help-13

[upper abyss]

Yeesh

[nocturne furnace]

yeah it worked tysm!

[upper abyss]

That's not to take away the awful webassign happening here

[nocturne furnace]

yeah I only have one more math class then I'm done with webassign

I enjoy math just not some of the hw lmao

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[ancient vortex]

Hi, I managed to get to the point highlighted in the screenshot but not sure how to make the jump to the final correct answer

[nocturne furnace]

are you required to simplify?

[ancient vortex]

Yes, from the highlighted fraction to the given answer

This is the question

[nocturne furnace]

did you work out multipling both sides by 1+ln(t+1)?

that will get rid of the fraction at least for now

[ancient vortex]

I don't really understand how that would help me get to t = 26/1+ln(t+1) - 1

[nocturne furnace]

honestly I suck at simplifying too but I'd imagine its a weird factoring trick

[ancient vortex]

Probably something stupid simple that I'm somehow missing 😅

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[glad mortar]

Can someone walk me through on how to solve this

[cedar kiln]

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@glad mortar Has your question been resolved?

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@glad mortar Has your question been resolved?

[glad mortar]

<@&286206848099549185>

[hearty arch]

I just want to point out maybe one thing to notice, which is that the cosine function has a very strict range of outputs. whatever you put into the cosine function, it will spit out a value between 1 and -1.

so pcos(5x) can only output values between 1*p and -1*p

no matter the input of x, pcos(5x) only outputs values between p and -p

[glad mortar]

oh I completely didn't see ur message

but thank you so much I understand now

I just had to sub 0 for x into cos to find the maximum

then I solve it

cos(5(0)) = 1

so p + q <= 0

then bring q over

p<=-q

answer si c

is(

is*

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[hearty arch]

cos(0) is 1

@glad mortar

[glad mortar]

yea i meant 1 typo

p*1 = p

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[tranquil ivy]

Hello! So I have a couple of months free so I decided to refine and relearn my math foundations. Currently in sets and proofs and I’m doing these little exercises.

[tranquil ivy]

So number 5, I looked it up on Desmos and apparently there is more than one solution, 3 AND -1. But how can I prove that on paper?

[warm crescent]

it doesn't matter

I think P only if Q is read P --> Q

n=3 --> n^2-2n-3=0

T --> T is a true statement

[tranquil ivy]

Sorry if all of this is really basic . Anyway would “only if” not imply <—> or I have that wrong?

[warm crescent]

to be honest, trying to interpret some expressions as they are read in English could be ambiguous

P only if Q, P then Q: P --> Q

P if and only if Q, P is equivalent to Q: P <--> Q

[tranquil ivy]

Makes sense! Even I get confused because “only if” and “if and only if” kind of just sound redundant on their own 😅

But thank you so much. For now my concern is resolved.

[warm crescent]

the most common are probably

if P then Q, Q if P, P therefore Q: P --> Q

[tranquil ivy]

Noted. Thanks a lot

[warm crescent]

to explain a bit, P only if Q means P is T when Q is T

looking a truth table would make sense to have P --> Q

[tranquil ivy]

That enlightened me a bit!

i see the idea now

[warm crescent]

ok I was about to send an image but ok

the value of P doesn't matter

but if Q is false, then P-->Q is false

[tranquil ivy]

Yeah sorry if I am rushing you too 😭 just the way I type please don’t worry

[tranquil ivy]

I see

Thank you : )

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[livid stratus]

how do you determine if a function is equal to another function

[livid stratus]

would just saying "they have the same domain" enough?

well i think no because if you take for example

[hot crag]

no??

[livid stratus]

1/x-2 and 2/x-2

they both have the same domain

[hot crag]

x^3 and x^2 for example have domain of all reals

yes

[livid stratus]

yeah

so how can u determine then

[hot crag]

they must have the same domain and same range i think

wait-- no

same example

xD

,w range of 1/(x-2)

[wraith dagger]

Results provided by WolframAlpha

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Requested by justarenegade

[hot crag]

,w range of 2/(x - 2)

[wraith dagger]

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[hot crag]

yea see

[livid stratus]

yea

[flint plinth]

equality means they have the same domain and they send they satisfy f(x) = g(x) for every x in the domain

[livid stratus]

now if i gave u a function

would u sit there

[flint plinth]

and technically they need to have the same codomain too

[livid stratus]

and plug every number in the domain?

[hot crag]

codomain?

[livid stratus]

what is codomain?

[flint plinth]

like:

f : A -> B

A is the domain, B is the codomain

the image is some subset of B, not necessarily all of B

[livid stratus]

isnt it just how the function is written

[flint plinth]

and let's say you have f(x) = exp(x)

and g(x) = exp(x)

where f : R -> R

and g : R -> R+

(where R+ are the positive real numbers)

they "look like" the same function

but f has a larger codomain

in particular it's not surjective

whereas g is

so technically they are not the same function

[livid stratus]

if their codomain is R and R+ which i dont even know what codomain is but i guess its what i think of it, could u even say they both are equal to exp(x)?

