help-0

[rapid gate]

i know that int of 3x^2 is x^3

but -1/x^2 i have no idea

[ocean hawk]

write it as -x^(-2)

[lone heart]

@rapid gate Has your question been resolved?

[ionic coyote]

hi! @rapid gate are you familiar with indice laws?

[rapid gate]

hi im back

[ionic coyote]

helloo

[rapid gate]

sorryyyyyy

i

hi

[ionic coyote]

so the second point on the left column

is the one you wanna be focusing on

[rapid gate]

haha i always forge them :D

ok

[ionic coyote]

no worries :D

[rapid gate]

-1/x^2

is

[ionic coyote]

yep!

[rapid gate]

-x^-2

[ionic coyote]

yes!!

[rapid gate]

ok and so then

by power rule

its

[ionic coyote]

gee i didnt even have to say anything haha, good job!

[rapid gate]

-x^-1/-1

which is

x^-1

i think

what about smth like

x^1/2(x)

$x^{\frac{1}{2}}(x)$

[ocean seal]

LW

[rapid gate]

,w x^(1/2) *(x)

[ocean seal]

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[rapid gate]

o?

[ionic coyote]

oop

sorry let me back track a bit

[rapid gate]

o

ok

i undetsand it

a^m*a^n=a^(m+n)

[ionic coyote]

so we know its $f(x) = x^3 - x^3/2$

[rapid gate]

i solved it

[ocean seal]

ZoZo

[rapid gate]

mind if i ask another?

[ionic coyote]

oh

sure

[rapid gate]

b

idk how to do fractions

i got a right w/o looking at answer

[ionic coyote]

you can change the $z^3$ into an exponent

[ocean seal]

ZoZo

[rapid gate]

into?

is it

hm

idk

[ionic coyote]

$z^-3$

[ocean seal]

ZoZo

[rapid gate]

hmmmmmmmmmm?

[ionic coyote]

the indice rule

[rapid gate]

$z^{-3}$
u mean?

[ionic coyote]

yeah

sorry

[rapid gate]

hmm

ok so

[ocean seal]

LW

[lone heart]

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[rapid gate]

.reopen

[lone heart]

✅

[rapid gate]

$\int z^{-3}\cdot\int 3z^4+2z dz$

[ocean seal]

LW

LW

[ionic coyote]

so what do you have currently? after you changed the fraction into an exponent?

[rapid gate]

im not sure

[ionic coyote]

$3x^4+2x+z^{-3}$

[ocean seal]

ZoZo

[rapid gate]

its z^{-3}

:D

uh?????????????

huh

isnt it times

isnt it

[ionic coyote]

times? why?

i havent differentiated it yet

[rapid gate]

$(3z^4+2z)\cdot(z^{-3})$

not this??

[ocean seal]

LW

[ionic coyote]

hm

😭

sorry my bad

somethings wrong with me today

[rapid gate]

o

haha

wait

by index it lwas

its jusst

[ionic coyote]

so it would be $3z+2z^{-2}$

[ocean seal]

ZoZo

[rapid gate]

$3z+2z^(-2)$

$

[ocean seal]

LW

[ionic coyote]

{} 🤭

[ionic coyote]

now you just do the power rule for this

[rapid gate]

o

[ionic coyote]

the answer should be?

[rapid gate]

uh

[ionic coyote]

oh i meant for you to solve it 😭 not show me lolll

thats fine

so we change the $2z^{-2}$ into a fraction

[ocean seal]

ZoZo

[rapid gate]

gonna have lunch

back 15mins

[ionic coyote]

ok 👍

[lone heart]

@rapid gate Has your question been resolved?

[rapid gate]

hii

[lone heart]

@rapid gate Has your question been resolved?

[lone heart]

@rapid gate Has your question been resolved?

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[void crown]

Capture-Recapture problem

My answer is always 30 when I try but the real answer is 150

I don't know how to get there though

[languid bluff]

how are you setting it up ?

[void crown]

x/n = 4/x-10

[languid bluff]

almost

basically since you know off the last statement that the lions he caught on thursday was a fifth of the total it would be

x/5x = 4/x-10

try solving that and lmk what u get

[void crown]

I got x = 30

ohhh

then 5 times 30

which is 150

[languid bluff]

yea

[void crown]

ty ty

[languid bluff]

np

[lone heart]

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[alpine sable]

Did I do the top right

Specifically 9.c

[lone heart]

@alpine sable Has your question been resolved?

[uncut mauve]

Don't believe so.

And why are you doing 4.6 x 10?

g = 10, I get that, but that's not really correct to do.

Like the downwards speed, assuming originally at rest is TimeTakenToFall x g, idea is good regarding the magnitude thing, but your vertical speed is wrong which makes it incorrect

[lone heart]

@alpine sable Has your question been resolved?

