help-13

[north otter]

hi

@sonic thistle i need more wisdom

is it

0=-1/4|x-3|+5

[sonic thistle]

yes

and now find x

[north otter]

ok bet

first -5?

each side^^

<@&286206848099549185>

[lucid drift]

yes i’d do that

@north otter

[north otter]

alr

i did it

[lucid drift]

whole thing?

[north otter]

i need more help

do i divide both sides by -1/4

[lucid drift]

id multiply the -1/4 and |x-3| first

to make this

and then times both sides by -4

to make |x-3|=20

then

x-3=+-20 should give you your two answers

[cedar kiln]

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[toxic moat]

LOL what

oh angle

i read area

[meager plinth]

do you know what to do?

[toxic moat]

p sure

the red r =

green r =

then from there u shld b able to find the shaded

[meager plinth]

ok lemme try

[toxic moat]

idk whats the property called

go google

circle angle properties or smt

[meager plinth]

i got 47 degrees

thanks @toxic moat

[toxic moat]

yay

np

💕

[meager plinth]

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[elfin plaza]

Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that 0<theta<pi/2

sqart(x^(2) -36)/x

x=6sec (theta)

I tried to use tan^2 + 1 as sec theta^2 but it doesnt work

[cedar kiln]

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[crimson sedge]

Hi

[crimson sedge]

<@&286206848099549185>

None of it makes any sense at all so explain it to me like im 5

[silent tide]

So there's a function that gives seach number an image

And it works as long as you give it some number bigger than or equal to 0

What we want to find out is "what can it give out?"

@crimson sedge understand so far?

[crimson sedge]

I’m sorry I just now saw this

I kinda get it

How would I go about a problem like that step by step

Also if you’re familiar with Desmos I’m allowed to use that

[silent tide]

If you can use desmos...

Than just look at where the lowest y value is

[crimson sedge]

Wym

[silent tide]

Just a minute

What is the lowest y value here?

[crimson sedge]

0?

[silent tide]

Yes

So then you can say that "the range of f(x)=x² is all real number ≤ 0"

[crimson sedge]

That’s not an answer choose

Choice

[silent tide]

Yes it's not

Because the function is different

[silent tide]

Here the function is f(x)=x²

[crimson sedge]

Alright so what would I input into desmos

[silent tide]

You would input your function

[crimson sedge]

I have a fraction?

[silent tide]

$$f(x) = {(x-2)}^{2}+3$$

[wraith dagger]

jafar/جعفر

[silent tide]

This is your function right?

[crimson sedge]

Ye

[silent tide]

Input that in desmos

[crimson sedge]

Whoops

I got 7

[silent tide]

Also i forgot to mention something that may be important

Make sure to add ∀x≤0

[silent tide]

The reason is because it said "the domain of f is all real numbers greater than 0"

[crimson sedge]

An upside down A??

[silent tide]

It means for all

[crimson sedge]

I don’t even see that

Where would I add that

[silent tide]

"for all x bigger than or equal to 0, f(x) is defined like so... For x that do not meet this criteria, f(x) is undefined"

[crimson sedge]

Do you have time to help me with some more questions

[silent tide]

Oh wait that's not a thing on desmos

[obsidian coral]

I think you can restrict the domain by doing something like ${x \geq 0}$ in desmos

[wraith dagger]

dldh06

[obsidian coral]

Include the curly brackets

[crimson sedge]

Y’all are way too advanced for me 😂

[silent tide]

I guess this one requires understanding rather than some specific steps

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[stone lion]

Quickest way to do it?

Note: this is a 1 mark question

[latent bloom]

Cosine rule

[stone lion]

Extending BC?

[latent bloom]

a^2 = b^2 + c^2 -2bc(cosA)

[crimson sedge]

Cosine rule or the weird shoelace method that I heard about

[latent bloom]

Shoelace needs coordinates I think

[stone lion]

coasA?

[crimson sedge]

Oh okay

Makes sense

Non-right

[latent bloom]

This is not a right angle triangle

It doesn't apply here

[latent bloom]

Yep

A is the angle opposite of a

a is the side you want to find

b and c are given sides

[stone lion]

How would I find A then?