R - > R+ seems to be some kinda function with a root in its denominator so that only positive real numbers are in domain

[flint plinth]

well that's the point, the definition / specification of the function isn't complete unless you specify the domain and the codomain

and (at least from a set theoretic point of view), f and g above are not the same function even though they have the same domain and satisfy f(x) = g(x) for all x in the domain

[livid stratus]

yeah

[flint plinth]

in many situations we don't bother making the distinction, but in other cases it matters, really depends on context

[livid stratus]

they both satisfy that for all their domains, but their codomains are different

so the first step in these type of questions would be to look at the functions domains

thanks for ur help

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[gloomy snow]

How do i do this theres a example in the second picture

[hollow yarrow]

bro

[gloomy snow]

What💀

[hollow yarrow]

can u convert to english

[mint garnet]

calculate the total no.of shapes first

[gloomy snow]

Im so ass at math dont judge me Lmao

[gloomy snow]

16

[hollow yarrow]

what grade is that

[mint garnet]

then calculate blue or red shapes

[gloomy snow]

6

[mint garnet]

then divided blue or red/total x 100

you got your percentage

[gloomy snow]

Yeah but look wait

Do yk what this means x) the x means a random number

For example 7)

7. means like a multiply thingy

And i dont know what to multiply it with

[hollow yarrow]

wheres 7)

[cedar kiln]

@gloomy snow Has your question been resolved?

[gloomy snow]

Noo

Like in that problem i have to write first that how many patterns are there and theres 16 so /16 and then it asks how many blue or red patterns there are so if i chose blue theres 8 blue patters so 8/16 now i have to multiplie it with a number but i dont know why and i dont know with which number

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[worthy hawk]

Im in igcse Math 0607, for a paper 6 investigation question im having difficulty in solving 5.a and b
https://pastpapers.co/cie/IGCSE/International-Mathematics-0607/2019-May-June/0607_s19_qp_61.pdf

[worthy hawk]

This is where im at

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<@&286206848099549185>

[crimson sedge]

Whats the problem?

[violet obsidian]

is this the original question or

[crimson sedge]

Im lost at that paper

[violet obsidian]

is that the original problem

what u asking frfr

[crimson sedge]

Shshhs, you are doing an investigation. The best thing you should do is ask help HEAVILY to your teacher or whoever is your examiner for this. You are asking for one question from your investigation i doubt NOT that youll have more questions in the future.

@worthy hawk

[worthy hawk]

That is q5

Investigation questions as linked

The investigation part is q1-5

[worthy hawk]

My teacher’s really busy and theres no examiner so i asked here

And ye i prollybwill im not comfortable with investigation papers

[crimson sedge]

You have to know what your investigation is all about. I am DEFINITELY sure that you dont know the whole math stuff that you should do to answer each and every question to your investigation. You have to learn the solutions for each questions. You must ask your teacher for help for all of that. You dont have time for procrastination. You must focus on learning the solutions.

[worthy hawk]

Ye i tried believe me

I got the equation

But i dont know what to do moving forwards

[crimson sedge]

I had the same experience too, thats how i know.

[worthy hawk]

I attempted the 5b too but it says more than 2 teams and the 2 roots i got one is 2 and other is less

[crimson sedge]

You gotta ask a lot of help to pass your investigation.

[worthy hawk]

R u in igcse?

[crimson sedge]

No

[worthy hawk]

Ye so mine and ur investigation papers arent same

[crimson sedge]

But i know the feeling of not being able to figure out the investigation paper you have

[worthy hawk]

There is 1 investigation and 1 modelling question in paper 6 of 0607 for me

[crimson sedge]

Trust me, i know the feeling.

[worthy hawk]

So what do i do

[crimson sedge]

Yep, it seems like u have something more on your way

[worthy hawk]

Look the teacher is busy with higher grades’ mock exams

10th and 12th grade

[crimson sedge]

Ask your teacher and other math teachers for help. Take notes of what they say to you.

[worthy hawk]

He has to correct em

[worthy hawk]

Bro for that he’ll have to go through entire paper

[crimson sedge]

Dont care, either you pass this or not.

[worthy hawk]

Itll take a lot of tome

Fot him to get back to me

[crimson sedge]

You know you have your faults too for not focusing on your classes sufficiently.

[worthy hawk]

Bro

Im in the accelarated batch

That means theres 2 math courses pf 2 years each

[crimson sedge]

Then you know all the details about it.

[worthy hawk]

Which we havr to cover in 2 tears total

And p6 investigation wuestion

We have just done 1 in class

[crimson sedge]

You have to be strong

[worthy hawk]

Ok bro thanks

.close

[crimson sedge]

Not only smart, but mentally VERY STRONG

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[fathom star]

6 - (-7) = 14
-2 - 7 = -9
?