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[waxen owl]

,rotate

[waxen owl]

Does the answer for r^2 have to be plus minus 0

[lone heart]

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[remote fulcrum]

how does e^(-pi*i) = -1

[ocean seal]

guinearW

[last ether]

Like

The reasoning why?

[remote fulcrum]

is that just a rule?

haven’t learnt it yet

but what is the reasoning?

[last ether]

Bevause Euler's identity states that $e^{iθ} = \cos(θ) + i \sin(θ)$

[ocean seal]

Umbraleviathan

[last ether]

Which is due to properties of e^x

[remote fulcrum]

oh eulers form

i got it thanks

[last ether]

So if you plug θ = π

[remote fulcrum]

yup

thankyou

.close

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[molten frigate]

need help with equations

[molten frigate]

how to slove f(x) = 0 for the equation 3(x-(1/5))^2+11/6

#help-0

<@&286206848099549185>

.close

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[strong frigate]

just a question, is -2c+1/2(7-3c) equal to - 2c-1/2(3c-7)?

[vestal stag]

Yes

You can think of it as factorising -1 out of the parenthesis

[strong frigate]

oh okok thank youu

.close

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[cinder sundial]

that is indeterminated

my instinct tells me that the whole thing equals to -8

[zealous lichen]

what is f(x) though

[cinder sundial]

that is wrong right

it have to be transformed into the determinated form then we can tell the value

[cinder sundial]

that is off-topic

[zealous lichen]

how do we calculate the limit without knowing f(x)

[cinder sundial]

the f(x) is not given, it only states that f(1)=-2

[zealous lichen]

hmm

[cinder sundial]

emm

[zealous lichen]

then it looks similar to the definition of derivative

[cinder sundial]

im just to make sure my reasoning is correct

[cinder sundial]

it is

[cinder sundial]

^

[zealous lichen]

what equals -8

[cinder sundial]

that looks like (0-0) - 8

[zealous lichen]

0-0???

the 1/(x-1) becomes 1/0 though

[cinder sundial]

i will close the channel

.close

[lone heart]

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[lone heart]

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[hardy path]

Why when we multiply a number with a row or column in determinant we also take that number common but for matrices we dont

[vale wigeon]

wdym by "take that number"?

[hardy path]

Common forgot to write that

[vale wigeon]

are you looking at some worked solution rn?

[hardy path]

No

[vale wigeon]

maybe you are talking about some related but different processes or methods...?

[hardy path]

Like when multiplying a number with lets say x in determinants we write that outside the determinant as well which i get

But for matrices we don't

[vale wigeon]

sorry i really don't understand what context you're getting "for matrices we don't" from

[hardy path]

So when multiplied by x y and z we also wrote them outside the determinant

Whereas in matrices we don't write them outside is what I'm trying to say

[vale wigeon]

can you get an example for "in matrices we don't write them outside"

[hardy path]

Does my question make sense?

[vale wigeon]

well it's starting to, now.

right so

ultimately a determinant is a number

or more like

det is a function that takes matrices as input and produces numbers as output

[hardy path]

Okay?

[vale wigeon]

and it has some properties like, if you take a matrix A and scale one of its columns by c to get a new matrix A', then det(A') = c det(A)

and that's what is being done in those factoring-out steps

on the other hand the second one you showed is finding the inverse of a matrix

basically solving AX = I where A is the matrix you want to invert and I is the identity

and the way you would write that out "longform" is by a series of steps that look like "premultiply both sides by <elementary matrix>"

which you write down as elementary row operations

[hardy path]

So tldr they have diff properties!

?

[vale wigeon]

no

they are different processes entirely

saying they have different properties is like saying elephants and planets have different properties

[hardy path]

Same thing

Thank you very much kind human

For I will insert this knowledge in the upcoming test

.close

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[onyx zephyr]

how to check if this series converges?

[rose sigil]

i think it is similar to your previous ones

you can use dirichlet's test

ugh actually

no not that simple

[onyx zephyr]

yeah, that's the thing

[lone heart]

@onyx zephyr Has your question been resolved?

[rose sigil]

oh actually it converges absolutely by comparison with the previous one you did

[onyx zephyr]

i also just realised, that since 1/3^n converges and (-1)^n*sin(n)/3^n < 1/3^n, then this one also converges

but how to check if it converges absolutely or conditionally 🤔

[rose sigil]

|(-1)^n sin(n)/3^n| < 1/3^n for all n

so actually very simple lol

expected it to be more complicated

[onyx zephyr]

oh, actually right lol

[onyx zephyr]

yeah, firstly i didn't even realised because of those expectations XD

anyway, thanks for help

[rose sigil]

^_^

[onyx zephyr]

.close

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[undone mango]

Is tangent always perpendicular to the radius of a circle?