[latent bloom]

And A is in between b and c

[stone lion]

Only C is given

[latent bloom]

Well this will become c^2 = a^2 + b^2 -2abcosC

a and b are 2 and 5 respectively

And C is the angle

You then get c^2

[stone lion]

Ok pls let me take a few minute to look into it

[crimson sedge]

Doing cosine rule is somehow more annoying than implicit differentiation with quotient rule

Wow

[latent bloom]

Mood

Remembering the rule is a hastle

I always use sine rule

[crimson sedge]

I forgot the derivation. I am pretty sure it was just with vector projections

[latent bloom]

I remember proving it but it wasn't easy

And I forgot the proof

[crimson sedge]

Yeah same I think

[stone lion]

Yes thanks! It's a very quick way to do it!!

Thank you very much

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[crimson sedge]

Can someone help me??

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[wind glade]

Which part do you need help on?

[cedar kiln]

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[zealous compass]

a map can only have an inverse if it is bijective?

[zealous compass]

is that correct

is that an iff?

ie. a map can only have an inverse if and only if it is bijective?

[still thorn]

Think about it like this, injectiveness is implied reasonably right

[zealous compass]

yes

[still thorn]

So it kinda has to apply both ways

Because the inverse of the inverse is your original function

[zealous compass]

ok so the answer is yes

right

oh wait

you have a point

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[sour meadow]

ive been trying to figure out this question for a long time

[sour meadow]

anyone can help me?

i have to find k

[tribal verge]

5/3

[sour meadow]

can u show me how u got it?

[tribal verge]

Num become a to the power 3/2

Denominator become a to the power 2/3

Then use a^m/a^n =a^(m-n ) rule

[sour meadow]

oh

ill study what u said

thanks

[tribal verge]

Its basic exponent formula

Of 7 grade ig

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[crimson sedge]

so the older brother takes 30 minutes to go to school, the younger brother takes 40 minutes. how long will it take for the older brother to catch up with his little brother?

[crimson sedge]

ye and younger brother started to walk 5 minutes earlier than the older one

[cedar kiln]

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@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

<@&268886789983436800>

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@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

.close

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[unborn sonnet]

is it that x

in the denominator

[south sandal]

idk

[gleaming cloud]

u = ln x

@south sandal

[cedar kiln]

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[languid drum]

How would I go about answering this

[dim atlas]

I'd suggest try playing around with some small examples

[languid drum]

Yeah ive created a subset of 1,2,3,4,5

but idk what to do from thee

there*

[dim atlas]

So what is reflexivity

what does it mean for a relation to be reflexive

[languid drum]

its if each element matches itself?

[dim atlas]

Nope

So, you are thinking of = (which is a specfic equality relation) defined on the reals

[languid drum]

dont they both have to be in the same set?

[dim atlas]

what do you mean?

[languid drum]

like if its 2<= 2 its reflexive

cus they both equal eachother

idk how to explain it

[dim atlas]

So we should start with the definition of relation again

What's your definition?

[languid drum]

A relation on x is a property on x which may or may not hold for each element of x

[dim atlas]

That doesn't seem correct

Think of relation as a function that takes in two inputs and tells you if they are "equal" by however you define equality

Let's look at an example

Our relation R is defined on Z x Z and we say A R B if and only if A and B are both even, or both odd

Then, 2 R 4 is true, 2 R 3 is false, 3 R 3 is true

do you follow

[languid drum]

Yep

[dim atlas]

Okay, so reflexivity is a potential property of a relation

it means for your relation, A R A is always true

[languid drum]

Oh ok is that because it says A and B must be even

So its reflexive as both are even

So I can use A=2 and B=4 as an example

And say both are even, so reflexive

[dim atlas]

No

Its saying any element is always related to itself

[languid drum]

So what would I say for my question

[dim atlas]

In this case, A R A is true always

If A is odd, then A R A is true as both inputs are odd

if A is even then A R A is true cause both inputs are both even

[languid drum]

Why is it A R A

Isnt it A R B

[dim atlas]

So we are checking reflexivity

[languid drum]

yh

[dim atlas]

Reflexivity is that A R A is always true, for all elements A

[languid drum]

ok

[dim atlas]

so this relation is reflexive right?

[languid drum]

yeah i get that example

[dim atlas]

ok, then let's try your problem

Is your relation reflexive

[languid drum]

So my question is saying A is only related to B if and only if both A and B are even

Surely it is reflexive

Its saying they r related if and only if they are both even

[dim atlas]

this isn't your problem?

[dim atlas]

talking about this one right?

[languid drum]

yh yh

im just tryna word it in my way

[dim atlas]

Your question says A is related to B if and only if the cardinality of their intersection is even

[languid drum]

Oh the cardinality

I dont have a scooby then

[dim atlas]

scooby?

