help-26

[craggy haven]

you want the exact number

not 1.167

[neon iron]

what is P

[craggy haven]

P is the point of intersection between the line and the parabola

[neon iron]

oh

[craggy haven]

we don't know where that is yet

,calc 2*(1.167) - 8*(1.167)^2

[thorny flame]

Result:

-8.561112

[craggy haven]

i don't think the curve intersects at 1.167

[neon iron]

so like that line divides it into even parts

[craggy haven]

yeah

[neon iron]

wow I wish I had a math brain fr

visualizing and failing makes me wanna rush it

I have no idea how to set this up

maybe I can find the area for the whole thing and divide by 2

thats the only way i can think of

[craggy haven]

that's a good start! that gives you a target

how would you find the green area, for example?

[neon iron]

well if I knew what that p line was I would do top function minus bottom function

but idk what p is

which kind of sucks

and ofc integral it

[craggy haven]

we don't know where p is

but if you notice i said that the x value of p was located at a

so what's the y value of P?

[neon iron]

A is like the x value

okay okay

hmmm

how to find y using the x value

the y value is p(x)

?

[craggy haven]

hint: the point P is on the line, but it is also on the parabola

[neon iron]

do you have to make two things equal to each other?

[craggy haven]

let me make this slightly simpler for you

the point P is at (a,b) and it is on the parabola y = 2x - 8x^2

what is b?

[neon iron]

b is y?

like

I apologize if Im giving u a headache

I see the a is on the x spot so thats why i said b is y

[craggy haven]

yes b would be the y value

now

if x = a

[neon iron]

so if you want to find b you should plug in a into all the x values

[craggy haven]

yes

so the line passes through the origin and P

do you think that's enough to find the equation of the line?

[neon iron]

yes why not

[craggy haven]

okay

so do you think you can find the area of that green region?

[neon iron]

tbh no because I know ab that equation but idk how to use it to find certain spots

like section it off

[craggy haven]

uh

did you say you had an equation for the line?

and we know we have an equation for the parabola

so.... we should be able to find the area between two curves

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[twilit robin]

I'm sure I know how to solve it I just forgot what the method is (this is like some precalc practice thing in calculus before the semester begins)

[twilit robin]

Long division maybe is it?

Idk

[vivid flame]

do you see any common factors you can factor out right off the bat?

[twilit robin]

x

x^2

?

[vivid flame]

yep thats one

you can also factor out a 2

[twilit robin]

Ohhhhh

Okay so 2x^2

[vivid flame]

so try to factor out 2x^2 from 2x^4+2x^3-112x^2

yep

[twilit robin]

2x^2(x^2+x-66)?

wait

56

[vivid flame]

yep

[twilit robin]

So then its 2x^2(x+8)(x-7)

[vivid flame]

yep, great job :D

[twilit robin]

Awesome

Okay now for this one

My brain is thinking of adding a 0x but that again might be long division or something else

I think I'm thinking about these factoring problems wrong

Cuz the rest havent given me any trouble

[vivid flame]

its not a good habit to jump right to long division, think about difference of squares

[twilit robin]

yeahhhhh

Hmm

Yeah I can see they're both squares now that u mention difference of squares actually

Lemme see if I remember how to do that

[vivid flame]

ok 👍

[twilit robin]

This is how its done right?

Like the method

[vivid flame]

yep :)

[twilit robin]

Sick

Now this one

The last one that's been tricking me

but now that you've reminded me of the others

my brain says long division or factor out the x

and my brain now says factor out the x

and then I have it

is that right

then I can factor the top

[vivid flame]

factoring the x would be only part of the solution, you must fully factor the numerator and denominator

[twilit robin]

and the denominator would be x+6 so a zero

Here lemme just do it]

[vivid flame]

oki

[twilit robin]

x goes on the outside of the fraction right?

[vivid flame]

not quite, just focus on factoring the numerator and denominator for right now, then send me your result

[twilit robin]

So something like this

?

[vivid flame]

yep, now we can see what can cancel

[twilit robin]

x(x+6)?

[vivid flame]

perfect

canceling those will leave you with what?

[twilit robin]

(x+7)

[vivid flame]

great job

[twilit robin]

Awesome thanks for the help

[vivid flame]

no prob

[twilit robin]

.close

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[prime forge]

Any tips

[prime forge]

don't even know where to begin

[drifting swift]

this is stars and bars with some modification

but also point value

is this a test?

[topaz sinew]

@prime forge Has your question been resolved?

[gentle night]

Yep
I think it is not correct to solve it unless he showed that he solved it wrong or correct or something like that.