[zealous lichen]

yes

[undone mango]

In question no 42
Can we find out the equation of the radius and check its slope
If the slope of tangent and slope of radius when multipled=-1, then the line is tangent?

[zealous lichen]

sure

[undone mango]

I tried this

But ain't working

Slope of radius is 4/3

But the slopes of the lines given in option is different

[zealous lichen]

you don't have a single radius

[undone mango]

One is -3/4 But the others are 4/3,-4/3

[undone mango]

[zealous lichen]

if the tangent line touches circle at a point, we take that point and connect to center

that's the radius that's perpendicular to the tangent line

[undone mango]

Even if I check with the equation of that radius

It's not going to work

If I take y axis as tangent

The circle touches it at (0,4)

The centre is (5,4)

I got the equation of the radius

But since in the options each line has different slope I don't think so this method will work

[zealous lichen]

can you show your work

[undone mango]

I am confused why this method will not work because radius is always perpendicular to the tangent

[zealous lichen]

the equation you got

[undone mango]

Equation of the circle x²+y²-10x-8y+16=0

Centre (5,4)

[zealous lichen]

why is (2,0) not on x axis

[undone mango]

I plotted that wrong

Does it make any difference?

[zealous lichen]

what about the equation for radius

[undone mango]

From the centre to point (2,0)

That's a radius

So I get the slope of the radius as 4/3

[zealous lichen]

.

you need to find the intersection point of the tangent line and circle

that's the point to connect to center

not (2,0)

[undone mango]

That's (0,4)?

[zealous lichen]

no

it's different for differnt tangent lines

[undone mango]

Different tangent lines have different slopes

[zealous lichen]

find the point D first

[undone mango]

How am I going to find that

[zealous lichen]

set the equation of circle and tangent line be equal

for 42(1) solve 3x-4y-24=x^2+y^2-10x-8y+16

[zealous lichen]

hmm

[undone mango]

Now?

[zealous lichen]

oh you should solve 3x-4y-24=x^2+y^2-10x-8y+16=0

mb

system of equations 3x-4y-24=0 and x^2+y^2-10x-8y+16=0

[undone mango]

Solving this I will get (x,y)?

The method is too lengthy

[zealous lichen]

hmm

idk if there's faster way

[undone mango]

After I get (x y)

What should I do

[undone mango]

I found one in Google

Find the radius
Find the length of the tangent (given in options) from the centre
If both are equal, tangent
If not, no tangent

[undone mango]

But I want to know more about this method too

[zealous lichen]

wait the length of tangent is given?

if there's only 1 intersection [pint then it's tangent

[undone mango]

No we have to find that
There's a formula for it

Distance of a perpendicular line from a given point

ax1+by1+c/root a²+b²

x1,y1 is the point

[lone heart]

@undone mango Has your question been resolved?

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[twin jewel]

Hey i need

[twin jewel]

I don't get this question

[half hemlock]

No. Of tickets with the number 39/total no. Of tickets

[twin jewel]

idk what uyou mean

[half hemlock]

Don't be confused by the colours of tickets

[twin jewel]

hm

so i add all of them up and divide by 3?

[half hemlock]

Each year students have gotten 80, 75 and 90 tickets
How many tickets will have the number 39?

[twin jewel]

3

[half hemlock]

Now divide that by total tickets

That's your probability

[twin jewel]

so 90 + 75 + 80?

/ 3

[half hemlock]

The opposite

Remember in probability the total number of outcomes goes as the denominator i.e. the bottom value

[twin jewel]

0.0122448979591

[half hemlock]

No need for that

You can keep it a fraction

[twin jewel]

oh

so

3/245

[half hemlock]

If the answer requires it to be decimal just round off after 2 or 3 decimal points

[twin jewel]

ty vm

[half hemlock]

👍

[twin jewel]

I need help with this question

[half hemlock]

Never in any question do you need to go past 2 decimal values btw you can round off the 3rd

[twin jewel]

i just skipped the ones that i didn't understand

[twin jewel]

ok

how to do this one?

[half hemlock]

A,b or c?