[queen marlin]

yurp

whats the issue

[fathom star]

Its wrong

[queen marlin]

its v-u

not u-v

[fathom star]

...

oh

[queen marlin]

also that was 13 not 14 but u get it

[fathom star]

welp, alright then.

Thanks lol

[queen marlin]

nw

[fathom star]

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[robust aspen]

What's the strategy for 2.5 * 10^2x = 7.5 -10x These are two fuctions who we want to find where they intersect, with other words where thay are equal to each other, what do I do now?

[robust aspen]

I know I can both divide by 2.5 and add 10x

to isolate the answer

10x + 10^2x = 3

then what

are you supposed to rewrite 10x

to like (10^1)x

Cause I suspect you are supposed to use log to get that exponetial down

<@&286206848099549185>

[cedar kiln]

@robust aspen Has your question been resolved?

[robust aspen]

<@&286206848099549185>

[cedar kiln]

@robust aspen Has your question been resolved?

[robust aspen]

<@&286206848099549185>

[storm anvil]

?

[robust aspen]

hey

need some help

[robust aspen]

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[hardy prawn]

i got k from the example problems at the beginning of the lesson for c-14 but my teacher pretty much expects us to use class notes rather than that and i have 2 missing variables rather than just 1

[hardy prawn]

thats how i got k

im doing question 8 btw i did all other questions

hold up i think i came up with smth

nvm

[carmine bronze]

What was your thought?

[hardy prawn]

y=1/2*a but that didnt lead to anything but a false equation

[carmine bronze]

Let's say you had an arbitrary original mass of a = 100, would you be able to calculate what y equals?

[hardy prawn]

i thought that edits the msg

it doesnt give how much c14 is left

it only provides 2 variables

out of 4

[carmine bronze]

You don't need to know how much is left, you only need to know the percentage of the original amount left.

[hardy prawn]

OHHHH

ty

i think i got it now

.close

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[hardy prawn]

i didnt read that lol

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[vital nova]

How is (x^2) > 5 equal to x < -√5 & x > √5? Can someone prove this? I mainly need help understanding why (x^2) > 5 is equal to x < -√5, and why it changed the inequality sign. Thanks!

[modern sparrow]

the best way is picture this is by graph

firstly, do you agree that the solution (root) to x^2=5 is sqrt(5) and -sqrt(5)?

[cedar kiln]

@vital nova Has your question been resolved?

[vital nova]

Sorry I'm back. Yes. I do agree

[modern sparrow]

ok good, so rearranging x^2>5 to x^2-5>0, the question is basically what values of x, such that f(x) = x^2 -5 is greater than 0 right?

[vital nova]

Yes

Right

[modern sparrow]

cool, now let's draw the graph of f(x)

it looks like this

where the roots are at x = +- sqrt(5)

so remember the question is, when is f(x) > 0?

[vital nova]

When it is above the minimum?

[modern sparrow]

not quite

[vital nova]

Wait sorry

Im slow

When it is less than -root 5, bigger than root 5

Ohhhh

[modern sparrow]

yes, so when x>sqrt(5), and when x<-sqrt(5), the graph f is above the x-axis.

[vital nova]

Okay thank you I understand now

[modern sparrow]

you're welcome

[vital nova]

Have a blessed day dude

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[modern sparrow]

thx, you too

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[proven vale]

looking for help with how to find an explicit formula from a sequence

[proven vale]

the sequence is {2, 3, 6, 15, 45, 157.5} and I know the explicit formula is n!*2^2-n but i have no idea how to go from the sequence to that formula

like the workflow

[buoyant latch]

Is there more context to this problem

[buoyant latch]

Try writing explicitly what a₂ and a₃ looks like

[proven vale]

a2 = (2x2)/2 = 2
a3 = (3x2)/2 = 3
a4 = (5x6)/2 = 15

[pallid python]

u go through the sequence and simplify it

and u will get the pattern I guess

[proven vale]

i guess so, professor introduced sequences and never did any problems involving factorials then gave us this, thx for helping 🔥

.solved

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[rare sundial]

can someone explain how to do this

[silver forge]

what is the perimeter of the rectangle?

[rare sundial]

yes

[silver forge]

do u know?

[rare sundial]

no

[silver forge]

like an expression

how do u find the perimeter

of a rectangle

[rare sundial]

you add the perimeter

[silver forge]

u add all the sides right?

[rare sundial]

yes

[silver forge]

so what is x+7+x+1?

$x+7+x+1$

[wraith dagger]

axxy

[silver forge]

like simplified?

[rare sundial]

x8

2x+8

[silver forge]

correct

wait

so we did that right

but we just added 2 sides

[rare sundial]

yes

[silver forge]

perimeter of a rectangle is
2(length plus width)

so we multiply the expression by 2

[rare sundial]

alr

[silver forge]

what do we get now?