[prime forge]

it's a practice quiz/paper paper @drifting swift

[drifting swift]

ok

do you know stars and bars generally

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[prime forge]

.reopen

[topaz sinew]

✅

[prime forge]

nope

is that a method?

counting method

[drifting swift]

yes

though there are a couple of wrinkles that need to be worked out before it can be applied here

[fossil coyote]

Basically grouping identical stuff in distinct groups

[drifting swift]

namely the "visited each country at most twice" bit

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[fierce shuttle]

Hello im trying to calculate the percentage of time increase

[fierce shuttle]

like comparison of times

and see what percentage of one time is another

for example i have 144,000 seconds

and a faster process is 15,120 seconds

what is the percentage of time decreased

[drifting swift]

15120 is how many % of 144000?

[fierce shuttle]

yes

[drifting swift]

this wasn't a yes/no question.

[fierce shuttle]

im not sure how to solve

[drifting swift]

do you know how percentages work in general

[fierce shuttle]

0.10 is 10 percent

100.00 is 100 percent

25 is 25% of 100%

[drifting swift]

one of these is bad + this does not answer my question

ok no

[fierce shuttle]

so nah i guess not

[drifting swift]

15120 is what fraction of 144000?

[fierce shuttle]

144000/15120? right

[drifting swift]

no, you have that the wrong way around.

,w simplify 15120/144000

[thorny flame]

Results provided by WolframAlpha

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Requested by ann_dec

[drifting swift]

15120 is 21/200 of 144000.

or to put this another way, it is 21/200 * 100 = 10.5 percent of 144000.

[fierce shuttle]

that makes sense

[cold wagon]

help me with a quadratic equation

[fierce shuttle]

so its 10.5 percent of 144000

[drifting swift]

please open your own channel. read #❓how-to-get-help for instructions.

[drifting swift]

so the reduced time is 10.5% of the original time

[cold wagon]

okay.

[drifting swift]

by how many percent was the original time reduced?

[fierce shuttle]

89.5?

i believe

[drifting swift]

well 100 - 10.5 = 89.5 of course what else could it be

try to not second-guess your own arithmetic so much

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[grim swift]

GUYS

If i Divide whole equation with this form of form

is it actually

making the exponent negative?

so then I just do like that?

or

like division makes it reciprocal so it make exponent negative just

[half edge]

$\frac {eqn}{(\frac wr)^{\frac 13}}$

[thorny flame]

Stephen

[half edge]

This?

@grim swift

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[tropic gull]

how do i do this

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[tropic gull]

<@&286206848099549185>

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[molten geyser]

i was just working on some problems and came across a problem which told me to write down the interval where |x-6| was differentiable. I don't know why I got it wrong. did i do interval notation wrong? what's going on?

[molten geyser]

nevermind i am a dumbass

.close

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[dim panther]

I have the equations of the lines

How to find the coordinates of vertices of the triangle?

[frail fiber]

ok

[dim panther]

Help pls

[frail fiber]

assume you have to two lines..either they would intersect or they won't right?

[dim panther]

Hmm

[frail fiber]

okay now tell how would you find whether they would intersect or they won't

[foggy bronze]

Solve two lines simultaneosly by elimination or substitution method so you will get the point of intersection the lines that will be the verex of triangle

[frail fiber]

?

[dim panther]

If they intersect they will have a common point

[frail fiber]

okay..now you have 3 points..let's assume all will intersect each other

[dim panther]

I did that but I think I am getting the wrong vertices

[frail fiber]

now take any 2 at a time to find those intersection points

show your working then

[dim panther]

I can't understand

They have given the equation

I need to find the points

[frail fiber]

yes you have 3 equations..take any 2 at a time which will lead you 3 possibilities and will give you 3 intersection points

[foggy bronze]

find coordinates and put it in the formula of Area of triangle

[frail fiber]

brother slow down..let this person find out the points first

[foggy bronze]

Okay okay

Btw can u help with my qs?

[frail fiber]

open a different channel

not here

[foggy bronze]

ive done alrdy snce 11:03

[dim panther]

I did the substitution method

[dim panther]

I got a as (-5,0) when I put y as 0 in the equation x-2y+5

Then I found coordinates of B using substitution method

[foggy bronze]

ur ans are wrong

[dim panther]

I know

Where am I going wrong

[frail fiber]

recheck your calculations my friend

do it slowly and accurately

[foggy bronze]

see your B and C vertex are righ

right*

[dim panther]

Oh shi

I found my mistake

I will do it again

Nooo

[dim panther]

Wbu A

[foggy bronze]

Thats only wrong

[dim panther]

Which equations should I use

To find A

[foggy bronze]

which u used for B?

dont write whole eq

[dim panther]

Bc and ca

[foggy bronze]

say it as 1 / 2 /3

[dim panther]

1 and 2

[foggy bronze]

and for C

[dim panther]

2 and 3

[foggy bronze]

so which remains?

