2x + 5 : 40 using the value you found for x

[odd edge]

@cosmic sentinel Has your question been resolved?

[cosmic sentinel]

ok

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@cosmic sentinel Has your question been resolved?

[cosmic sentinel]

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[hoary marsh]

Hello

[hoary marsh]

What are differential equations?

[quasi sparrow]

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

[hoary marsh]

Are they different from normal differentiation of functions?

Is ordinary differential equations above calc 3?

[quasi sparrow]

Yes

[hoary marsh]

What about the differentiation we learn in calc 1, 2, 3

Are they not differential equations?

Am so confused

[quasi sparrow]

.

[hoary marsh]

I still don't understand

"In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.[1]"

So I assume implicit differentiation is also a part of DE?

[quasi sparrow]

Yes unknown function

[hoary marsh]

Are Lagrange Multipliers also a part of DE?

Jacobian Transformation?

[forest sky]

a differential equation says "this is a relationship between a funcion and its derivatives, solve for the function" for example [ \odv yx - 3 y = e^{3x} ]

[clever fjord]

cloud

[quasi sparrow]

"a part of" is silly

And pointless really

[hoary marsh]

Implicit differentiation?

[mental storm]

if youre asking whether it's included in a curriculum on DEs likely no to both

[hoary marsh]

I know LM and JT are included in calc 3

But like

[mental lotus]

differential equations are related to differentiation the same way polynomials relate to equations of lines

[hoary marsh]

I thought we learned about differentials in calc 1, 2, 3

[mental storm]

DEs is more about solving for unk functions involving derivatives

in a nutshell

its not just computation

[hoary marsh]

Ohhhh I see

[forest sky]

you learned how to take the derivatives of known functions in calculus, differential equations says "given a function has this relationship with its derivative, find the unknown function" which still uses derivatives but in a different way

[hoary marsh]

What are we learning in calc 1 then?

Just differentiation?

[mental storm]

differentiation rules i expect

[hoary marsh]

I guess differentiation ≠ differential?

[mental storm]

differential is just the adjective i suppose...

oh wait @hoary marsh do u go to uw?

[hoary marsh]

Yes

Are you Canadian

[mental storm]

cool me too

[hoary marsh]

No way

Which program

[mental storm]

ece

[hoary marsh]

?

Are you '26 or below?

[mental storm]

i'm '27

[hoary marsh]

You're not in the '27 dc

But that's cool

[mental storm]

are you newer than 27

[hoary marsh]

You should be in 2b ig

Yeah

[mental storm]

i'm assuming you havent taken 205 yet

[hoary marsh]

Am taking it rn

[mental storm]

oh lmao good luck then

[hoary marsh]

😭

Thanks everyone though

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[blazing quiver]

Yo

[blazing quiver]

Idk how to divide if there's another algebra

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@blazing quiver Has your question been resolved?

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[willow oak]

I'm kind of stuck now... the teacher doesn't care for the right answer just a good reasonable estimate and how we got it. I hope im on the right track but like now im kind of stuck moving forward. could someone help me explain what i need to be thinking about

[exotic oar]

52 weeks / year * 12.5 gallons / week * 82.63% drivers * 78.66% people * population of USA

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[willow oak]

ouu okay okay ! thank you

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[exotic oar]

that was just questions 5 you still need 6 and 7

[odd edge]

Please don't occupy multiple help channels.

[vernal yacht]

Forget it, they don’t seem stuck.

[willow oak]

I'm actually stuck on number 6 ! (ToT)

i think we need to convert it into something but i don't exactly know how

[exotic oar]

so the answer from #5 is gallons/year

gallons / year multiplied by pounds / gallon will give us pounds / year

the answer from #5 (gallons / year) multiplied x * by 6.073 pounds/gallon

[willow oak]

Do we need to account for the “20 pounds of co2” anywhere in the equation?