[languid drum]

I dont have a clue

On what to do

its a saying haha

[dim atlas]

So we want to check if A is always related to A

What are the inputs to this relation

[languid drum]

what do u mean by inputs

[dim atlas]

what is A

[languid drum]

A subset?

[dim atlas]

of?

[languid drum]

R

[dim atlas]

no

what is A a subset of

[languid drum]

the set 1 to 100

[dim atlas]

Yes

[languid drum]

power set*

[dim atlas]

no

[languid drum]

oh

[dim atlas]

the power set is the set of all subsets

A is in the power set

which means A is a subset of {1, ..., 100}

[languid drum]

Ok

So by A and B what does that mean

[dim atlas]

A, B are elements

R is your relation that tells you if A, B are related or not

[languid drum]

Yep

[dim atlas]

ok, so let's say A is {1, 2, 3}, B is {2, 3, 4}

Is A R B true or false?

[languid drum]

The cardinality is 3 so its false?

oh wait

NONOONO

Cardinality is 2

so its true

[dim atlas]

yes

[languid drum]

The cardinality of a and b is |{2,3}|

so 2

[dim atlas]

So is the relation reflexive?

Is A R A always true?

[languid drum]

Not always

You can have odd cardinality which isnt true

Like A={1,2,3} B={1,4,5}

Cardinality is 1

So its odd and not true\

[dim atlas]

Ah but your inputs are the same

reflexivity means that for your relation, whether some element A is always related to itself

[languid drum]

So I dont get why its always true

Why cant i do what i did

[dim atlas]

Because A and B are different

A R A means your two "inputs" are the same

[languid drum]

arent a and b different in this

[dim atlas]

Yes, but I was just checking that your understood what it means for two elements A, B to be related

[languid drum]

oh ok

[dim atlas]

again, a relation is reflexive if every element is related to itself

[languid drum]

so A={1,2,3,4} B={1,2,3,4}

Does that work

[dim atlas]

This needs to hold for all elements

So it works when A= {1, 2, 3, 4}, cause A R A is true iff cardinality of A intersect A is even, which we can see A intersect A is just A, which is even cardinality

Does it work for all subsets of {1, ...., 100}

[languid drum]

Yes

Because its only true if the cardinality is even

You cant do A={1,2,3,4,5} as A intersect A has an odd cardinality

@dim atlas ?

[dim atlas]

Yeah,s o your relation isn't reflexive

reflexivity means A R A is true for all choices of A

but if A = {1, 2, 3, 4, 5}, then A is not related to A

[languid drum]

Ah ok

[cedar kiln]

@languid drum Has your question been resolved?

[languid drum]

What about the other ones?

[cedar kiln]

@languid drum Has your question been resolved?

[cedar kiln]

@languid drum Has your question been resolved?

[cedar kiln]

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[prime lily]

yo

[prime lily]

how is tanx = tan x-180

[patent cape]

since youre doing this stuff i assume youve lesrned about the graphic representation of trig functions

technically a full resolution has occured on the trig circle

[prime lily]

ik the graph

but what about the proof

[patent cape]

oh proof wise

dunno that

sey

sry

[prime lily]

dang

okay

what are the conditions for sinx = sin180-x

[narrow fiber]

suppose you take a rod (OA) in the first quadrant
tan x=h/k
then when you rotate it by 180⁰ (or subtract 180 from x) you get OB in the 3rd quadrant
tan x=-h/-k = h/k

[prime lily]

how is rotating it by 180 degrees equal to substractibg 180 from x

[narrow fiber]

what's 360-90

[prime lily]

270

[narrow fiber]

that's the negative y axis

what's 270-90

[prime lily]

180

[narrow fiber]

that's the negative x axis

basically you're rotating a rod through the axes

[prime lily]

alright

coololo

do you guys like math

[cedar kiln]

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[zinc vortex]

How are those randians obtained?

I'm referring to the ones marked in red.

[prime lily]

through sick maths

[cerulean sail]

Add 2pi to the first two?

[zinc vortex]

Oh

Got it

Thanks

What about those?

[cerulean sail]

Hmmm I’m not quite sure tbh, I do know they’d give you -1 though which might be it?

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[crimson sedge]

@vague beacon 1 + u = v, so dv = ... ?

||derivate both sides||

Why

Well

Don't u see something similar in both sides?

When u derivate this

[crimson sedge]

For example, supose 2x = y, so 2dx = dy, and how about this one?

Why "1+"?

Yes but 1 is a constant

And the derivate of constant is?