2 (2x+8)?

[rare sundial]

4x+16

[silver forge]

correct

now how do we find the perimeter of a triangle?

[rare sundial]

we do the same thing

[silver forge]

so what is the perimeter in terms of x for the triangle?

[rare sundial]

4x

4x+16

3x+37

[silver forge]

correct

now they say that the perimeters r equal

so $4x+16 = 3x+37$

[wraith dagger]

axxy

[silver forge]

now solve for x

[rare sundial]

i got 21

[silver forge]

that is correct

u r done

[rare sundial]

wait

i have 1 more

[silver forge]

sure

[rare sundial]

i got 10 but says its wrong

[queen marlin]

10 sounds right

[rare sundial]

alr

[molten vine]

10 is correct

[rare sundial]

ill just ask my teacher later

.close

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[wary estuary]

Could somebody verify if that makes sense? Can’t really verify and qwould like to know if im on the right track.

[wary estuary]

Sorry about the dark picture

I feel like I missed something lol

[cedar kiln]

@wary estuary Has your question been resolved?

[wary estuary]

Now I'm sure it's incorrect though, but no clue where

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@wary estuary Has your question been resolved?

[cedar kiln]

@wary estuary Has your question been resolved?

[cedar kiln]

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[granite hill]

i’m curious what’s wrong with this false proof

[harsh ledge]

(1/i)^2 = -1

?

[granite hill]

i think they multiplied by i in both sides

not squared

[harsh ledge]

oh

[frigid escarp]

Maybe 5?

[rigid lava]

sqrt(a/b) isn't equal to sqrt(a)/sqrt(b)

so sqrt(1/-1) != sqrt(1)/sqrt(-1)

[frigid escarp]

That would be i(1/1)

[rigid lava]

?

[frigid escarp]

I’m agreeing with you

[granite hill]

isn’t that what i is ?

[frigid escarp]

They didn’t sqrt properly

[ionic finch]

i think the \sqrt{ab}=sqrt{a}sqrt{b} holds iff both a, b >=0

i didn't tex

[frigid escarp]

I’m just trying to visualise this

[rigid lava]

i^2 = -1 is how the imagiary number is defined, but the equation z^2 = -1 has two solutions, i and -i

[rigid lava]

the LHS gets the solution i, where as the RHS gets the solution 1/i = -i

[frigid escarp]

sqrt(4/16) = 2/4 = 1/2

So possibly this rule could hold true

(1/i)^2 does equal 1/-1

[shut meadow]

it is true iirc

1/i is i^3 iirc

or -i

so like its iffy

[frigid escarp]

i^3 is -i

[rigid lava]

its true for positive reals, not for all complex numbers

the counter example is literally in the screenshot

sqrt(1/-1) != sqrt(1)/sqrt(-1)

LHS is i, RHS is -i

[granite hill]

that’s interesting

thank you

.close

[cedar kiln]

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[cedar kiln]

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[quiet girder]

The diagram below represents a cross section through a focusing lens used in solar panels to concentrate the rays of the sun to a focal point (P). Point O is the centre of the lens, Point D lies on the circumference and lines AP and BP are two mirrored tangents from the circumference of the lens to the focal point, P.
Angle ADB on the circumference is 75°.

Determine, with geometric reasoning, angle APB.

[quiet girder]

i hate bearings

[hollow totem]

We meet again

[quiet girder]

oh hi

[hollow totem]

Hmm

Im not gonna give out answer but will guide u to get it

[quiet girder]

thanks

[hollow totem]

Now, for angle APB, how do u think we can get it

[quiet girder]

figure out circmufrence?

[hollow totem]

Nope

Here's the hint

[quiet girder]

label the P angle?

[hollow totem]

no

See the shape?

What is it?

[quiet girder]

a triaganle

[hollow totem]

no...

Its a quadrilateral

[quiet girder]

HUH

OH RIGHT

[hollow totem]

Now whats the total sum of all angle of the quadrilateral?

[quiet girder]

180?

[hollow totem]

no

[quiet girder]

😭

[hollow totem]

180 is for triangle

Google it

[quiet girder]

360!

[hollow totem]

Okay

In that quadrilateral, whats angle we already known/ given by the problem?

[quiet girder]

A AND B

90 90

[hollow totem]

Good

So?

To find APB we only need to find?

[quiet girder]

what eequals 360? 90+90=180

360

[hollow totem]

Take a look at the quadrilateral again

How many angles are there in a quadrilateral

[quiet girder]

3?

[hollow totem]

tri-angle...

[turbid pilot]

the struggle is real

[hollow totem]

Be patient

[quiet girder]

um!

[quiet girder]

WHAT

OH

4

[turbid pilot]

keep working at it

[hollow totem]

We know 2

There's 4

So there's 2 unknown angle

one of which is the angle we need to find

[hollow totem]

...