[exotic oar]

yes

so you have pounds / gallon multiplied by gallon / 20 pounds of CO2

[willow oak]

Ohhhhh!!! Okay okay thank you now!! Sorry it took me awhile to respond, I was trying to write it down and eliminate the units ! Let me just finish calculating everything and then taking a look at the last question and see if I can work it out before seeing if I need some help on it! Thank you

[odd edge]

@exotic oar Has your question been resolved?

[exotic oar]

You're welcome

[odd edge]

@exotic oar Has your question been resolved?

[odd edge]

@exotic oar Has your question been resolved?

[cursive field]

@exotic oar please don't occupy two channels

may i close this one?

...?

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[kind mica]

When it says find exact values it’s asking for it in degrees?

[kind mica]

For example the first would be sin45?

[viscid flint]

π/4 is the same thing as 45º

they're asking for sin(π/4)

[golden marten]

I'm assuming it wants you to calculate the exact value

[viscid flint]

which is the same thing as sin(45º)

here is a unit circle diagram

,tex .unit circle

[clever fjord]

hayley is not layla

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[thorny prism]

Can some1 explain how on earth id do this

[limpid root]

First, find "p" and "q" with a system of equations. Then, you need to find the maximum of the function using the derivative

[thorny prism]

Ima need this to be dimmed down a lil bit

Please

[limpid root]

To find p and q:
When x = 0, the height of the ball "h" is 25 m.
When x = 60, the height is 0 because it's "in the ground"

[thorny prism]

Okay gimme a mo

So like that?

But what next

[mystic saffron]

have you learnt differentiation? @thorny prism

[onyx cloak]

you dont really need to use differentiation

find the x coordinate of the vertex of that parabola

thats the top point of the tracjectory of that particle

[odd edge]

@thorny prism Has your question been resolved?

[thorny prism]

Thats the one u use to go from acceleration to velocity right

[mystic saffron]

Er nvm.

You can find the point of symmetry of the parabola where it is the maximum / minimum point.

[thorny prism]

Is that right?

[mystic saffron]

well thats what i got for the x axis.

But should be right if u used the correct values.

[thorny prism]

Im pretty sure i did

[mystic saffron]

Remember to write the correct equations, 0.783x-0.02 x2 + 25.

[mystic saffron]

shld be right

[thorny prism]

Perf thanks guys

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[chrome elbow]

previously i asked which method to use for integrating this and it was through partial fraction decomposition.
I want to know can i just sub in any value of X to obtain my respective A B and C?

[cursive field]

yes

[chrome elbow]

oohhh icc ic
so my A(x+2)(x+3) + B(x+1)(x+3) + C(x+1)(x+2)
i just gotta sub
x = -1 to find A
x = -2 to find B
x = -3 to find C
am i getting the right idea here?

[cursive field]

yes

absolutely

[chrome elbow]

ah thank you for the clarification!

[cursive field]

nw

[chrome elbow]

.close

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[chrome elbow]

why does the 2nd cos become 0 after being integrated?

[cursive field]

what do you mean

[signal yacht]

become 0?

[chrome elbow]

i was looking at the past working and it just leads to 0, i might be getting the wrong thing here

[cursive field]

wrong

not 0 otherwise

[chrome elbow]

ooh

[cursive field]

sorry mb

i meant it's 2 cos x if x is b/w -0.5pi and 0.5pi

misread that so badly

[chrome elbow]

what is b/w

[cursive field]

between

[chrome elbow]

ah

Aaahhh i got it now, thanks thanks!

[cursive field]

np

[chrome elbow]

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[woeful rivet]

what do nature mean?

[nimble blaze]

type

[woeful rivet]

um

what are the types

[nimble blaze]

e.g local min, max, inflection

[woeful rivet]

what is inflectionm

[nimble blaze]

location where concavity changes

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@woeful rivet Has your question been resolved?

[woeful rivet]

oh

how do we find nature

[nimble blaze]

second derivative test,
considering whether slope changes sign around the specified location

didn't you get notes on this?