[twin jewel]

tbh i got none of them right

last attempt

[half hemlock]

Ok so let's start with ¢

A*

Best estimate means greatest probability

[twin jewel]

ok

[half hemlock]

Take the outcomes / total outcomes for each person

That's their probabilities

Then compare the probabilities

[twin jewel]

21/80

20/50

23/70

[half hemlock]

Good now, to compare you'll need to make the denominators same

[twin jewel]

i need to fill this

so i need a number

and name

[half hemlock]

Yeah compare their probabilities find out which value is the greatest

[twin jewel]

how

lets simplify

5

7

8

instead of 50

70

80

[half hemlock]

Good

[twin jewel]

what next?

i forgot

[half hemlock]

Then find out their lcm

[twin jewel]

xD

ok]

hmm

wth its 2800

lcm

[half hemlock]

Honestly nvm

Just eyeball

You can make an educated guess

[twin jewel]

im not educated tho

xD

[half hemlock]

Try

[twin jewel]

you help

me

[half hemlock]

Look at the fractions try to visualise

[twin jewel]

i can't

[half hemlock]

And think which is the highest

[twin jewel]

im dumb

id say 20/50

[half hemlock]

That's right

[twin jewel]

almost half

[half hemlock]

Be more confident bro

[twin jewel]

ok shrek

i mean mango

mangoez*

[half hemlock]

Now for b, combine all their number of times they got 2

And calculate a total probability

[twin jewel]

how'd you do that

[half hemlock]

Do what

[twin jewel]

calculate total probability

[half hemlock]

Just calculate probability

[twin jewel]

64 times

than what

64 minecraft item cap lol

sry

[half hemlock]

Adding all the desired results / total number of spins

[twin jewel]

ok

what do you mean by this "desired results"

[half hemlock]

Desired results means whatever you are trying to calculate the probability of in any question

Here, it is the number of times spinner lands on 2

[twin jewel]

64/200?

[half hemlock]

Yes

[twin jewel]

0.32

[half hemlock]

Good

[twin jewel]

hmmm

[half hemlock]

You can answer C yourself

[twin jewel]

i got it wrong thos

[half hemlock]

Because "have" isn't an answer neither an explanation

Think

[twin jewel]

thats the only option xD

have or haven't

[half hemlock]

You can't type?

[twin jewel]

nope stupid bot

mcqs only

[half hemlock]

Is there any place to write an explanation?

[twin jewel]

i have to write on my book

:/

but that wont make a diffrence

[half hemlock]

Then how is it weong

Wrong*

[twin jewel]

which suggests the answer is wrong

[half hemlock]

Skip it then the bot is coded wrong or something

[twin jewel]

i will get detention 😦

[half hemlock]

The other two are correct

Wait a sec

[twin jewel]

i don't want to stay 50 mins after school 🙂

just for 1 question

[half hemlock]

Bruh how then

[twin jewel]

can you calculate>

?

[half hemlock]

I did

Both of the other 2 are correct

[twin jewel]

i thinks its 0.4 tbh

my gut says it is xD

[half hemlock]

Yeah write 0.4

[twin jewel]

whoops

:0

new question cuz its wrong

[half hemlock]

I GTG now

Cya

[twin jewel]

ok bye

wait

can you dm me

.close

[lone heart]

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[short crystal]

Hello, I need help with Algebra

[white turret]

nooneisrespondingmymessage.exe

first you need concept of course you do

know

so

(4/9)^(2x+4) = ((2/3)^2)^(2x+4) = (2/3)^(4x+8)

and reverse

2/3 = (3/2) ^ (-1)

so (3/2)^(-4x-8)

[short crystal]

I'm trying to process

[languid bolt]

What he's basically trying to say is:

[ \frac{4}{9} = (\frac{2}{3})^2 = (\frac{3}{2})^{-2} ]

[ocean seal]

help

[white turret]

thx

now i know how to use frac

[languid bolt]

And it's simple algebra from that point on.

[short crystal]

What's the next step?

[white turret]

that looks like this:

$[(\frac{3}{2})^{-4x-8} < (\frac{3}{2})^{3x+21}]$

whats wrong with you bot...

wait

[short crystal]

Alright

[ocean seal]

A_Note

[languid bolt]

no need the [ @white turret

i just use it as a replacement for $

[white turret]

lol

[short crystal]

Alright

Tho what's the next step..

[white turret]

ok

do you understand the concept of exponential graph?

it looks like this

[short crystal]

I'm not sure.

[white turret]

uh

then

it's very simple

there's a function

f(x) = a^x

if a>1, the graph looks like this

if a<1, the graph looks like this

i am supposing that you are here and seeing!

so

[short crystal]

I'm here yeah.

Alright, what's the next step?

[white turret]

look carefully at the graph

when a>1,

a^x1 > a^x2

-->

x1 > x2

so It is an increasing function

if a<1,

a^x1 > a^x2

-->

x1 < x2

so it is an decreasing function

[short crystal]

Alright

[white turret]

so

the given inequality

$[(\frac{3}{2})^{-4x-8} < (\frac{3}{2})^{3x+21}]$

[ocean seal]

A_Note

[white turret]

the base is bigger than 1

therefore -4x-8 < 3x+21

i'm sure that you can solve this...