[dim panther]

So for A
1 and 3?

[foggy bronze]

yup

[dim panther]

Noice

Thanks bro

[foggy bronze]

No worries

got the ans?

[dim panther]

I got the coordinates of A as

(3,4)

[foggy bronze]

ok

now find the area

[dim panther]

Ok

I got the right answer

Thank you

[foggy bronze]

No Worries

[dim panther]

.close

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[strange estuary]

i do not understand this solution at all

can someone pls take me thru it

[halcyon slate]

the last one?

[strange estuary]

all the parts

a.b,c

[halcyon slate]

ehh... I'll just tell you the logic and I hope you can take it from there

first things first

do you know the definition of an odd and an even number?

@strange estuary

[strange estuary]

odd isn't divisible by 2, even is divisble by 2

[rough plover]

2p-1 and 2s-1 are forms of odd numbers, adding them together gives 2(p+s-1), and since p+s-1 is an integer then 2(p+s-1) is even

[halcyon slate]

yeah but you need to elaborate more

so here the definition they're using is that a number (positive integer) is even if it can be written as 2 times another positive integer

and an odd number is 1 less than 2 times something hence 2p - 1 or 2k -1 or 2 "something" - 1

then just add things and see the form of the new number

[strange estuary]

ahh okay

so when I get 2 (P-1+s) how do I know its even?

ahh nvmm

[halcyon slate]

cause it is of the form 2 times something

[strange estuary]

im too dumb

thank u very muchh

[halcyon slate]

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[supple rampart]

need confirmation for third part

[supple rampart]

I got rank as 4 and nullity as 4

but in the answer given at the end of assignment it says rank = 6 and nullity = 2

as you can see here

this is the answer given

but I got different range space
I got it as span of {(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, -1)}
i just wrote the matrix in tuple form but you can understand

ping me if you answer

[exotic meadow]

what linear transformation is this in relation to?

there is no (iv) on the first screenshot

is it for (iii)?

if so can you clarify what img(c) means

[supple rampart]

if you have a + ib then the img of that complex number is b

[supple rampart]

what do you mean

[supple rampart]

yes I said third part

[exotic meadow]

okay

consider a basis for $M_{2} (\mathbb{C})$

[supple rampart]

it would have 8 basis over R

[thorny flame]

swifteeee

[exotic meadow]

right

[supple rampart]

I mapped all of em

[exotic meadow]

oka

y

which 4 do you claim end up in nullT?

[supple rampart]

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
i 0 0 0
etc
etc
these are matrix in tuple form if you get what i mean

[exotic meadow]

no

can you please tex

[supple rampart]

hm how do i write matrix in tex

can I take a photo and send it

[exotic meadow]

look it up

https://www.overleaf.com/learn/latex/Matrices

[supple rampart]

the third column, fifth, sixth and eigth span null space of transformation

[exotic meadow]

only two of the basis vectors were mapped into null T

per your picture

[supple rampart]

no

4 of them were

[exotic meadow]

i only see $$\begin{pmatrix} 0 & 0 \ 1 & 0 \end{pmatrix}$$ and $$\begin{pmatrix} 0 & i \ 0 & 0 \end{pmatrix}$$

[supple rampart]

the rank of matrix representation here is 4
its impossible to have only 2 dimension of null space

it would fail rank nullity theorem

[thorny flame]

swifteeee

[exotic meadow]

dim rank T isn't 4

it's 6

[supple rampart]

how'd you find that out

[exotic meadow]

6 of the basis vectors aren't mapped onto the 0vector

[exotic meadow]

because 2 of the basis vectors are mapped to the 0 vector

this is what your calculations show

[supple rampart]

I only see 4 pivots
infact, its impossible to get 6 rank here
there are only 4 rows so maximum rank it can achieve is 4

[exotic meadow]

we're working with complex matrices remember

regardless, focus on my argument

a linear transformation is uniquely determined by what it does to the basis vectors

[hot furnace]

it's easier to just find the kernel, and then use rank=dim(domain)-nullity

[exotic meadow]

it sends 2 of the basis vectors to nullT

so by linearity dim null T = 2

rank nullity implies that dim range T = 6

[hot furnace]

so we want
$$\m{\bar a&\Re(b)\\Im(c)&-\bar d}=\m{0&0\0&0}$$

[supple rampart]

how is that possible tho? if only 4 rows exist then at maximum you can only have 4 pivots

[thorny flame]

tutor named finger (nix)

[supple rampart]

that means only 4 linearly independent columns at maximum you can have

[hot furnace]

right?

[supple rampart]

right

[hot furnace]

okay. so if $\bar a=0$, then what must $a$ be?