[quiet girder]

P

[hollow totem]

We need to find P remember?

[quiet girder]

yea

[hollow totem]

We know A and B

So in order to find P we need to find?

[quiet girder]

90 90

[quiet girder]

the other angle?

[hollow totem]

Yes

whats the other angle?

U should start use 3 letters to call an angle

[quiet girder]

is it the circle i have no idea

[hollow totem]

Whats both angle = 90 that we known of? (Use 3 letters to call it)

[quiet girder]

im confused? right angle?

[hollow totem]

Look at this

A and B = 90 right

[quiet girder]

yep

[hollow totem]

but i want u to call it by 3 letter name

For example P angle in 3 letters name is APB

So A and B in 3 angles name = ?

[quiet girder]

aob?

[hollow totem]

no

[quiet girder]

APB

[hollow totem]

no

[quiet girder]

abd?

[hollow totem]

angle P = APB = BPA

The only thing matters is the middle letter = the that angle

[quiet girder]

OH

[hollow totem]

usually, we put a hat on it to indicate its an angle

So for angle A?

[pallid python]

draw a line from O to P

[hollow totem]

Stop

This is not helping

[quiet girder]

PAB? BAP?

[hollow totem]

So angle A in 3 letters format?

[hollow totem]

Nope

[quiet girder]

😭

oh hell no

this is hard

what

[quiet girder]

i thought the letter

Oh

[hollow totem]

How this is hard...

[quiet girder]

so

BAO

oab

[hollow totem]

no...

[quiet girder]

ive never done this before

[hollow totem]

Its really logical

[quiet girder]

i dont understand i put the A in the middle

[hollow totem]

So

for angle P

We get it by travelling from A to P to B

So P = APB

Now

For A, why would we travel from what to A then to what?

[quiet girder]

for angle A i travel to

[hollow totem]

from .... to A to ......

[quiet girder]

a to o to b? a to p to b

idk

[hollow totem]

A need to be in the middle

So we need to select 2 points

[quiet girder]

OH

B to a to P?

[hollow totem]

Why B?

B doesnt connect to A?

[quiet girder]

O to A to P

[hollow totem]

Cause if B connect to A we get a triangle

[hollow totem]

YES

[quiet girder]

ohh

FINNALY

[quiet girder]

Ur handwriting looks like mine

[pallid python]

in the car lol

[hollow totem]

The point is she doesnt understand the concept,....

[quiet girder]

whats L for?

[quiet girder]

facts

[pallid python]

not L

is engle

[quiet girder]

OH

[hollow totem]

Now, to find APB, we have 2 facts:

1. Sum of angle in quadrilateral = 360
2. OAP = OBP = 90

So we need to find what?

Hmm

@quiet girder Express the sum of all angle = 360 please

Write all angle down

[quiet girder]

mmmm

[hollow totem]

here's the pic

[quiet girder]

It says O is 150?

[hollow totem]

U dont even know why O = 150

[quiet girder]

the whole angle is 75 ABD anf the centre angle is Two times the cirmunce which equals 150?

[hollow totem]

Okay

Good

[quiet girder]

so thats why o is 150

[hollow totem]

yeah but im trying to teach u why we need to find O at the first place

[quiet girder]

oh

[hollow totem]

The quadrilateral sum of angle = 360; we know 2 angles and the P is the angle we need to find, thus by finding O, we can get P

[hollow totem]

The thing is u read this and it disrupt the whole process

[quiet girder]

i didnt even read that i just rember this from class

[hollow totem]

We then we can find P then

[pallid python]

Due to the radius of circle, I connect O to D and it would be a isosceles
And angle ODA=OAD=75/2
Due to the internal angle of a triangle =180 hence angle AOD=180-75/2-75/2=105
Angle AOD+BOD=2angle AOD=105*2=210
Minor Angle AOB=360-210=150
Internal angle of quadrilateral =360
360-90-90-150=30

[quiet girder]

im not readint this

[quiet girder]

add up to 360 90 + 90 = 180 + 150 = 230

so do i just find out the other number

360-230=130??

😭

[hollow totem]

Nope

[quiet girder]

oh

[hollow totem]

150 + 90 +90 +P = 360

[quiet girder]

OH

so its 30?

[hollow totem]

180 + 150 = 330 not 230

[hallow linden]

it is a 4 sided polygon insides have to add up to 360, so yes.

[quiet girder]

WOOHOOOOOO

so thats angle APB?

[hollow totem]

360 - 330 = 30

U made a mistake here

[quiet girder]

Yeah i relized now

[quiet girder]

OHH

[hollow totem]

Thats 150 = 75 * 2

[quiet girder]

so 30 is APB?