Yes

So dv = du

No problem

[crimson sedge]

And now just sub in the integral and u will have $$-1000 \int \frac{1}{v^2} \dd v$$

[wraith dagger]

SamuDoki

[crimson sedge]

Got it?

Oh, okay

[crimson sedge]

Did u understand this one?

So, if u have a du there u can put dv that sub the du

Because they are the same

Sorry if its confused english is not my main language

[queen junco]

That looks difficult

have fun

[cedar kiln]

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[fickle imp]

How do you do this?

sin = -2/3
cos = ?
csc = -3/2
sec = ?
tan = ?
cot = ?

[dull oxide]

Do you know your trig identities?

Or your unit circle quadrants?

[fickle imp]

yeah, this one is in quadrant 3

[dull oxide]

yes precisely

Okay, and first question, do you know your trig identities?

[fickle imp]

yeah, tan = sin/cos, sec = 1/cos etc

[dull oxide]

yup

There's one more super important which I suppose is the one you need

[fickle imp]

1-sin^2 = cos^2

[dull oxide]

yup

Strange way of writing it imo, but that's the one

[fickle imp]

hmm so I would square -2/3 and subtract 1

1-(4/9) = 5/9

[dull oxide]

(-2/3)²

yup

[fickle imp]

oh so 5/9 = cos^2, cos is √5/3

[dull oxide]

halfway there.

It's also possible that cos=-√5/3

[fickle imp]

oo true, it is in third quadrant

sin = -2/3
cos = -√5/3
csc = -3/2
sec = -3/√5
tan = 2/√5
cot = √5/2

[dull oxide]

lgtm

[fickle imp]

thank you

.close

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[winged pewter]

for b in a,b

we got equaiton (x-5/2)^2 + y^2 = 25/4

b is 0 becayse nothing is follwing after y^2

right

?

i can just tell from that line

[cedar kiln]

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[winged pewter]

Mistake

3.14

delete ur messages

its covering mine

my question isnt answered

[inland patrol]

yes

you can view it the same way as (y-0)^2

[winged pewter]

thanks

.close

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[misty cobalt]

How come the zero divisor for 4 is 2x2
but the same does not go for 9 with 3x3?

[misty cobalt]

I understand how 2x2 is a zero divisor of 4, but can't wrap my head around why 3x3 is not a zero divisor for 9.

<@&286206848099549185>

[cedar kiln]

@misty cobalt Has your question been resolved?

[cerulean sail]

What do you mean by zero divisor?

[misty cobalt]

Its an element of a ring where multiplying elements from the ring a*b mod n where n is the size of the ring, we end up with 0

In this case we're allowed to do a=2 and b=2 and we get 2*2=4
4mod4=0

That makes sense

However we are not allowed to do 3*3=9
9mod9=0
Which I don't understand.

[cerulean sail]

Hmm, do you have any more context to that by any chance? As in a book/notes you got that from?

[misty cobalt]

https://en.wikipedia.org/wiki/Zero_divisor
https://www.oliverboorman.biz/projects/tools/rings.php

The calculator is what started this question

Since I thought it was odd. I looked around and every other source states the same

https://pages.uoregon.edu/adding/courses/392/hw4_sol.pdf
This states that z4 has one zero divisor namely 2.

z9 has the zero divisors 3 and 6. Where the one with 6 is 6*6 which is 36
36mod9 is 0 makes sense

3*6 is 18
18mod9 is 0 again makes sense

3*3 is not a zero divisor however.

even though 9mod9 is 0

[cerulean sail]

Hmm, personally I would think that it would be a zero divisor, are you wondering why it doesn't show here?

If so, I think that calc just demonstrates it for some value, not necessarily all of them

[misty cobalt]

It should show all.

[cerulean sail]

It could have equally used 3*3 in my opinion, unless I'm missing something

[cerulean sail]

Show all of the (nonzero) zero divisors, or all possible ways to get zero (from a given zero divisor)?

[misty cobalt]

All zero divisors I believe

[cerulean sail]

Well, it does show all of the (non-zero) zero-divisors there, but not necessarily all ways to get them?

The definition of a zero divisor (say $a$) from wiki is basically that there is some nonzero $x$ such that $ax=0$

Finding one such $x$ is enough to prove $a$ is a zero-divisor

[wraith dagger]

chartbit

chartbit

[cerulean sail]

You wouldn't need to find all of them as proof, no?

[misty cobalt]

Ok so finding 3x6 and 6x6 is enough then?