[short crystal]

Alright I'll try.

[lone heart]

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[chilly sparrow]

My question is:

prove that: (cot theta + cosec theta -1)/(cot theta - cosec theta + 1) = cot theta/2

Ive got an exam tomorrow so please be fast.

I tried expressing everything in terms of sin and cos which gives:

(cos theta +1 - sin theta)/(cos theta - 1 + sin theta) but after this i have no idea how to proceed.

[dawn zephyr]

1 = cosec²X - cot²X = (cosecX + cotX)(cosecX - cotX)

substitute that in place of 1 in the numerator and then factor out (cosecX + cotX)

and no, you don't really have to express everything in terms of signs and cosines, that'll make things more complicated

[lone heart]

@chilly sparrow Has your question been resolved?

[chilly sparrow]

let me try, one sec

[chilly sparrow]

[cot theta + cosec theta -(cosec^2 theta - cot ^2 theta)]/(cot theta - cosec theta +1)

=
[cot theta + cosec theta - {(cosec theta - cot theta)(cosec theta + cot theta)}] / cot theta - cosec theta + 1

am i on the right track? what can i do after this?

[dawn zephyr]

factor out cosexX + cotX

rearrange terms first

you'll get 1 - cosecX + cotX

then rearranging terms in the denominator, it should cancel out

[chilly sparrow]

"To rearrange perform the same operations on both sides of the equals sign so that eventually this variable is by itself on the left hand side" this what you mean?

[dawn zephyr]

uhh no

wait

you have cotX - cosec X + 1 in the denominator

you can write that as (1 -cosec X + cotX)

and in the numerator

cotX + cosecX = cosecX + cotX

[dawn zephyr]

so facotring out

(cosecX+cotX)(1- cosecX + cotX)

[dawn zephyr]

and this was your denominator, these terms cancel out

[chilly sparrow]

ohhh alr got it thanks, which grade are u in btw

[dawn zephyr]

rather not say..

[lone heart]

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[flint cedar]

not sure if ive gotten the correct answer

do i just leave it as -5costheta plus c or do i sub for theta

im so confused

@lone heart

<@&286206848099549185>

[round geyser]

you found theta = arcsin(x/5)

so put it in and find the integral in terms of x instead of theta

[alpine sable]

if u got integration of 5sin(0)/5cos(0) u can make it tan theta and go for by parts
(using 0 instead of theta)

[flint cedar]

is this right

can someone send the correct answer pls

<@&286206848099549185>

<@&286206848099549185>

[alpine sable]

this one seems right

so does the second one

[alpine sable]

but ig this one will make more sense

[lone heart]

@flint cedar Has your question been resolved?

[flint cedar]

how do u know if u should integrate with respect to x or respect to theya

theta

dont understand

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@wary solar Has your question been resolved?

[lone heart]

@wary solar Has your question been resolved?

[wary solar]

.close

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[nocturne hare]

Can somebody help me do this using the method of recurrence

[exotic canopy]

is it $3^n$ or $3^m$

[ocean seal]

artemetra

[nocturne hare]

N

Both sides

Oh and n is a natural

<@&286206848099549185>

I found it

.close

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[limber geyser]

couls somebody help me with this pls

[gray dawn]

So

$(2x+a) (x+b) = 2x^2 + 11x + 5$

[ocean seal]

Alice

[gray dawn]

Expand LHS

And balance coefficients

[lone heart]

@limber geyser Has your question been resolved?

[lone heart]

@limber geyser Has your question been resolved?

[gray dawn]

So

$(2x+a)(x+b) = 2x^2 + ax + 2bx + ab$

[ocean seal]

Alice

[gray dawn]

$= 2x^2 + (a+2b)x + ab$

[ocean seal]

Alice

[gray dawn]

$a+2b = 11 \ ab = 5$

[ocean seal]

Alice

[gray dawn]

@limber geyser close the tab when you're done

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[ocean seal]

gkeocog

[lone heart]

Please don't occupy multiple help channels.

@tame cove Has your question been resolved?

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[exotic narwhal]

Just double checking, for sin i got 3/5, tan=-3/4, cot= -4/3, sec = -5/4, csc =5/3

[void nymph]

it's correct

[exotic narwhal]

Sweeet! Thank you 🙂

[void nymph]

yay lmao

[exotic narwhal]

I was doubtin myself haha

I might be back but I'll close for now, thank you for helping folks mad respect

.close

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[wraith inlet]

Question 296, I don't understand why -pi/2 +2kpi is less than and equal to x while the other side isn't greater than or equal to x.

[pliant orbit]

Do you need to plot a graph or something?