[thorny flame]

tutor named finger (nix)

[supple rampart]

0

[hot furnace]

correct. so a has to be zero.

[supple rampart]

yeah

[hot furnace]

using this same logic, what must d be?

[supple rampart]

0

[hot furnace]

yes

[supple rampart]

so thats 4 dimension actually

since our field is real numbers here

[hot furnace]

that's true

the real vector space of complex 2x2s is 8 dimensional

alright, now if $\Re(b)=0$, then what must $b$ be?

[thorny flame]

tutor named finger (nix)

[supple rampart]

and even if we try to understand our matrix representation here, its not possible for nullity to be less than 4
because if nullity is less than 4 then that means rank is more than 4
but it can't be the case here as we have only 4 rows

0 + iu

i think

[hot furnace]

yes. the real part must be zero, but the imaginary part can be anything

[supple rampart]

yeah

[hot furnace]

so $\opn{span}\bdef{\m{0&i\0&0}}$ is in our kernel

[supple rampart]

yes

[thorny flame]

tutor named finger (nix)

[hot furnace]

so then, using similar logic, if Im(c)=0, then what other vector is in our kernel?

[supple rampart]

$\opn{span}\bdef{\m{0&0\1&0}}$

[thorny flame]

thus spoke zarathustra
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[supple rampart]

oof

can i write it in tuple form

[hot furnace]

i have a lot of custom commands lol

i see what you meant though. $\m{0&0\1&0}$

[thorny flame]

tutor named finger (nix)

[supple rampart]

yeah

[hot furnace]

for future ref, the latex for that is
\begin{pmatrix}0&0\\1&0\end{pmatrix}

[supple rampart]

alright, thanks

so we got these 2 vectors that span null space

[hot furnace]

but anyway. so yeah.
$$\ker(T)=\opn{span}\bdef{\m{0&i\0&0},\m{0&0\1&0}}$$
so what is the nullity of $T$?

[thorny flame]

tutor named finger (nix)

[supple rampart]

well nullity would be 2

[hot furnace]

right

[supple rampart]

and therefore rank must be 6

[hot furnace]

exactly

[supple rampart]

but this is the doubt im having
according to the matrix representation we create
we can't exceed the rank of 4 but here we did

this is the matrix representation i got btw

[hot furnace]

A should be 8x8

since the dim of the domain and codomain are both 8

[supple rampart]

hm yeah you're right

[hot furnace]

this is why i just did it directly without trying to find a matrix. because it'd be way too much writing

[supple rampart]

did I make a mistake somewhere

according to my matrix its mapping an 8 dimension to 4 dimension

[hot furnace]

if you want these commands to work btw you can paste this in #latex-testing or something

,preamble --add
\newcommand{\m}[2][p]{\begin{#1matrix}#2\end{#1matrix}}
\newcommand{\opn}[1]{\operatorname{#1}}
\newcommand{\bdef}[1]{\left{ #1\right}}

[hot furnace]

yes. this is a linear operator, so it wouldn't make sense for the dimensions to differ. the matrix should be square

i.e. its a map from a vector space to itself

[supple rampart]

could you figure out where I made mistake? because i just wrote elements of the each matrix in each column

oh my dumbass

i directly wrote the matrix in column form

I forgot you had to write the map in linear combination of the domain bases

thats the mistake i made

damn my bad guys im kinda dum

[hot furnace]

it'd be more accurate to say you have to write the images of the domain basis vectors as a coordinate vector with respect to the codomain's basis

[supple rampart]

right

thanks again tutor named finger (nix)

[hot furnace]

lol just nix is fine

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[silk beacon]

Would I use combination or permutation to solve the highlighted question?

[molten raven]

Does the order of the number matter?

Eg. does 123=231?

[silk beacon]

Well it doesn't specify that so Im assuming not

[molten raven]

So does the order of the digits matter?

[silk beacon]

Nope

[molten raven]

Uh it does, because 123 isn’t equal to 231, if we change the order of the digits we get a new number

[silk beacon]

Oh

So I would use permutation since order matters?

[molten raven]

Yes

[silk beacon]

Alright thanks so much

.

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[tropic zephyr]

Why does this work?
https://youtu.be/d7DKFsH_0xg?feature=shared

[balmy ruin]

Is there a specific part you're confused on?

[tropic zephyr]

No I'm just curious why it works

[balmy ruin]

It looks like it's primarily because of the use of u-substitution and that technique of making an indefinite integral definite

both general techniques useful for solving an integral

[tropic zephyr]

I wouldn't have ever thought of that before

[tropic zephyr]

Is there a way to apply this to other equations or this just a special case

[raven sparrow]

Not this method in general. At the end of the day, all they did was rewrite the original equation through a clever integration, but I doubt this is applicable directly to any problem.