I would not need to prove that 3x3 is one as well?

I am curious since I got a question to find all zero divisors of Zx where x changes. 9 was one of them however it feels odd that 3x3 would not beed needed

[cerulean sail]

Matter of fact, proving 3*6 = 18 = 0 would be enough to show that both 3 and 6 are zero-divisors, I'd think?

Swapping their roles around

[misty cobalt]

or just knowing that 3x6 is just double 3x3

[cerulean sail]

But you just have to show there's some nonzero x, as far as I'm concerned?

[misty cobalt]

Ok thanks dude

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[ornate wren]

sorry

tbh, i dont know where to start

integral? but what are the bounds

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[bold pond]

dumb but quick question, how did they just change the sign

[cedar kiln]

@bold pond Has your question been resolved?

[dire geode]

u = -v, du = -dv

[bold pond]

so just divided du=-dv by -1?

[dire geode]

no division happened

[bold pond]

literally nothing else changed? im blanking hard on how it goes from -du to du

[dire geode]

this is v

if you prefer, v = -u and dv = -du

[bold pond]

alright, i think i got it.

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[crude flicker]

Hello!

[crude flicker]

I could use help with this

How do i graph that @.@

[cedar kiln]

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[cedar kiln]

@crude flicker Has your question been resolved?

[rich moss]

first set 3x-2y equals to 7

then graph that line by isolating y

now, since 3x-2y is larger than 7, 2y is smaller than 3x - 7

this is kind of instinctual , but if 2y smaller than 3x-7, then it doesnt matter how much you increase x since something that is larger than another thing will remain larger if you increase it, so you fill out the graph to the right of the line. Do the same thing for 2x + 5y, and fill out the part where both lines overlap

do the same for the other line

@crude flicker

here is an example of the system of equations being drawn in desmos, your graph should look like this but only fill out the purple part

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[cedar kiln]

@dapper aurora Has your question been resolved?

[dapper aurora]

<@&286206848099549185>

[unborn sonnet]

19.2

22

answer

[cedar kiln]

@dapper aurora Has your question been resolved?

[unborn sonnet]

@dapper aurora

[dapper aurora]

those are not options

the very bottom

the sentence

the options for the first on is median mode and mean

and the second one is does and doesn’t have an outlier

[latent bloom]

Okay mean is you sum up all numbers

Then you divide them

By the number of numbers

For your case: you have 6 numbers

And their sum is 115

So your mean is 115/6

You got it right

[latent bloom]

No the first number is an outlier compared to the other numbers

You have common numbers like 21, 22, 23, 24

1 is out of place here

[dapper aurora]

mhm

would that be the mean?

[latent bloom]

Nope. The mean is affected greatly by the outlier

Median doesn't care about the value of the outlier. It cares only about ordering of numbers

1, 21, 22, 23, 24, 24

Your median is between 22 and 23

Which better describes a suitable average number for your data

While the mean is 19.17, which is below the data range even

Below the 21,

That's why median is better here

@dapper aurora

[dapper aurora]

so the answer would be median because it has an outlier

[cedar kiln]

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[unborn sonnet]

can someone help me in determinants?

[unborn sonnet]

i dont know how to use the properties of determinants

?

.close

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.reopen

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[unborn sonnet]

@crimson sedge

HERE

[crimson sedge]

yh

[unborn sonnet]

tell me

lemme send you a quetsion

[crimson sedge]

i dont know this one sorry i am low level math person

[unborn sonnet]

ohh

[crimson sedge]

determants

[unborn sonnet]

np

yup

[crimson sedge]

ok sorry

[unborn sonnet]

@zealous compass help

[latent bloom]

Yes

[unborn sonnet]

how to solve this one

[latent bloom]

Ok so

First thing you have to do is put your signs

[unborn sonnet]

we have to find determinat of this

[unborn sonnet]

where?

[latent bloom]

First row

[narrow fiber]

don't you dare directly solve it 💀

[latent bloom]

That's the only way I know lol

[unborn sonnet]

idk what r u saying

?

[narrow fiber]

do you know how to simplify it?

[zealous compass]

@unborn sonnet he's manually calculating the determinant

💀 my lin alg is shit i cant help sorry

[unborn sonnet]

@narrow fiber dude i have to use properties

of determinants

[narrow fiber]

could you state the properties u have to use

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[glossy grail]

n

[cedar kiln]

@glossy grail Has your question been resolved?