[wraith inlet]

The objective is to find the domain of the equation only in the positive regions or in the areas where it reaches 0 on the y axis

It's not necessary

looking at desmos i see that it's true i just don't understand why both aren't with the equal condition included.

[lone heart]

@wraith inlet Has your question been resolved?

[wraith inlet]

<@&286206848099549185>

[lone heart]

@wraith inlet Has your question been resolved?

[wraith inlet]

Eh, i just think it's a book error then... I have another question though.

How do i draw an equation like y=(3x+1)/(3-2x) by using limits? I forgot the concept which the teacher showed us.

[wraith inlet]

I don't know if i can ping more than once, i'll do it this time because i've waited around an hour after the first ping but please tell me if i'm also breaking a rule here since i didn't mean to. <@&286206848099549185>

[lone heart]

@wraith inlet Has your question been resolved?

[wraith inlet]

The question wasn't solved. I'll open another question though, i hope that the next time it'll be answered

.close

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[sly nacelle]

how many intersections at most can 2 triangles have on a spherical geometry

[sly nacelle]

and if a triangle loops back around on a spherical surface and passes through itself, does it still count as a triangle

[prime badge]

probably

[sly nacelle]

if we assume that the triangles that pass through themselves aren't triangles, how many intersections at most can 2 triangles have on spherical geometry

[prime badge]

if that's possible

[sly nacelle]

i'm kind of failing to put numbers to get a definitive max number

[lone heart]

@sly nacelle Has your question been resolved?

[sly nacelle]

eh looks like it will not be answered

maybe next time

.close

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[wary glacier]

could someone check if this is correct please!

[lone heart]

@wary glacier Has your question been resolved?

[wary glacier]

<@&286206848099549185>

[winged lava]

hole doesnt mean the limit doesnt exist

limit goes to infinite at -13, hence the asymptote

what about -14?

the limit is defined for x = -12, and x= -14

[wary glacier]

the question is worded strangely, i thought it was asking for either find the limit as x approaches c or prove why it doesnt exist at -12 -13 and -14 which i found confusing because it exists at -12 and -14 but not -13. so i decided to do the first part. idk if this makes sense at all

[winged lava]

it was asking to either find the limit or explain why it doesnt exist as x approaches c for those given values. so you need to evaluate 3 different limits for each value of c

[wary glacier]

what i was doing is finding the limit, because that's probably easier than evaluating for 3 different limits. was my work wrong or would it actually be easier to just evaluate the 3 limits?

[winged lava]

your working is correct, but you need to consider x = -12, and x= -13 as seperate limits. x = -13 is an asymptote, so no limit= that reasoning is valid
x = -12 is a hole, no limit -> this reasoning is wrong. evaluate the limit seperately for x = -12
then do the same for x = -14

[wary glacier]

okayy i'll do that and come back then

[wary glacier]

thank you for responding lol

.close

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[frosty geode]

Ok so before getting to this lesson I was solving matrix equations and this is the final question in this homework and I am so lost because I feel like it went from 0 to 100 real quick, or I'm just making this way overcomplicated then it actually is. I'm not sure what's going on with what's in the Parentheses on the top and how it correlates with the problem below it. Please help!

[lone heart]

@frosty geode Has your question been resolved?

[frosty geode]

<@&286206848099549185>

[north lagoon]

Why do you ping so much for helpers

It's kind of annoyin

[glacial patrol]

Bruh just take off helpers role then he followed the 15 min rule

[glacial patrol]

Err the pare theses just show it's a vector, like (1,2,3)

Is this q really that drastically different form the previous ones?

[frosty geode]

@glacial patrol I believe so yes, the previous questions did not have whatever is in parentheses above the equation. And all the ones before this had at least a few examples to follow and this one provided nothing, it's also the first question that's asked for the answer in an ordered triple

But it may also just me overthinking this problem

[glacial patrol]

well you said you've done matrix equations already

Oh

Did they already give you the matrices in the form Ax = b?

If so this is basically the same thing but you gotta figure out what A, x, and b are

after that you solve it the same way (assuming they've asked you to solve these already)

[frosty geode]

I think I'm understanding. Could you expand a little on what it means to write coordinates on terms of Z?

[glacial patrol]

For instance, you assume $z$ is fixed

[ocean seal]

992qqoloy

[glacial patrol]

And solve for the other variables in terms of $z$

[ocean seal]

992qqoloy

[glacial patrol]

well I think here the instructions p much give away that the set of solutions is at most 1 dimensional but

You could also have like, say $(x, y, f(x, y))$ where f is a function

[ocean seal]

992qqoloy

[glacial patrol]

if the set of solutions happened to be two dimensional

you'll know cus when you do gaussian elimination

If you make into RREF then the number of isolated leading terms (like, leading terms that are the only such element in that row) would be 2

[frosty geode]

@glacial patrol Thank you I appreciate your help, I'm still not understanding completely but I'll ask my professor for additional help TMR. Thank you anyway I appreciate it!