One thing this reminds me off is that while doing integration (especially for trigonometric functions), you can easily derive very intricate identities if you take two different approaches to the integral (say, doing u-sub for sin and solving, then trying to u-sub cos ans solving).

[tropic zephyr]

What other ways can I solve algebraic problems using calculus, i know it sounds overkill

[raven sparrow]

Hmm

Well one example I guess could be using generating functions to solve recurrence relations. This is a pretty interesting bridge between calculus and counting problems.

Other than that, you might want to search online to find some other examples. I know Michael Penn does a series called overkill where he solves problems using complicated methods https://www.youtube.com/watch?v=RK1DewTkKT8&list=PL22w63XsKjqx8nFAU8ew8-YM2YOOClNGw

Idk if this links the whole playlist

[tropic zephyr]

That's interesting. Yeah I watch Michael penn everyday lol

But thanks for the explanation I just wanted to find other ways to solve problems

I still dream of solving sinx/x integral by myself

from 0 to inf

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[neon iron]

i need help

[leaden tusk]

don't we all...

[empty sail]

Then send your question and wait for help to come

[ember lodge]

?

[neon iron]

one sec

[neon iron]

150,000/(1+0.04/6)^6=4,126

is it set like this

@ember lodge

[ember lodge]

Simple interest

not compound interest

the principle is 15000

the interest rate is 4%

and 6 years

[uncut gale]

uh are you sure

[ember lodge]

let me see

[uncut gale]

i dont think the principle is 15000

[ember lodge]

the present value

[neon iron]

this

[uncut gale]

ur looking for the principle

[ember lodge]

wait lol

ok

[uncut gale]

I = PRT and ur looking for P so just make P the subject

[ember lodge]

so let P be the principal

P * 4% * 6

15000 is the interest?

or the total amount?

I bet it's amount

[neon iron]

so PxRxT

[ember lodge]

so P(1 + 4% * 6) = 15000

[ember lodge]

ys for interest

cuz idk 15000 is interest or amount

[neon iron]

so theres no to the power when computeing simple interest

[ember lodge]

ys

The differences

[neon iron]

so in this case 15,000 x 0.04 x 6

[uncut gale]

why are you doing 1 + 4%

[ember lodge]

ys if 15000 is the interest

[ember lodge]

cuz my english is bad, idk 15000 is interest or amount

[uncut gale]

15000 is the interest

and since the formula is I = PRT and all u have to do is solve for P

you can just sub in the info you already have

15000 = P * 4% * 6

[ember lodge]

oi, thx

[neon iron]

so is the form currect

[uncut gale]

mhm then just isolate P from there by diving both sides by 4% * 6

[uncut gale]

this is in the form i = prt

[neon iron]

so 15,000 x 0.04 x 6?

or 15,000 (1+0.04+6)

[uncut gale]

no

[uncut gale]

you understand how i got here yes?

[neon iron]

the princibal ie the money invested times the rate and times the time

@uncut gale

[uncut gale]

no its the other way

the interest is equal to the principal x rate x time

I = PRT

following?

[neon iron]

1,000 * 5% * 3 its a exanple i found then you divied by 100?

[uncut gale]

wait dont go too far ahead

wait wait

[uncut gale]

that finds the interest

we aren't looking for the interest

just let me finish

you understand that the question needs us to use simple interest right?

[neon iron]

yes

[uncut gale]

okay

now

lets sub in

all the info we have

the rate is 4%, its invested for 6 years, and we need to have 15000 in interest money

so when you sub it in to our formula I = PRT

what do we have

[neon iron]

should i convert the 4 percent to a decimal

[uncut gale]

if you want

it doesn't matter

[neon iron]

15,000x0.04 x 6

[uncut gale]

no

very close

but the 15000 isnt the principal

[neon iron]

so its just 0.04x6

[uncut gale]

the question is asking how much money do we need to invest in order to gain 15000 as interest money

[neon iron]

ohhh so its just 0.04 times 6

[uncut gale]

we're given one more value

nope

I = PRT

you've entered the R and the T

so you have I = P * 0.04 * 6

but you need to sub one more value

[neon iron]

i'm stumped

[uncut gale]

okay

lets start from the beginning

what's the question asking us

[neon iron]

to find what you need to invest in order to get 15,000

[uncut gale]

yes

that's good

knowing that we are investing money in order to get 15,000

is the 15,000 our principal

or our interest

remember that:
Principal = the money you invest in order to gain interest
Interest = the money you gain after you invested money

[neon iron]

so at this point in the problem we cant not use our prinsibal since thats our target to make

[uncut gale]

exactly

yes

good

so we have I = P * 0.04 * 6, where does the 15000 go if our target is to find the principal

[neon iron]

it goes before the formuila we are building

[uncut gale]

so do i replace the 15000 with I or P?