[woeful rivet]

no

[nimble blaze]

try looking up a vid/notes on
determining nature of stationary points

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[elder wasp]

The sum that I derived is not defined for any k less than 2

But if I skip case when k = 1 I get the correct answer

What do you do when you have a sum where one index is not allowed like in my case?

ths one

Can I just rewrite the denominator of the binomial to (n-k) = ((n-2)-(k-2)) and then change the sum index to start from k = 2 to n - 2?

[quasi sparrow]

Yup

Anything with negative index should be zero because the derivative of the terms multiplying x^(k-2) aren't actually there for k<2 because the derivative of a constant is zero

[elder wasp]

I'm sorry, but what do you mean by the derivative?

I'm just thinking that the factorial of negative numbers is not defined

[quasi sparrow]

Oh. I thought you differentiated earlier to get the first line

In the first line k=0 and k=1 term are both zero

So the sum should have started from k=2 from the beginning

[elder wasp]

This is what the textbook provided , the task was to verify that the first term becomes np^2(n-1)

Yeah you're right lol, I kept mixing the starting indexes

k = 1 makes the first sum 0

so all valid cases are from k = 2

Thank you bnuuy ❤️

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[cursive field]

no

because it's not correct lol

what...?

what is that logic

evaluate it at, say, -1, and 0

-2/e + 1

which is (e-2)/e

clearly more than the 0 at 0

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[tired gyro]

For what values of b do the following quadratic trinomials become perfect squares?
(6b-5)x^2 - 5(b-1)x + 2b -6

[tired gyro]

We know that for a perfect square we need D = 0

<@&286206848099549185>

after opening the ( ) I get
6bx^2 - 5x^2 - 5bx + 5x + 2b - 6
D = (-5b+5x)^2 - 4((6b-5)(2b-6)) =
= 25b^2 + 50b - 48 + 144 + 40b - 120 =
= 25b^2 + 90b - 24

[hoary pasture]

1

[limber glade]

you ain't supposed to give out direct answers

guide them to answers

[tired gyro]

the answer is -1 or 37/48

@hoary pasture

[mint mirage]

I think you messed up some algebra somewhere

[tired gyro]

Will try once more

[mint mirage]

So let's start with expanding (-5b+5)^2

What do you get?

[tired gyro]

25b^2 + 50b + 25

[mint mirage]

Not quite

That middle term is wrong

[tired gyro]

ah

-50b

[mint mirage]

Yes so (-5b+5)^2 = 25b^2 - 50b + 25

[tired gyro]

yup I'll go from there

[mint mirage]

Now expand (6b-5)(2b-6)

[tired gyro]

12b^2 - 36b -10b + 30

12b^2 - 46b + 30

[mint mirage]

Now multiply it by -4

[tired gyro]

-48b^2 + 184b - 120

-23b^2 + 134b - 95

[mint mirage]

Yes that looks better

[tired gyro]

23b^2 - 134b + 95 = 0
D = 17956 - 8740 = rt8740
x1 = ( 134 + rt8740 ) / 46
x2 = ( 134 - rt8740 ) / 46

[mint mirage]

You messed up here
17956 - 8740

[tired gyro]

my fault

D = rt9216

x1 = 134 + 96 / 46 = 230 / 46 = 5
x2 = 134 - 96 ) / 46 = 38/46

[mint mirage]

I'm pretty sure 38/46 can be simplified

[tired gyro]

19/23

[mint mirage]

Yeah looks right

[tired gyro]

but our answers are either b = -1 or b= 37/48

[mint mirage]

Then you might have typed the problem wrong

,w (-5b+5)^2 - 4((6b-5)(2b-6)) = 0

[clever fjord]

Results provided by WolframAlpha

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

Requested by captainnova22

[tired gyro]

Most likely the book answers are wrong then

cuz that's happened before

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[brazen raptor]

How do you evaluate?

[odd edge]

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

[brazen raptor]

1

[dense moth]

Use l hopitals bro

[low locust]

no

[dense moth]

Yeah it can be done by basic formula but why not?