[glossy grail]

<@&286206848099549185>

what would it be

also im not allowed to use plot tools

so yeah itll be great if theres a way without using them

and im sure there is

like do i need to plot the square root

part

[cedar kiln]

@glossy grail Has your question been resolved?

[glossy grail]

is my question confusing

if so tell me ill edit

[cedar kiln]

@glossy grail Has your question been resolved?

[random thistle]

i am kinda confused, what do you need to solve? What do you need to do? What do you want help with?

@glossy grail

[glossy grail]

g(0)+h(4)

[random thistle]

where is n(x)?

[glossy grail]

@random thistle

[random thistle]

or is that part of the problem?

I might not understand it correctly

g(t) = n(A)
but where is n()

[glossy grail]

the number of elements

of set A

as t changes

[random thistle]

No idea then. Maybe someone else might help. Sorry

[glossy grail]

<@&286206848099549185> rn

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[cinder wyvern]

ive done question 1 and researched about s4 but i dont even know where to start

i

[crimson delta]

isomorph means that the groups are the same just with different names

[cinder wyvern]

oh

[crimson delta]

so you need to find some elements in S_4 that behave exactly like 1, -1 and +-i

in relation to each other

[cinder wyvern]

how would i go about finding a group like this

[crimson delta]

for example what is the order of i

[cinder wyvern]

like $i^{n}$

[wraith dagger]

Techno

[crimson delta]

the order of an element g is the smallest positive number n so that g^n=1

[cinder wyvern]

youve lost me now

[crimson delta]

ok forget that then

you'll see it later again probably

notice that the powers of i follow a pattern. i, -1, -i, 1, i, -1, -i, 1 etc

can you find an element which follows a similar pattern?

a, something, something, 1, a, something, something, ... ?

and what are those somethings

[cinder wyvern]

erm

like what you said before?

like its i^n for n = 1, 2, 3, 4,...

[crimson delta]

• can you find an element in S4 which follows a similar pattern

[cinder wyvern]

ive been looking for ages

i cant find one :/

dont tell me the answer but nudge me harder yk what i mean

am i looking at the right thing? @crimson delta

i dont know what correlates

[dire geode]

did you watch the video yet

[cinder wyvern]

i watched some of it but i couldnt understand most of what she was saying

so i watched some different ones

[dire geode]

longer but more examples
https://www.youtube.com/watch?v=gmSgQ6iZYcg

watch enough until you are able to do group operations

[cinder wyvern]

.close

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[lusty marlin]

solutions for this question are required by using the counting techniques, not the formula

answer is 64

[floral forge]

8 different colors means 8 different types of cars depending only on color. each car can either be manual or automatic, that gives a total of 16 possible combinations of color and gear transmission. after that we have 4 types of different wheels that each of the 16 possible combinations of color and gear transmission cars can have, do you see how they get the answer 64 from there?

[lusty marlin]

why do u times 8 by 2

[floral forge]

because there are 8 cars with different colors that have manual, and 8 that have automatic

[lusty marlin]

ohh

[floral forge]

the same logic can be applied to the wheels

[lusty marlin]

y does it sound like it is saying that "each car from the cars with 8 different colour" cuz that is what I thought

[floral forge]

no idea what it is you are trying to say

[lusty marlin]

like each car from the cars with 8 different colours can be manual or automatic

[floral forge]

well yes that is what it is saying

you can have a green car which has automatic but you can still have a green car with manual

[lusty marlin]

oh now I get it

thx

[floral forge]

👍

[lusty marlin]

.close

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[bitter nacelle]

Please help

[bitter nacelle]

I just need a answer, then i can see the professional explanation

Thanks!

[crimson sedge]

prob something like -0.8x

[cedar kiln]

@bitter nacelle Has your question been resolved?

[floral forge]

for a line $y=mx+b$ where $b$ is the y intercept and $m$ is the slope aka rise over run

[wraith dagger]

Duh Hello

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[winged pewter]

I’m lost

It says integrate by parts but first makes substitution

Can someone push me in right direction what substitution. To make first

[cedar kiln]

@winged pewter Has your question been resolved?

[rotund hinge]

Make theta^2 be u

Like you have

And you should have ucos(u)du

[hoary notch]

ucos(u) / 2

[rotund hinge]

Yeah

[winged pewter]

Ty

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[idle thicket]

Is this correct?

[rotund hinge]

Idk did it mean 5 percent per year or in the whole ten years?

If it's per year it's correct

[idle thicket]

5% in 10 years

[cedar kiln]

@idle thicket Has your question been resolved?