[neon iron]

with i

[uncut gale]

yes

perfect

15000 = P * 0.04 * 6

now we have to isolate P

how do we do that

[neon iron]

simplfy the formuila by multipleing them together the 0.04 times 6

[uncut gale]

okay we can do that

15000 = P * 0.24

then what

[neon iron]

you dived both sides by 0.24

[uncut gale]

P = 15000/0.24

then simply evaluate

,calc 15000/0.24

[thorny flame]

Result:

62500

[uncut gale]

and that's it

so we need to invest $62500 and after 6 years with a 4% interest rate

we get $15000 interest

[neon iron]

and thats the final equasion?

[uncut gale]

yep

I = PRN

15000 = 62500 * 4% * 6

[neon iron]

is this part correct?

[uncut gale]

ye

that works

[neon iron]

how did you get rid of the 1.44

[uncut gale]

what 1.44

[neon iron]

my bad sorry

[uncut gale]

okayy

anything else?

[uncut gale]

okay our first step

is to identify which part of the table we need to use

firstly which column do we use

single, married filing separetly, etc

[neon iron]

married/filling jiontly

[uncut gale]

good

now what's the tax rate?

[neon iron]

24% for the money they earn

[uncut gale]

good

their gross income is 180,000

so what's the tax

[neon iron]

12% of there gross income

[uncut gale]

what

[neon iron]

do you mean the satdered decutsion

[uncut gale]

no not yet

thats later

if they earn 180,000 and they get taxed 24% of that, how much do they get taxed

[neon iron]

you would first dived the percentage by 100 to get it converted into a decimal

[uncut gale]

i mean if you wanna do that sure

then what

[neon iron]

then subtract from the gross income with that decimal percantage

[uncut gale]

subtract?

[neon iron]

what do you do in that step

[uncut gale]

you earn 180000

24% of that is taxed

you converted the 24% to 0.24

what do i do next

if i subtract it all i'll get is 180000-0.24

[neon iron]

you dived 18,0000 by 0.24

[uncut gale]

good

well you mean 180 000

wait no

not division

[neon iron]

yes

what form

[uncut gale]

24% of 180000

do you know what "of" means in maths?

[neon iron]

no

[uncut gale]

of means

to multiply

for example

50% of 2 is 1

because

50% * 2 = 1

0.5 * 2 = 1

[neon iron]

so it would be 180000 x 0.024

[uncut gale]

not 0.024

[neon iron]

keep it as 24

[uncut gale]

no what you said before was right but you changed it to 0.024

you changed 24% into a decimal, but 24% isnt equal to 0.024

[neon iron]

so do we multiply the p with the rate

[uncut gale]

this isnt interest formulas

all you need to do as of now

is find 24% of 180000

since they earn 180,000 and get taxed for 24% of that

[neon iron]

so would you dived 180,000 with 0.024

[uncut gale]

not divide

[neon iron]

how then

[uncut gale]

i explained that "of" means multiply

and your doing 24% of 180000

[neon iron]

so 0.024 times 180000

[uncut gale]

again, 24% is not 0.024

if you change 24% to a decimal you get 0.24, not 0.024

[neon iron]

i mean 0.24 x 180000

[uncut gale]

yes

good

now lets calculate that

[neon iron]

sorry i had other formuilas in the briain

[uncut gale]

,calc 0.24 * 180000

[thorny flame]

Result:

43200

[uncut gale]

no worries

happens all the time

so now we get taxed 43200

but

the question asks us to use a standard deduction

so how much is standard deduction

knowing that the gross amount is 180,000

[neon iron]

25,100 is the satdered decutsion

[uncut gale]

good

now we add our standard deduction and the amount taxed

,calc 25100 + 43200

[thorny flame]

Result:

68300

[uncut gale]

and thats the total amount taxed

so that's how much they owe

[neon iron]

can i show anuthor one

[uncut gale]

yeah

sure

[uncut gale]

so its asking us how much we have to pay in interest

so we have to find two numbers here

our first one

wait

the question isnt specific enough

[neon iron]

theres 3 veribles p t r

[uncut gale]

is the 1.5% assuming per year or per month?

if it doesnt state it

then

[neon iron]

i think assumeing the rate is staying at 1.5 for the entire 5 months

and theres no mension like at end it will change to x rate

[uncut gale]

oh wait no i got everything confused

okay

simple interest formula

i = prt

we're looking at how much interest

we need to pay

so our target is i

we are given p, r, and t

[neon iron]

so isolite i

[uncut gale]

its already isolated so that's all good

input our other values

[neon iron]

p=8,000 r= 1.5 T=5

[uncut gale]

hmmm

remember that i = prt

in this formula

t is the number in years

we are given 5 in months

so we have to convert 5 months into years

how would i do that?