[low locust]

because this limit itself is whats needed to be able to use lh in the first place

[nimble blaze]

If you're going to involve derivatives, apply the definition of the derivative

(the work ends up being essentially more or less the same)

[low locust]

if you dont wanna do that, write x as e+h

[brazen raptor]

ok

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[velvet badger]

By definition only a square matrix can (possibly) be invertible right?

[fluid tundra]

that is correct

[frail silo]

Guys

I have a question that i thinking it every day

Normally, most people have asked this question, but I'm just wondering what the answer is.

[velvet badger]

.close

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[frail silo]

Ok i see no one want it

[tacit wasp]

.reopen

[odd edge]

✅

[tacit wasp]

Now you can

[fossil hawk]

Go ahead

[nimble blaze]

should claim a new channel if asking.
if the names don't match the owner of the channel, people are less inclined to help/answer.

.close

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[young galleon]

just here to check if my answers are correct

a) i got 2

b) y=2x−2

c) x≈1

[wanton bison]

for both?

[nimble blaze]

a) is asking for two values,
which one is 2 for?

[spark cargo]

How’s f(2) = 2?

[young galleon]

oh ok wait no

.close

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[tame star]

Hi! I'm taking a course on statistics and it's very beginner stuff but I'm a bit confused about the question wording and how to tackle it. So far, I've answered these 4 questions and I'm stuck on the last two.

I am asked the two following questions:

When you do a z transformation, you are taking a normal (or approximately normal) distribution of your random variable, X, and recentering it (over a mean of 0) and restretching it (to a variance of 1).

This is achieved by taking every possible value of X and subtracting the mean of X and dividing by the standard deviation of X. These new values now make up the z distribution.

How many z distributions are there?

---

Draw the z distribution and identify the point that corresponds to X=86.0 in the distribution of random variable X, chipmunk weight.

Label all the other components of the z distribution that correspond to the elements you labeled on the distribution of random variable X, chipmunk weight, for question 4 (the picture with the graph).

[odd edge]

@tame star Has your question been resolved?

[odd edge]

@tame star Has your question been resolved?

[hollow quarry]

It's a little unclear to be honest. For the first question, I think it's asking whether z transformations are unique. For example, if you have two different normally distributed random variables and you perform a z transformation on both, would their resulting z distributions differ?
For that question, my hint would be: what are the properties of the resulting distribution(i.e. after z transformation)

[tame star]

I find the question unclear as well. I have always thought there is only one Z distribution. So would I just explain why there will only be one Z distribution for the first question?

[hollow quarry]

I assume so

And yeah, there's only one Z distribution

[tame star]

Okk thanks! and for the second question do I just find the Z score for when X = 86 while the mean is 85? and explain the different components such as Z score, mu, sigma??

[hollow quarry]

You're welcome!

Yeah, that's all you need to do

[tame star]

Thank you so much, I really appreciate your help :)))

[hollow quarry]

It's no problem

[odd edge]

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[glacial pollen]

https://www.youtube.com/watch?v=3yE0TPQZeKY

I dont really understand the operations used.

also

2(x+3) is the same as (x+3)^2?

[wanton bison]

(2+3)^2 doesn't even have x

[glacial pollen]

read it again

[wanton bison]

also no

wrong

what they did is factorize (x+3) the common term

and then

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

[clever fjord]

bacc

[vernal yacht]

Obviously not

[glacial pollen]

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[pastel orbit]

how can I show that if $n \neq 4k$ and $n \neq 4k + 1$ for some $k \in \Z$, then ${n \choose 2}$ is odd?

[clever fjord]

higher!

[pastel orbit]

I feel like this shouldn't be that hard, but I've been stuck on how to even start proving this for a while now

perhaps the contrapositive is easier?

hm, let me see what I can do with that idea

[dawn scarab]

nC2 is n!/[2(n-2)!] right? Maybe you can simplify stuff and make out the definition of an odd number in there? I assume you‘ve already tried that

[pastel orbit]

yeah, nC2 gets us n(n - 1)/2 = 2k for some k

and then we have n^2 - n - 4k = 0

hmm

where's this headed

[dawn scarab]

Wait, you did nC2 = 2k+1 for some k and went to this?