[rotund hinge]

Then it's wrong

It would just be 46(1+.05)^1

[idle thicket]

I meann

yeah im lost

[rotund hinge]

Well if it only grew 5 percent in the whole ten year period

Then the ten year period would be a period of one 5 percent growth

Rather then ten 5 percent growths compounded

[idle thicket]

sooo

46(1+0.5%)^10

0.5 x 10 yrs

5% grouth

🥱

[rotund hinge]

What you have there is 5 percent per year

But if it only grew 5 percent in the entire ten years then it would be just raised to the first power

[idle thicket]

it said in 10 years it grew by 5%

[rotund hinge]

So then it grows by 5percent every ten years not every year

[idle thicket]

yeah every 10 years

0.5 per year

right?

[rotund hinge]

?

[idle thicket]

tbh idk

[The farm started with 46 cows and in the next 10 years their population grew by 5%]

[idle thicket]

uhh would this be right?

diff question^

[cedar kiln]

@idle thicket Has your question been resolved?

[idle thicket]

<@&286206848099549185>

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@idle thicket Has your question been resolved?

[rotund hinge]

What even is b

Otherwise it looks good

[cedar kiln]

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[sinful yew]

A problem from Spivak's Calculus:
find all (real) x such that:
x + 3^(x) < 4

[dire geode]

you know 1 + 3^1 = 4

just show something about the growth of the function

[sinful yew]

sorry i should have been clearer.
I know the intuitive solution for x=1, then since x + 3^x is always increasing it will only cross the line y=4 once, and so for all x<1, it holds.
What I'm looking for is an analytic way to solve this for perhaps a more general case

ive tried using logs to try and simplify but that hasnt helped

<@&286206848099549185>

[modern compass]

I don't think there's a quick and easy way to get an exact answer for questions like this.

you can approximate one with intermediate value theorem

[sinful yew]

i was worried that'd be the case

as a slight aside before i close it:

the best i got when i took it to the tutor for my current math paper, we got to the point that in the form y=x + a^x, its always increasing for a >= 1 and so something like Newtons method for root finding would be a great tool here. just for intrewrest ig

.close

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[fluid topaz]

What did I get wrong in here

I can't find the mistake

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[misty otter]

an ofw, upon permanent return to the country,decides to invest us $5,000 in a money market that yields 8% interest. how much more should she invest in another money market scheme that yields 10% interest in order to realize a total annual income between us %800 and us $940

[misty otter]

<@&286206848099549185>

[cedar kiln]

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[tranquil oracle]

8% and 10% is per annum?

what have you tried for the calculation so far @misty otter

[cedar kiln]

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[mortal musk]

I'm seeing conflicting answers to this, is this regular?

[mortal musk]

I've made this DFA

yet I see people claiming it's non-regular by using PL

and isn't a* b* a regular express for it

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[atomic flower]

Hello?

[atomic flower]

It said find the sin alpha but i cant find the formula

(On the last part and it is not cos)

<@&286206848099549185>

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[cedar kiln]

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[scarlet garnet]

do you know how to approach this?

[crimson sedge]

idk maybe like we have to do something wiv derivatives

[scarlet garnet]

it does

how exactly would you start?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

like maybe

first write down the equation of v

then

1st principle ?

which is dy/dx

[scarlet garnet]

wait

you kinda need more

[crimson sedge]

like

[scarlet garnet]

since V has 2 parameters

you wont get a nice derivative

[crimson sedge]

exactly

[scarlet garnet]

you aren't done with all the requirements the task gives you

[crimson sedge]

so like what i have to do to get all parameters

[scarlet garnet]

I mean look whats given, you want a maximum volume, but there is also a restriction here

[crimson sedge]

whats that?

[scarlet garnet]

how would you consider the maximum amount of material you may use in a volume function?

[crimson sedge]

if the amount is less then 0 then its max

whereas if its greater than 0 it should be min

[scarlet garnet]

thats not what I asked

we aren't doing derivative yet

[crimson sedge]

oh

[scarlet garnet]

so, you have the equation for the volume right?
can you tell me?

[crimson sedge]

pie r^2 h

[scarlet garnet]

$πr^2h$ yes

[wraith dagger]

Jigglyproff

[scarlet garnet]

so you have h and r there

[crimson sedge]

yeah..