[neon iron]

give me 4 mins ill brb

[uncut gale]

alr ping me when ur back

[neon iron]

@uncut gale

[uncut gale]

sup

[neon iron]

how meny years does the conversion need to be in

[uncut gale]

its just 5 months

into years

like 12 months is 1 year

do you know how we can solve that?

[neon iron]

would it be like 12/5

[uncut gale]

close

other way around

[neon iron]

5 dived by 12

[uncut gale]

there are 12 months in a year

so each month is 1/12 of a year

we have 5 months so its 5 months / 12 months in a year
= 5/12

[neon iron]

so it would be 5/12

[uncut gale]

yep

so i = prt

i = 8000 * 1.5 * 5/12

,calc 8000 * 1.5 * (5/12)

[thorny flame]

Result:

5000

[uncut gale]

damn clean answer

[neon iron]

how cani keep this open so i can refer back to it

[uncut gale]

just close it for now, then u can open another help if you need more help

[neon iron]

can i copy the answers before closing it

thank you btw @uncut gale

[uncut gale]

sure as long as you understand

the steps taken

[uncut gale]

yw

[neon iron]

what went wrong here

@uncut gale

i sort of failed my quiz

@uncut gale can i ask what went wrong with our forms

[uncut gale]

wait im reading

oh sorry my mistake

its meant to be 1 + 0.24

15000/1.24

= 12096.77

[neon iron]

i sort of failed my quiz

[uncut gale]

show what else?

i mightve forgotten to account for the initial principal amount

[neon iron]

nearly all of them

i got 2 out of 5

[uncut gale]

show me the other omes

ones*

[uncut gale]

ye sorry shouldve been FV = PV(1 + (r * t)) for the previous question my apologies

hm

for this question

im a bit confused

but you might have to

apply each tax rate to the respective income range

then add them up

[uncut gale]

ah i think i got it

here

calculate the tax rate for each bracket up until the money you have right

its 180,000 minus standard deduction

154,900

then apply each tax rate there

sorry i have to be right back but my mistake for that

[neon iron]

so i should have just used the sat decuctsion automaticlly since the number had alreddy been calulated for me

[uncut gale]

nono

the questions a bit weird

first, apply standard deduction

180000 - 25100

154900

THEN we have to apply each tax rate

so for the first 19,900 of your 154900, you apply 10% tax rate

[neon iron]

we get the rate rate from the sat deductsion

[uncut gale]

nope

[neon iron]

where do we get the tax rate from agin?

[uncut gale]

you apply all of them

haha its hard to explain

im thinking about how to explain it

so you know the 180,000 is the gross income

right

[neon iron]

yes

[uncut gale]

apply standard deduction to get 154 900

now

for the first 19,900 of that 154,900

we apply 10% tax

,calc 154900-19900

[thorny flame]

Result:

1.35e+5

[uncut gale]

now for the next 61149 of 135000

,calc 81050-19901

[thorny flame]

Result:

61149

[uncut gale]

we apply 12% tax

does this make sense? or not really

[neon iron]

not really

[uncut gale]

in other words

ok how about

[neon iron]

lost me how you form the percentage of p

[uncut gale]

u understand the deduction bit right?

[neon iron]

yes

[uncut gale]

we have to calculate the tax per each tax rate

bracket

so we use the 10% tax rate until we reach the next bracket

the bracket ends at 19 900

so we find 10% of 19 900

[neon iron]

dived 10 by 100

[uncut gale]

then we use the next tax bracket

which is 12% of income from 19 901 to 81050

then we use the next tax bracket

and u keep on doing this

until u run out of money

sorry i got these questions wrong btw finanical isnt really my strong suit

[neon iron]

i should have asked before i took the quiz for my last attapt

[uncut gale]

do u understand this?

[neon iron]

not really its not really close to the formuila i got for the homework and what i was thought even that form is wrong

[uncut gale]

whats the formula u got for the hw

okay lets think of it this way

ill give a much simpler example

lets say ur income is $20

lets pretend this our tax table

we'll use the standard deduction of $2

so our income is now 18 dollars

now we use the tax table

so out of our 18 dollars

dollars 1 to 5 will have 10% tax = $0.5
dollars 6 to 10 will have 15% tax = $0.75
dollars 11 to 18* will have 20% tax = $1.60

*because 18 is all the money we have

so our tax is 0.5 + 0.75 + 1.60 = $2.85

now if that makes sense

you can try applying the same thing to the other question

out of our 154,900

dollars 1 to 19 900 = 10% tax rate
dollars 19 901 to 81 050 = 12% tax rate
dollars 81 051 to 154 900 = 22% tax rate

hope that makes sense

@neon iron

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

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[neon iron]

is it allowed to do u substitution while ur integrating by parts?