[pastel orbit]

oh hold on

[dawn scarab]

I‘ll let you cook

[torn notch]

hello

[amber schooner]

if n≠4k or 4k+1 then it must be 4k+2 or 4k+3

you can just rewrite (n)(n-1)/2

using those two

and then manipulate it to be of the form 2k+1

[dawn scarab]

Ah that‘s smart

[odd edge]

@pastel orbit Has your question been resolved?

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[fast ivy]

can someone give me some tricky question for identifying sig figs
i want to make sure i got this down good

[fast ivy]

thnx

like hold up

0.0305

for this

how is it not 4 sigs?

becuz they said a 0 after a decimal point is sig

so it would be 0.0305?

nonzero is sig and interior 0 is sig and 0 after a dec point

so 4

[upper coral]

Only for cases like 0.00 (2 significant figures)
0.0305 is insignificant because it's a leading zero

[fast ivy]

ohh

ok perfect

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[tidal marsh]

My work:

The scratched out numbers on the left are 3 and -100 in numerator (I rewrote the - in front of 7), and 100 and 3 in denominator

I'm not sure where I went wrong

[orchid torrent]

It already says “decreasing” in the question

So it’s just 7/400

[tidal marsh]

O nah I'm actually blind 💀

Tysm

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[verbal schooner]

So in the last bit I was doing the sign would switch in the denominator right? -5/-inf = +? So it’s + 5/0?

[amber schooner]

what is this??

[verbal schooner]

Um differential calculus

[amber schooner]

i’m aware

lol

your work

[verbal schooner]

It’s my work

[amber schooner]

incorrect btw

no calculus in sight

you’re in a calculus class

[verbal schooner]

So was that right or incorrect

[amber schooner]

this isn’t calculus though

[amber schooner]

horribly incorrect

[verbal schooner]

Okay so I leave the negative?

[amber schooner]

what

[amber schooner]

oh god

where do we even begin

[verbal schooner]

Ima just ask somewhere else

[verbal schooner]

.close

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[remote cloud]

Why are these linearly dependednt?

[remote cloud]

Or more importantly, why are they not independent

[wanton bison]

[1,0] + [0,1] = ?

[remote cloud]

I thought if you had more vars than equations they are independent

[remote cloud]

So if you can add them its dependednt?

[forest sky]

any 3 vectors in R^2 must be linearly dependent

[remote cloud]

ah

[wanton bison]

[1,1] can be written as a linear combination of [1,0] and [0,1]

so it is not independent

[remote cloud]

anyone have a good resource of this? Im trying to learn but every video I watch keeps confusing me

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[strange frigate]

The tangent line to y=f(x) at (10,-10) passes through the point (0,1). Give exact answers for f(10) and f prime (10)

[strange frigate]

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[rare glade]

What did I do wrong?

Hold up, let me get better pictures of my word

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[pastel orbit]

how does this proof look?

[pastel orbit]

I'll take any feedback

hmm

let me change smth

the writing at the start is a little better now I think

I need to prove the other direction now, but I just wanted this one checked first

[brittle beacon]

I'm happy

[pastel orbit]

next half is written up

oh no

[brittle beacon]

Bear in mind that the empty set is also open under the finite complement topology (but doesn't have finite complement)

[pastel orbit]

okay but this is a trivial case

[brittle beacon]

Other than that,

[pastel orbit]

f^{-1}(empty) = empty

lemme fix this

[brittle beacon]

just thought it would be worth at least a small comment on the fact where it says "by the definition of the finite complement topology"

[pastel orbit]

fixed

[brittle beacon]

[pastel orbit]

thank you chartbit

.solved

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[limpid garden]

This is Q

[limpid garden]

Would it just be cos(5x+1)-sin(2x-1)?