[pallid python]

I totally forgot this principle

[hollow totem]

Yep

Good job

[quiet girder]

ok great

thank u!!

i wont fail now

🥳

[hollow totem]

practice more

[cedar kiln]

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[civic crypt]

I'm stuck

[civic crypt]

I don't know how to proceed further

[digital fog]

what happens when you switch some bases around

log2 x = log3 x / log3(2)

then u sub

[civic crypt]

Oh right, that didn't come to mind

Lemme try

[digital fog]

things should cancel out a bit

[cedar kiln]

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[foggy solar]

I had to draw a Hasse diagram for this assignment and I don’t exactly know what it means when it tells me to order it by set inclusion. Is this close to right? And what does that specific description of order mean in this context? Thanks!

[cedar kiln]

@foggy solar Has your question been resolved?

[foggy solar]

<@&286206848099549185>

[tacit nymph]

1. what you have written is completely right
2. how the set is "ordered" in the context of a Hasse diagram just means what we're ranking it against - for example, when you put {2,3} above {2}, you're using the order to do that. It's related to the set-theoretic idea of an ordered set, but here it just means, 'of all the ways we could choose to organise this diagram, which one are we going to use?'

[cedar kiln]

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[north wyvern]

very simple question here

[north wyvern]

i honestly have no idea what to choose for A, B, C, im not creative enough, the problem is super easy after finding these

problem is, I am not creative enough to think of such an A, B, C

obviously, we let U = {1, 2, 3, 4, 5}

[rigid lava]

double check me but i think A,C = U and B = {} works

[north wyvern]

good point

i knew it was probably something super simple like this

thank you

[rigid lava]

👍

[north wyvern]

.close

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[north wyvern]

.reopen

[cedar kiln]

✅

[north wyvern]

hold on, it says nonempty

lol, almost missed that detail entirely

[rigid lava]

oh

then

let B be a singleton

and A=C=U

[north wyvern]

okay, i think that works

[rigid lava]

in fact, B could be any non empty subset of U, and A=C=U should work

[north wyvern]

thank you!

.close

[cedar kiln]

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[rigid lava]

non empty proper subset*

[cedar kiln]

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[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[true escarp]

how do you even begin? i tried differentiating a constant 4 times to get the general deflection formula and using the small deflection condition i figured out what dy/dx needs to equal. im not sure if that right

[true escarp]

@gleaming path

<@&286206848099549185>

.close

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[grizzled anvil]

could anyone explain why ln(k-4) = ln(p) and k - 3 = 8? is that a log rule or?

[runic garnet]

you should give more context

but it looks like they just grouped the ln terms together and the non ln terms together

[cedar kiln]

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[vocal patio]

need help understanding how the 1/2(c-1)^-1/2 becomes (sqr(4)-sqr(1))/3

[runic garnet]

is the original function y = sqrt(x-1)

[vocal patio]

yes

[runic garnet]

did u understand the previous step

f(5) - f(2) / 5 - 2

[vocal patio]

i understand the numerator, but idk why it needs the denominator part

[runic garnet]

thats how you go about mean value theorem problems

[vocal patio]

ooh the sqr is just from the original function

[runic garnet]

exactly

[vocal patio]

ah i see

[runic garnet]

f(5) = sqrt(5-1) = sqrt(4)

[vocal patio]

thanks!

[runic garnet]

np

[vocal patio]

wait

one last question

could you explain the reasoning for the denominator part in the mean value theorem?

[runic garnet]

f(b) - f(a) / (b-a) gives u the slope of the secant between the two endpoints. in our case, the endpoints are 2 and 5. the f(b) - f(a) represents the net change in the function (change in y), and the b-a represents the change in x.

[vocal patio]

OOOHHH

[runic garnet]

believe it or not i just realized that too xD

i dont think anyone ever explained it to me that way

but it makes sense

[vocal patio]

so since the f'(c) is basically the slope at c, you need a rise over run thing, so its numerator being the y axis change, and denominator being the x change?

so change in y / change in x becomes the slope at c

[runic garnet]

yea, thats the essence of the MVT. the instantaneous slope at a point C in the interval [a,b] will equal the slope of the secant line connecting (a,f(a)) and (b,f(b))

[vocal patio]

could you please clarify secant?

ik its supposed to be 1/sin

or something like that

[runic garnet]

change in y / change in x over the interval becomes instantaneous slope at c

[vocal patio]

but like, whats its importance?

[runic garnet]

secant line means average rate of change between two points

its also just a line passing through 2 points

[runic garnet]

but here, this is how we're using it

[vocal patio]

ok i see

this the same secant right?

just line between two points

[runic garnet]

yes, exactly. its just in that image, we're applying the concept to a circle

[vocal patio]

awesome man! clarified so much in short span of time

appreciate it!

.close

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[runic garnet]

@pastel vault did u just killsteal me LOL

[pastel vault]

shhhhh they'll never know if you don't point it out

I technically didn't say anything

[runic garnet]

xD

[pastel vault]

xdxd

[runic garnet]

bro i do that all the time

didnt know someone would do it to me

karmas real ig

[vocal patio]

@runic garnet when solving mean value theorem, i have to prove that its continuous by showing that its differentiable, and that for f(x) for x subset of [1,2] f(x) = 0, and that f'(c) can be differentiated to a value?