[glacial patrol]

np

[lone heart]

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[undone hornet]

I need to prove this property for the claim

[undone hornet]

With this being the other def

I am stuck on it and not sure how to prove it

Well I know that You can say that $X\subseteq \mathbb{Z}$

[ocean seal]

42

[undone hornet]

then say since $f(X)={x\in X$ and $x$ is even $}$

[ocean seal]

42

[undone hornet]

and so on

But I just don't know how to implement t hat into my proof

I need some hints on how to start

<@&286206848099549185>

[lone heart]

@undone hornet Has your question been resolved?

[undone hornet]

so im thinking opf thiis

then subbing f(X) in

then using the def 2nd def again

to finish the proof ig

ill try then send and hope someone can clarify my proof

Would this be ok?

I feel like it makes senes

[ocean hawk]

I think what you're being asked to show is $\forall X \in 2^{\mathbb{Z}}, f(X) \in 2^{\mathbb{Z}}$, right?

[ocean seal]

cwatson

[ocean hawk]

so your "suppose" should be $X \in 2^{\mathbb{Z}}$, not $X \subseteq 2^{\mathbb{Z}}$.

[ocean seal]

cwatson

[ocean hawk]

then your second line, the reason should be that it's just the definition of being an element of a power set; they're equivalent statements

and your last line would be $f(X) \in 2^{\mathbb{Z}}$.

[ocean seal]

cwatson

[undone hornet]

yeah ig, the function is $f\colon 2^\mathbb{Z} \rightarrow 2^\mathbb{Z}$

[ocean seal]

42

[undone hornet]

where the domain is $2^\mathbb{Z}$ and the codomain also being $2^\mathbb{Z}$

[ocean seal]

42

[undone hornet]

ig it makes more snese f or it to be $\in$ and not $\subseteq$

[ocean seal]

42

[undone hornet]

how can i change the proof so that the claim is valid when the codomain changes to $2^{2\mathbb{Z}}$

[ocean seal]

42

[undone hornet]

@ocean hawk

[ocean hawk]

then you'd have to show that $\forall X \in 2^{\mathbb{Z}}, f(X) \in 2^{2\mathbb{Z}}$, I think

[ocean seal]

cwatson

[undone hornet]

yeah

so the proof is fine but i change the subset to $\in$?

[ocean seal]

42

[undone hornet]

thats it ?

ill work on the other one now

[ocean hawk]

I think so

[undone hornet]

alrighty

is it ok if i ping u later on to see if my other proof is ok?

[ocean hawk]

I probably won't be on still

[undone hornet]

alr

ill close this one and ask for help if needed in another help channel then

.closae

.close

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[winged rune]

i need help
The base of a certain solid is the area bounded above by the graph of y = f(x) = 4 and below by the graph of y = g(x) = 25x^2. Cross-sections perpendicular to the y-axis are squares. (See picture above, click for a better view.)
Use the formula to find the volume of the formula.

V = ∫ b is upper and a is bottom A(y)dy
Make sure you are answering each question

1. The lower limit of integration is a=
2. The upper limit of integration is b= 4
3. The side s of the square cross-section is the following function of y =
4. A(y)=
5. Thus the volume of the solid is V =

[winged rune]

<@&286206848099549185>

[odd depot]

what value is the bottom of the parabola?

[winged rune]

no idea

[odd depot]

what value of x gives you the min value of g(x) = 25x^2

[winged rune]

uh

+-2/5?

all i managed to solve is the upper limit which is b

@odd depot

[odd depot]

2/5 is where the parabola intersects with f(x)

[winged rune]

okay

so how do i find he upper limit

[odd depot]

you mean the lower limit?

[winged rune]

yea

lower limit

[odd depot]

so it's the bottom of that parabola

what x value is that?

take a guess

[winged rune]

-2/5

[odd depot]

no

[winged rune]

2/5

[winged rune]

0?

[odd depot]

yup

[winged rune]

brah

thats so stupid

oky

how do i go about solving 3

[odd depot]

so you have the equation for the parabola

we need to find a function for s in terms of y

so start by taking the equation for y=g(x)

and solve for x

[winged rune]

so y=25x^2

[odd depot]

yeah solve for x

[winged rune]

which is just +-sqrt(y)/5

[odd depot]

right

so

[winged rune]

4-sqrt(y)/5

[odd depot]

no

so

you have the two values of x for the parabola at a given y

you can use that to get s

[winged rune]

how do i use that

[odd depot]

ok so I drew a sample value for y in orange

and the corresponding values of x

how long is that orange line?