[swift rock]

yeah

[limpid garden]

Ok one more

[quasi sparrow]

What's the question asking

[limpid garden]

Would this be -2((2x+3)^4) - (3(2x+3)^2) + 1

[limpid garden]

Derivative

[quasi sparrow]

Chain rule

[swift rock]

cant u use the sum rule thingy

add integral on all 3 terms

[quasi sparrow]

That too

[limpid garden]

Wait so that answer is wrong

?

This is what I got

[swift rock]

wait were u telling me the answers? in this question and the one before?

[limpid garden]

I was checking my answers

[swift rock]

integration isnt adding t = 2x+3

u should review ur notes on definite integration

[thin kelp]

is the qn different or am i tripping, cuz this is wrong?

[swift rock]

i thought they were modifying the question and splitting the terms into 2 integrals

i didnt realize that was the "answer"

[limpid garden]

The first picture I sent is the question

[limpid garden]

This was my answer

[thin kelp]

yeah that isnt the answer

[limpid garden]

For this

Ik haha

[swift rock]

.

[limpid garden]

If you use FTC pt 2 wouldn’t it be the answer I stated

I forgot to mention that we’re using that

[thin kelp]

how is that something u just forget?

[limpid garden]

Didn’t forget

Thought I wrote it already

But somehow didn’t write it

[leaden karma]

This one is also wrong

[limpid garden]

Wouldn’t you just replace t with x?

[quasi sparrow]

That's practically the definition of forgetting

[leaden karma]

Not at all..

[limpid garden]

Fair that’s on me

My bad

[leaden karma]

You are saying $\int_0^x f(t)\dd{t}=f(x)$?

[clever fjord]

kheerii

[limpid garden]

I had down $\int_a^x f(t)\dd{t}=A(x)$ and that $A’(x) =f(t)$

[clever fjord]

fre

[uneven osprey]

it is not just that, it is $A(x)-A(a)$

[clever fjord]

77²

[limpid garden]

Could someone do the problem out? Ik im wrong somewhere but I can’t figure it out

Its been over a year since I last took calc so im a little rusty and need to do some studying

Anyone?

[quasi sparrow]

Forgetting chain rule

[odd edge]

@limpid garden Has your question been resolved?

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[woeful rivet]

hi so im writing a report about complex numbers

[woeful rivet]

and i was wondering

where i could show them a complex plane

like imaginary over real

[brittle beacon]

As in plotting them?

[woeful rivet]

yes

:D

[brittle beacon]

Well, worst comes to worst, you can use any plotting (e.g. Desmos) using x for the real part, and y for the imaginary

[woeful rivet]

really

should i use the magnitudes instead

[serene axle]

Yea this is mostly used

[woeful rivet]

bcoz im finding how the curve changes

[brittle beacon]

Considering your screenshot (and that I've done similar), it might be more useful to!

[woeful rivet]

you have!??!

i dont get how this is useful for real life ):

[brittle beacon]

Incidentally, well not the joining part, but plotting z^n for a given complex number z

[woeful rivet]

what is this? z^n=r^n(cos(nθ)+isin(nθ)=re^n^inθ

[brittle beacon]

That's de Moivre's identity

(which makes the plotting much easier!)

[brittle beacon]

For a given complex number z, find its magnitude r and argument theta, then you can plot z^n by representing it as the point (r^n cos(n * theta), r^n sin(n * theta) )

[odd edge]

@woeful rivet Has your question been resolved?

[woeful rivet]

OHHH

[woeful rivet]

okok :D

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[unkempt island]

Can someone help me with long division of polynomials

[unkempt island]

The question is divide x^3-2x+1 by x-1

I started by

1 sec ill draw it

I divided x^3 by x

and got x^2

then multiplied x-1 by x^2

[proven cape]

Its wrong

[unkempt island]

which part

[sterile blaze]

its fine so far

[onyx oriole]

its correct

[unkempt island]

he just said its wrong

[proven cape]

the rest goes with the sign reversed

[sterile blaze]

but u could write an extra gap between x and x^3 to denote the 0x^2

[sterile blaze]

?