[runic garnet]

prove cont. by showing differentiable?

[vocal patio]

yea

[runic garnet]

also, why f(x) = 0 ?

[vocal patio]

to show that when x is 1 or 2, f(x) = 0... idk i just thought it would be same for mean value if its same for rolles?

or am i wrong there

[runic garnet]

im not sure, i recommend just opening a new channel and asking there cuz this one is gonna close soon

[vocal patio]

ok, thanks!

.close

[runic garnet]

its alrdy closed, dw, itll fully close soon

[cedar kiln]

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[candid cosmos]

uhhh would my answer be correct?

im not sure if i answered the question correctly 😭

[pastel vault]

Yeah, so you can just say that AB/BC = adj/hyp for the 60 degree angle

[candid cosmos]

ohhhhh

okok got it

thank youu

[pastel vault]

No worries

[candid cosmos]

but thats for all of them?

sin, cos, and tan?

i mean the ones where i can put 7, i can?

[pastel vault]

Yeah so sin 60 is indeed correct

[candid cosmos]

uhuhhh

[pastel vault]

Yeah you've gotten all of them correct

[candid cosmos]

WOOOOO

[pastel vault]

Cause the key step is figuring out what the hypotenuse and the adjacent side are

There is more than one way to do it

[candid cosmos]

truee

[pastel vault]

But I would use the fact that a 30-60-90 triangle has side lengths 1, sqrt(3), and 2

[candid cosmos]

mhm

[pastel vault]

So if AC = 7, that corresponds to the sqrt(3)

So you need to multiply everything by 7/sqrt(3)

[candid cosmos]

so it's safer to put AB and BC for the trigos?

[candid cosmos]

yeah

[pastel vault]

Well, for the trigonometric ratios, you should do it using the side lengths AB, AC, and BC

[candid cosmos]

uhuhh

[pastel vault]

I think it's a little weird as you can just show this smaller triangle is similar to the larger triangle

So the trig ratios will all be the same

But anyways

[candid cosmos]

yeahh i got ittt

thanks for checkingg 🙏

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[pastel vault]

No worries

[cedar kiln]

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[cedar kiln]

Please don't occupy multiple help channels.

[crimson sedge]

.close

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[candid cosmos]

huhhh what do i find?

[modern sparrow]

do you know what |v| represent/mean?

[candid cosmos]

yuhh

no

😔

absolute value of v

?

[modern sparrow]

for a real number yes, but here v with an arrow -> is a vector

it means the magnitude the vector v

i.e. the length

[candid cosmos]

yeahh

how do i find the vector?

im not sure i know what to do with the line

[modern sparrow]

well you don't need to know the vector here, note that v is on an xy-plane

and assuming each square represent 1 unit (in vertical and horizontal distance)

[candid cosmos]

uhhuhhh

[modern sparrow]

then it's 7 across and 1 up from A to B right?

[candid cosmos]

yes

soooo the vector is 1/7?

rise over run?

[modern sparrow]

no, that is the gradient, which is for a line (equation)

[candid cosmos]

oh, so slope then

buttt vector is different im assuming

[modern sparrow]

yes, you're asked the length of v

just think of AB as a hypotheneuse

of a triangle

[candid cosmos]

mhm

[modern sparrow]

with width 7 and height 1

how would find the length of the hypotheneus

[candid cosmos]

7 square plus 1 square

[modern sparrow]

almost

[candid cosmos]

and then square root

[modern sparrow]

yup

[candid cosmos]

ohhhhh

sooo

square root of 50??

[modern sparrow]

correct

[candid cosmos]

WOOOHOOOOOO

THANK YOUUU 🙏

[modern sparrow]

np

[candid cosmos]

.close

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[floral onyx]

x + 1/x = 4,

Find x.

What i did: -

x^2 + 1 = 4x

x^2 - 4x + 1 = 0

using the quadratic formula,

x = 2 +/- sqrt(3)

but it doesn't seem correct to me when i substitute the values

(sry if this was just a dumb question)

[wintry vault]

is it (x+1)/x = 4

or x + (1/x) = 4

[livid hound]

,w x + 1/x when x= 2 + sqrt(3)

[wraith dagger]

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Requested by ramonov

[floral onyx]

this

[floral onyx]

uhhhhh ok. alr

[wintry vault]

seems like you got the right answer

[floral onyx]

smth wrong with my calculations when i subsititute the values to verify then.

[wintry vault]

pretty sure

[wraith dagger]

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[floral onyx]

nvm i'll probably find it out then

yes

yeah

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[cedar kiln]

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[slender mango]

I dont follow how it got 45 and 65

nevermind I was on radians mode.........