[scarlet garnet]

so, if you were to take the derivative of V(r,h)=πr^2h... it would get extremely messy and you don't want that

also, you somehow didn't even consider the 600 π cm^2 limit for the material

[crimson sedge]

mhm

[scarlet garnet]

so you need a second line in your equation system that considers that limit

[crimson sedge]

okay...

so

[scarlet garnet]

hint

[crimson sedge]

mh

[crimson sedge]

still dont get it 💀

[scarlet garnet]

well

the task says that the area of the cylinder is 600 pi cm^2 right?

[crimson sedge]

correct

[scarlet garnet]

how would you formulate that as an equation with r and h

[crimson sedge]

pie r^2 h = 600

?

[scarlet garnet]

wait wait wait

$πr^2h$ is the VOLUME

[wraith dagger]

Jigglyproff

[scarlet garnet]

but not area

you need another formula

[crimson sedge]

OHHHH

BURH

MB

i didnt read the question properly

[scarlet garnet]

i feel you

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[final gorge]

what does this symbol mean

<@&286206848099549185>

[cerulean sail]

Product between k=0 and k=m of (a_{k} + 1)

[final gorge]

thanks

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[timber turtle]

wait i did something wrong

i thought y-axis was y=x

but its x=0

ok i got it

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[crimson sedge]

Why cant I just cancel the x^2 ?

[crimson delta]

because they are in a sum

set x=10 or something and then evaluate both the original expression and the one without x^2

you'll see that you don't get the same thing

[crimson sedge]

if x^2 was multiplied by 12x and x^2 multiplied by 5x

could I have then cancelled it

[crimson delta]

no. you can only cancel if the whole denominator and numerator are products

[crimson sedge]

ohh ok thx

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[barren bluff]

I need help

[barren bluff]

No. 15

<@&286206848099549185>

[tranquil oracle]

what properties do you remember determinant has

[cedar kiln]

@barren bluff Has your question been resolved?

[barren bluff]

Uh-

Well I remember 6 of em

1)Value remains unchanged if rows and col are interchanged
2)if any row/col is interchanged, sign changes
3)if any two are identical, value will be zero
4)if all elements are multiplied by constant k, value gets multiplied by k
5)if some elements are expressed as sum of two, determinant can be expressed as sum of two determinants

Yeah the 6th one is too long to type-

[barren bluff]

If you can help me solve that, that would me amazing

[tranquil oracle]

can you apply the properties to calculate?

like you can add a multiple of one row to another row right

[barren bluff]

I tried

But couldnt do it

[tranquil oracle]

what happened when you add a multiple of a row to another row

which multiple should you choose to make your computation easier?

[barren bluff]

I tried to make all the (a+x) turn into 0, then it will be easier

But dunno-

[tranquil oracle]

you can try subtracting the second row from the first row

[barren bluff]

So, R2--> R2-R1 right?

Kk lemme try

So in the first row it will be
X² -X² 0

Right?

[barren bluff]

@tranquil oracle

[tranquil oracle]

how did you get x^2

[barren bluff]

Oh yes 2x f mb

I feel dumb

Oof

[tranquil oracle]

yeah the rest should work out I guess?

[barren bluff]

Yess thanks alot

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[brittle field]

how to turn this into an equation?

[vagrant elbow]

do you know what type of graph that is

[brittle field]

parabola so its quadratic right?

isnt that slope?

cant be used for parabola?

[vagrant elbow]

yup

and you know the roots of the quadratic?

[brittle field]

wym by that?

[vagrant elbow]

the values for which the quadratic is 0 :P

[brittle field]

not sure

[vagrant elbow]

look at the graph

for what x values is the y value 0

[brittle field]

when x is at -4 and 4

y is 0

[vagrant elbow]

yeah

Do you know the general form of a factorized quadratic?

[brittle field]

is that the x^2 + x + 1 form?

[vagrant elbow]

$(x - \alpha)(x - \beta) = 0$

[wraith dagger]

NEONPerseus

[brittle field]

is that an a and b? whats this equation do?

[vagrant elbow]

alpha and beta

the roots of the quadratic

any quadratic with real* solutions can be represented in that form

if you know the roots you can build the quadratic

[brittle field]

do we know the roots?

[vagrant elbow]

yes you do

you already said so

4 and -4

[brittle field]

do i just plug in the 4 and -4 for x?

ive never used alpha or beta idk if this is what im supposed to do

[vagrant elbow]

hmm

[brittle field]

i need solution when function is greater than 0

[vagrant elbow]

just put 4 and -4 in place of alpha and beta

$(x - 4)(x + 4) = 0$

[wraith dagger]

NEONPerseus

[vagrant elbow]

this would be the equation of that graph