[elfin zodiac]

You don’t add, you subtract

[sterile blaze]

hi sammy again

[elfin zodiac]

That will change the sign

Hi 👋

[unkempt island]

im lost

[naive lily]

hello

[unkempt island]

so when I do (-2x) - (-x^2)

[proven cape]

The rest should be -x^3 +x^2

[unkempt island]

where

the top?

[onyx oriole]

it goes like this

[sterile blaze]

my eyes

[onyx cloak]

fr

[proven cape]

(x^3-2x+1)÷(x-1)

[unkempt island]

I didnt get taught it like that

can you tell me the steps

[proven cape]

Do you have to do this?

[proven cape]

.

[lethal wharf]

The answer Is x² + x - 1, otherwise you made a mistake

[onyx cloak]

they want the steps

[onyx cloak]

okay after this

what are you left with?

[onyx oriole]

x^3-2x+1 by x-1
here multiply (x-1) by x^2 then subtract it from x^3-2x+1 and so on

[unkempt island]

I didnt even finish the question yet

[unkempt island]

ok so

[proven cape]

🤦

[unkempt island]

the x^3 cancel out

[proven cape]

Yes

[unkempt island]

and I have to do (-2x) - (-x^2)

[proven cape]

No

[onyx cloak]

yes

so thats x^2 - 2x

[onyx cloak]

what no

[unkempt island]

I feel like card is just yapping

[onyx cloak]

fr

[proven cape]

It's not done like that

[onyx cloak]

it is done like that

what u talking about

[unkempt island]

astar can u just carry on

[onyx oriole]

then multiply (x-1) by -2 then subtract it again

[onyx cloak]

okay so now we have x^2 - 2x

what will u multiply (x-1) with to proceed further?

the normal way

[unkempt island]

it becomes this?

[onyx cloak]

yes

now continue

[unkempt island]

ok so i divide x^2-2x by x

[clever fjord]

Baby Einstein

[elfin zodiac]

!nosols

[odd edge]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[onyx cloak]

why

[unkempt island]

because everytime u do the subtract thing you have to divide the answer by x

[onyx cloak]

u multiplied (x-1) with x^3 in the first step, now what will u multiply (x-1) with?

[onyx cloak]

huh

who said that

[unkempt island]

let me give u an example

[clever fjord]

Baby Einstein

[unkempt island]

so like here

after we subtracted

we got -2x^3

we divide that by x

to get -x^2

isnt that what we do in the question we are doing rn

or no

[unkempt island]

yeah

oh so u divided x^2

by x

and u put x at the top

then multiplied x with x-1

then u subtract them 2

[onyx cloak]

uhhh

[unkempt island]

if u get what im saying

[onyx cloak]

i dont get what you are saying

i didnt divide anything

[unkempt island]

so how did u get the x at the top

[onyx cloak]

after the first subtraction i got x^2 - 2x

now

[unkempt island]

yea

[onyx cloak]

multiply (x-1) by x

that x goes at top

and at the bottom u get x^2 - x

[unkempt island]

where did u get that x from

tho

u just said multiply x-1 by x

from no where

[onyx cloak]

from the same place u got x^3 at the start

[unkempt island]

its not

x^3 at the top

its x^2

cuz x^3/x is x^2

[onyx cloak]

yeah x^2

my bad

oh u are taught like that

[unkempt island]

yh

can u teach me my way 😭

carry on

[onyx cloak]

ur way doesnt make any sense to me

[unkempt island]

ok so

first of all

I got x^2 from dividing the first term

by x

x^3/x

right?

[onyx cloak]

yes

[unkempt island]

then we multiply x-1 by x^2

to get x^3-x^2

x^3 cancels out

[onyx cloak]

ah you're doing it that way

yeah so i divided x^2 by x

[unkempt island]

we are left with -2x + x^2

[onyx cloak]

got that x at top

then multiplied (x-1) by x

got x^2 - x

[unkempt island]

x^3?