[winged rune]

uh

no idea

oh wait

1/5

[odd depot]

no...

[winged rune]

sqrt(1)/5

yea

idk then

[odd depot]

so 1/5 is half the size of the line at the top

the line at the top goes from -2/5 to 2/5, so it is 4/5 in length

does that make sense?

no sorry

[winged rune]

4/5?

[odd depot]

at the very top

where y=4

yes

so at some random spot y, the left side is -sqrt(y)/5 and the right is at sqrt(y)/5

what is the distance between the two points?

[winged rune]

0

[odd depot]

well if y is 0, yes

but let's say it's not

it's at some unknown value y

what is the length of that orange line?

in terms of y?

[winged rune]

uhhhhhh

[winged rune]

2/5

[odd depot]

i g2g

[winged rune]

brah

pass the answer then if you g2g

i been stuck on this problem for hours

[odd depot]

I'm not just going to tell you

[winged rune]

aint no way

[odd depot]

I'm at work so sometimes I have to shift my focus to work

[winged rune]

i needs it gang

alright then save us the trouble then

🙏

[odd depot]

do you see how the distance between the red line is 4/5?

[winged rune]

yea

[odd depot]

would it help to see this on a regular graph?

we are finding a function for the distance between the left and right side of the parabola

as a function of y

so we have those x values as +-sqrt(y)/5

[winged rune]

uh

yea idk how

[odd depot]

maybe make it concrete, what are those values for y=2?

[winged rune]

-0.29 and 0.29

[odd depot]

no

ok, yeah

approximately

0.29

[winged rune]

hmm

so would it be like -0.35 and 0.35

[odd depot]

for what y?

[winged rune]

y = 2.5

[odd depot]

actually it would be closer to y=3 going by the graph

but let's stick with y=2

what is the distance between those two points then?

when y =2 ?

what is the length of that specific orange segment?

[winged rune]

0.48

[odd depot]

not .48 ...

[winged rune]

bra

i counted the line

[odd depot]

is not .48

[winged rune]

what is it

🙊

[winged rune]

oh

it goes by 0.2

wait so how is it 0.9

shouldnt it be 0.8

[odd depot]

I mean maybe

yeah I think it is .8

[winged rune]

so then its 5.6

[odd depot]

ok then

so it is just double of .28

the left side is at -0.28 and the right is at 0.28

so the distance between them is double that, 0.56

right?

[winged rune]

right

[odd depot]

ok, so do the same with your equation in terms of y

[winged rune]

sqrt(.28)/5?

[odd depot]

hey I'm back,

so for y=2 you get

x= + or - sqrt(2)/5
x = + or - .28, approximately

and then the distance between those two x values is .56

What is the distance when y = y and not a particular number

[winged rune]

uhhhhh

y^2

yea idk dude

i got like 20 minutees left till this assginemnt is dude

anyway u can just give me the answer

[odd depot]

I'll give that S= (2/5) * sqrt(x)

then you just square that to get A

there you have 4/5

[winged rune]

yea but when i try putting the answer in

it says x is not defeinded in this context

defined

[odd depot]

oh sorry

S= (2/5) * sqrt(y)

I;m tired

then A is (4/25) y

[winged rune]

thank god

.close

[lone heart]

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[sweet nymph]

help

[sweet nymph]

log (6x -1) - log (x + 4) = log x

my brain is dumb

log ((6x -1)/(x + 4)) = log x

i reached this

then idk what to do

[last ether]

Make the equation the exponent of base 10

So like

[sweet nymph]

oh

[last ether]

10^(log((6x-1)/(x+4)) = 10^(log(x))

[sweet nymph]

i dont get it

[last ether]

Gets rid of the log

[sweet nymph]

wait, i got x^2 - 2x - 1

can i use cuadratic formula then?

[last ether]

Yeah

[sweet nymph]

log (6x -1) = log x + log (x + 4)

i went like this

log (6x -1) = log (x (x + 4))

is it okay?

[lone heart]

@sweet nymph Has your question been resolved?

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[lone heart]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tulip oasis]

I alr what i did is so wrong

1 min i show

[ionic jewel]

I think there is not a clean solution to this? its just "factoring" a cubic that only has one real root which is not easy by hand

[tulip oasis]

o

[ionic jewel]

the answer is like -0.8* and im not sure how you were expected to solve it by hand

[tulip oasis]

so this one need like ti-84?

calculator

[mint bone]

Wait

It should be 0.32

[ionic jewel]

how did you get this

oh thats right

[tulip oasis]

wait wat

[ionic jewel]

i did f^{-1}(-2)