[neon iron]

i have a problem im unsure about

[drifting swift]

well probably not at the same time unless you like getting yourself into a royal mess

but like if you do IBP then substitution, or vice versa, that's perfectly fine

[neon iron]

ok i got the right answer with that on another question even tho my teacher said thats the wrong way

can u help me with this question?

i got wrong answer by a lot

wait i already see one mistake

i did not correctly substitute the k back in

but the answer will still be wrong i think

[drifting swift]

first ibp looks messed up

you integrated du and not v du

you would have to be left with x ln^2(x) - 2 int ln(x) dx actually

[neon iron]

ah yea i saw that as soon as u mentioned the first part messed up. let me try to do it again

oh no

i lost a negative somewhere

everything else is right though

I don’t know what I missed

Can u take another look

@drifting swift

[drifting swift]

-2(-x) = +2x

[neon iron]

o my got

i forgot to distribute negative

thx

.close

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[weary plinth]

How do you use null factor law to find the value of X halfway between for example 0=(x-2)(x+2)

[jade thunder]

What’s the null factor law

Actually hold up

[weary plinth]

For quadratics

[craggy haven]

zero product

[jade thunder]

What does “X halfway between” mean

[weary plinth]

I’m not sure that’s what the question says

[jade thunder]

Yeah I know what it means I wanted you to explain it

Show the original question

Like take a picture

[weary plinth]

Question 2

[jade thunder]

Great wording mister author

(It’s bad)

[craggy haven]

could be mrs author instead

[jade thunder]

But I suppose it just means find the average of the 2 x values

[weary plinth]

The answers say 0 btw for 2a

[pseudo bear]

They want you to find the roots and the average of the roots.

[weary plinth]

But idk how they got to it

[jade thunder]

Well let’s first use the null factor law on 2a

What does the null factor law tell us?

[weary plinth]

One side equals 0

[pseudo bear]

No, it's about multiplying numbers together.

If you multiply some numbers together and get zero, the only way to get that is if at least one of your numbers was zero.

Like if you multiply 1 times 2 times 13, you can't get zero.

But if you multiply 1 times 0 times 13, you get zero.

Or 0 times 0 times 13.

Does that make sense?

[weary plinth]

Yeah what you said makes sense

But then what do I do in the question

[pseudo bear]

OK, so x - 2 and x + 2 are numbers multiplied together.

[weary plinth]

Yeah

[pseudo bear]

So, when we multiply them together, we get zero.

So, what does the null factor law tell us?

[weary plinth]

Yeah so one of them are zero right?

[pseudo bear]

At least one.

It could be both sometimes.

So, how would you use that information?

[weary plinth]

Substitute x with 0?

[pseudo bear]

No, we don't know that x is zero.

[weary plinth]

Ok so how do we know that x is zero

[pseudo bear]

We don't yet.

[weary plinth]

Nah I mean how do we figure it out

[pseudo bear]

What does the null factor law say in your own words?

[weary plinth]

I don’t know 💀

[pseudo bear]

It says that if you multiply a bunch of numbers and get zero, then what?

[weary plinth]

One of the numbers is 0

[pseudo bear]

Right, so x - 2 is zero or x + 2 is zero, right?

[weary plinth]

Yeah

[pseudo bear]

OK, so write those as equations.

[weary plinth]

Yeah I did

[pseudo bear]

OK, now solve those equations.

Isolate x.

[weary plinth]

X=2 and x=-2

[pseudo bear]

Yes, except we'd say 'or' because 'and' means it has to be all of them, and 'or' means at least one of them.

So, x = 2 or x = -2.

[weary plinth]

Bruh the answers say 0

[pseudo bear]

Right. So, we solved for x. What else does it ask us to do?

[weary plinth]

Find the value of x halfway between

[pseudo bear]

Right, so what number is halfway between 2 and -2?

[weary plinth]

Oh yeah 0

I see 😂

[pseudo bear]

OK 🙂

[weary plinth]

Love you bro

.close

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[weary plinth]

dont know how to do

Never mind I’m so dumb

.close

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[dim panther]

3x+4y=12

[dim panther]

Whats the x intercept?

[calm jackal]

The x interceptis where the graph touches/crosses the x - axis

._.

[dim panther]

Orange

Yes

Ohh so I put y=0 in the equation

Noice

Thanks

.close

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Channel closed

Closed due to the original message being deleted

[icy echo]

Idk what to do

Um

Do I redo this cause I think the channel is closed

[craggy haven]

yeah

don't delete the original message next time hehe

[icy echo]

Alr