[onyx cloak]

now continue this

[unkempt island]

u mean

[onyx cloak]

im talking about second step

[unkempt island]

ill put this here so i dont have to keep scrolling

[onyx cloak]

yes the second step

x^2 - 2x

[unkempt island]

yea

[onyx cloak]

divided x^2 by x

so = x

[unkempt island]

yep

[onyx cloak]

put that at top

then multiply (x-1) by x

[unkempt island]

yeah

[onyx cloak]

so x^2 - x

[unkempt island]

yeah thats what i was saying

[onyx cloak]

now continue

[unkempt island]

and u said u didnt divide anything

so the subtraction becomes -x

the result

then minus 1 at the top cuz -x/x

ok I get it

thanks

.close

[odd edge]

Channel closed

Closed by @unkempt island

Use .reopen if this was a mistake.

[onyx cloak]

yeah because i didnt, what i did was to think what to multiply (x-1) with to get x^2 at the start so that it cancels out

[odd edge]

Available help channel!

Send your question here to claim the channel.

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[woeful rivet]

(excuse me

[woeful rivet]

how do i write this in polar form

z = 1+i

[sterile blaze]

whats the magnitude

[woeful rivet]

it doesnt work

[sterile blaze]

it should be isin

[sterile blaze]

in this case i would be the y axis so, (sqrt2 cos45, sqrt2 sin45)

[woeful rivet]

what

wait

so how do i put taht into desmos

[sterile blaze]

exactly what i put in brackets

[woeful rivet]

it didnt work

[sterile blaze]

could i ask what the original question is?

[woeful rivet]

im doing a task

wair

[sterile blaze]

the task being?

[woeful rivet]

researching complex numbers

idk what to do

[woeful rivet]

it didnt work tho

[sterile blaze]

did u put the brackets as well

[woeful rivet]

yeah

and then i tried to put y=

and it didnt work too

WAIT

IT WORKED

[elfin zodiac]

It works

[woeful rivet]

wait

so now i do to the power of 2?

[elfin zodiac]

I just tried

[sterile blaze]

z^2?

[woeful rivet]

bc apparently its supposed to show a spiral or something

[woeful rivet]

yes

[sterile blaze]

for the nth power, take the magnitude ^n and take the angle*n

[woeful rivet]

so if im doing 2

magnitude is now 2

and angle is now 00?

90

?

[sterile blaze]

yes

[woeful rivet]

what did i do wrong..

[sterile blaze]

they are taking sqrt as 4 variables

they should be showing u the sqrt symbol instead

[woeful rivet]

is this better

[sterile blaze]

.

[woeful rivet]

they?

[sterile blaze]

desmos

[woeful rivet]

oh

so how do i fix this

OH

wait

[sterile blaze]

same as how the sqrt symbol is shown here

[woeful rivet]

OGG

is it supposed to look like this

that looks wrong

[sterile blaze]

the one on the first line is fine

the rest are not

[woeful rivet]

wait no

its a small dot

what

[sterile blaze]

it is a point

it is supposed to be a dot

[woeful rivet]

oh

ok

how am i supposed to see a pattern from this..

[sterile blaze]

graph the first 4 points

[woeful rivet]

okok

wait omg a spiral

is there anyway i can join these points together

[sterile blaze]

btw

u should change ur desmos to degree mode

[woeful rivet]

yes

[sterile blaze]

its in radian mode

[woeful rivet]

..

how to change it into degree mode

wtf

oh i found it

#problem solver

[sterile blaze]

im not sure. alternatively change all angles to radians

[woeful rivet]

do u know

how i can join these points together

[sterile blaze]

as u said

u can replace the numbers with t and see a spiral

[woeful rivet]

oh

[woeful rivet]

pardon what?

does this make the points join together in a line?

[sterile blaze]

((sqrt2)^t cos(45t), (sqrt2)^t sin(45t))

[woeful rivet]

omg it did one

wait but that only did one

[sterile blaze]

yes it is one spiral

it shows the values the z would take on as u vary its exponent

[woeful rivet]

how do i do the 2nd one