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[topaz osprey]

How do I convert my answer to a square root

[silver forge]

should it not be 1-(-2) btw

for the y coordinate

so 3

[topaz osprey]

My bad

[hot crag]

^^

FYI, you can just simplify

[wraith dagger]

ren

[hot crag]

i think you can do the rest...

[topaz osprey]

I got it

[hot crag]

:)

[topaz osprey]

Thanks

[hot crag]

!done

[cedar kiln]

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[topaz osprey]

.close

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[topaz osprey]

What's the deal with this one?

[modern sparrow]

how did you get 281.3 degree?

[topaz osprey]

I did tan-1 (5/1) which gave me 78.69

I don't know what quadrant V is in tho

[modern sparrow]

since it's 0 degree at positive x-axis, 90 at positive y-axis, 180 at negative x-axis, and 270 at negative y-axis, you can instantly tell that theta_v should be less than 270 degree (if the question wants it anti-clockwise from positive x-axis)

[topaz osprey]

Quad 2?

[modern sparrow]

quad 3

quad 1 is top right

then go anti clockwise

[modern sparrow]

why did you do tan-1 of (5/1)? It should be tan-1 of (1/5)

[topaz osprey]

I thought it was b/a

It's still not right

I figured it out

I had to round my answer

It was B/A

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[warm crystal]

this avaiable?

[warm crystal]

how do i solve (x+2a/a+4a/x-2a)* ax-3a^2/x^3

😔

[silver jungle]

I am not sure what the expression is supposed to look like, could you add some more brackets to denominators and numerators?

[crimson sedge]

cross multiply the first bracket and then just multiply by the second thing

[warm crystal]

yeah

[warm crystal]

the first bracket is not a multiplication tho

[modern sparrow]

he means combine the fraction

[warm crystal]

how

[sand cradle]

That's a +, not a /

[sand cradle]

Get it to the same denominator first

[warm crystal]

so i like ignore the brackets?

[sand cradle]

No?

[warm crystal]

i dont get it

[sand cradle]

Simplify $\frac{x + 2a}{a} + \frac{4a}{x - 2a}$ by getting these fractions to the same denominator.

[warm crystal]

how do i get them to the same denominator

[sand cradle]

You could multiply numerator and denominator of the left one by x - 2a, numerator and denominator of the the right one by a

Then both will have the denominator (x-2a)a

[warm crystal]

but theres no multiply ?

[warm crystal]

oh now i get it

can i still see this even if it closes?

[sand cradle]

yeah

[warm crystal]

k good

thanks bro

[sand cradle]

There might be some new messages in this channel, but you can always find this conversation by going to the search panel (top right or press CTRL + F) and typing "from: [your name]"

[cedar kiln]

@warm crystal Has your question been resolved?

[crimson sedge]

?

I know

lol

that's why i told him to cross multiply

then multiply by the second part of the q

[cedar kiln]

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[lean ledge]

Yoo how do i do this

[frigid sinew]

Idk how to explain to you without straight up giving the answer

[lean ledge]

Bro

[frigid sinew]

Can you somehow take the x away from 3

[lean ledge]

Divide by 3?

[frigid sinew]

Or you can divide by x

[lean ledge]

Ye

[frigid sinew]

And you divide x^2 by x

You obtain x(x-3)

[lean ledge]

But then whats the answer then

[frigid sinew]

Well

[lean ledge]

It says x is one of two answers

[frigid sinew]

From this

What do you think

=0

What should X be

[lean ledge]

-3 or +3?

Im dumb

[frigid sinew]

Why -3

[lean ledge]

Bc its x-3??

[frigid sinew]

-3 - -3 is 0?

[lean ledge]

Uhh

Hol up

3-3=0

[frigid sinew]

Yeah so only +3

Right?

[lean ledge]

So theres only one answer?

[frigid sinew]

No

[frigid sinew]

.

What else could x be

[lean ledge]

Ummm

Idk 😭

[frigid sinew]

0 my dude

[lean ledge]

Let me put that in

Damn

[frigid sinew]

??

[lean ledge]

Its rigjt

Ur smart

Its on a website

Oh ty

[frigid sinew]

0 times anything

Is 0

Just fyi

[lean ledge]

0 times 3

[frigid sinew]

0

[lean ledge]

I thought its subtracyion

[frigid sinew]

x(x-3)

It’s substraction and multiplication

[lean ledge]

I dont get it

Can u explain it more simpler

[frigid sinew]

it’s x Times (x-3)

So if x =0

It’s 0 times (0-3)

Therefore it’s 0

[lean ledge]

Byt 0-3 = -3

??

[frigid sinew]

Yeah and times 0

Try multiply -3 with 0

[lean ledge]

Let me try and work it out myself. Tell me if its right, ok?

[frigid sinew]

Alright

[lean ledge]

Did i duck up?