help-0

[tawny condor]

i mean the 1 and -9

they are on the same side

[meager bone]

Ohh wait yea

Sorry I was looking at the X’s

Let me try that

[tawny condor]

also when u had

$1 + 7x - 1 = 0$

[ocean seal]

redstoneplayz09

[tawny condor]

u dont need to move anything

its just...

1 - 1

so you're left with 7x = 0

think about it:

you have 1, you add 7x

and then you subtract 1

its the same as just having 7x

[meager bone]

Got it

Did I do it right?

[tawny condor]

yes

[meager bone]

YESSSSSSSSSSS

thank you so much

Omg

[tawny condor]

well done

i would suggest you revise basic algebra manipulations

[meager bone]

How many times can I send questions?

[tawny condor]

huh

there is no limit

[meager bone]

Sure I’ll look at some problems

[tawny condor]

this server is to help people

or, this section of the server at least

[meager bone]

Wait so you wouldn’t mind if I sent another one?

Because there’s only 1 more I have that I need help on

Wait actually hold on

Let me double check

[tawny condor]

try it yourself first

if its a similar question u might be able to do it alone now

if u get stuck make a help channel

[meager bone]

Sure

Do I come back here or do I start another channel? I don’t use discord at all so I’m new to this

[tawny condor]

whatever u want

u can close this for now

or keep it open

doesn't matter

[meager bone]

Hi sorry

Quick question

How do I factor something with 4 numbers inside the equation

It’s a cubic term and idk how to factor it

Nvm all good

[lone heart]

@meager bone Has your question been resolved?

[lone heart]

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[alpine sable]

I have the solution

But I don’t understand it

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

rd sharma?

lol

i know from that blue print

[alpine sable]

Yes

At this point, I can tell too lol

[alpine sable]

u see this:

these are qualifying questions my professor sent me to complete if i want to get into the Indian institute of science
he said these are baby stuff compared to what question we get in Indian Institute of Science

this is called math

real math

Nice stuff but I don’t understand any of that, so it’s pretty much irrelevant to me

[alpine sable]

ahhhh

Chairman of ISRO huh

[alpine sable]

yes

i am ehhehehehheheheheh

Well can you please help me with this problem? If you have the time

.close

[lone heart]

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[lone heart]

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[quick moth]

Can I get some help please

[tardy stag]

what do you already know how to do?

[quick moth]

Ik how to do most of perpendicular lines but forgot how to do this

[eternal tulip]

Perpendicular line have the negative reciprocal of the original slope

[quick moth]

Ok

Would This be right

[dry matrix]

where did the circles come from

[tardy stag]

you want it through A i thought

[lone heart]

@quick moth Has your question been resolved?

[quick moth]

Yeah I guess

But how would I do this

[tardy stag]

well it looks like you know how to make a perpendicular bisector

[quick moth]

I guess

[tardy stag]

can you use that?

[quick moth]

Probably I’ll try

This right?

Looks right to me

@tardy stag

[tardy stag]

seems legit

[quick moth]

K

Thanks it was right

[quick moth]

This right u think looks good to me

@tardy stag

[tardy stag]

this thing here? idk, that blue point on the line, where did it come from?

[quick moth]

Idk I can delete it it think

Anyway thanks it was. Right

[lone heart]

@quick moth Has your question been resolved?

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[frozen kite]

hi

[frozen kite]

y=x^2-4x+1 is translated by vector (1,2)

[alpine sable]

so, what have you tried

!status

[lone heart]

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

[frozen kite]

2

NO

3

but ik the answer

i tried it n

i didnt get anything right

the vector is always (b,a) right

or am i wrong

[placid zinc]

What's the question?

[dry matrix]

y=x^2-4x+1 is translated by vector (1,2)

[frozen kite]

ya

[grand girder]

the vector $\left(\begin{array}{l}1 \ 2\end{array}\right)$ represents $x=1$ and $y=2$ So the equation $y=a x^2+b x+c$ is translated to the left by I and translated to the up by 2.

[ocean seal]

adzetto

[frozen kite]

okok

so when im like

[alpine sable]

why translated to the left?

[frozen kite]

doing these types of questions

should i sketch a graph

to help me out

[dry matrix]

i think because example: y=(x-1) is translated to right and y= (x+1) is translated to left

[grand girder]

just try writing the transformation in the form f(a+b)+c

[frozen kite]

whats f?

n c

[grand girder]

source: https://www.onlinemathlearning.com/function-transformation-hsf-bf3.html

[frozen kite]

ok? 💀

no help whatsoever

.close

[lone heart]

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[alpine sable]

How do I solve this?

[placid zinc]

I assume you don't actually want the sum, just its convergence

This one is perfect for integral test

[grand girder]

just use ratio test, integral test is inconclusive

[lone heart]

@alpine sable Has your question been resolved?

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[bold panther]

help please

[lone heart]

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

[bold panther]

i have drawn a diagram

[tardy stag]

do you know the answer to (a)?

[bold panther]

yes

the distance is increasing

[tardy stag]

ok good

can i see your diagram?

[bold panther]

yes

[bold panther]

I tried solving it but I don’t think it’s right

[tardy stag]

you probably want to use a derivative somewhere in there

[bold panther]

Idk how to set up the equation :(

[tardy stag]

this one is all about related rates

[bold panther]

Yes I am aware

[tardy stag]

let's see what symbols are you using

B E R okay we'lluse those

so pythagoras says $B^2 + E^2 = R^2$

[ocean seal]

Hayley

[tardy stag]

and what we can do is literally just differentiate both sides with respect to t

[bold panther]

Oh

[tardy stag]

following the power rule and the chain rule

[bold panther]

Like this??

[tardy stag]

yehhh

now are there any of those values you know?

at 12:30

[bold panther]

dB/dt and dE/dt

[tardy stag]

more than that

[bold panther]

Hm..

[bold panther]

Would R be 50 miles?

[tardy stag]

we're looking for the situation as it stands at 12:30

E, in this case, should probably be the distance from Ernie to Bert's house, since that's the vertex of the triangle

[bold panther]

Would B and E both be 50 then?

[bold panther]

Nvm is B= 10and E = 70?

[tardy stag]

think about like
at 12:30, how long are each of these distances

[tardy stag]

that sounds right

yeah

[bold panther]

Oh ok and R would be:

[tardy stag]

yep

[bold panther]

:D

I plug these in and solve for dr/dt right?

[bold panther]

thank you for your help :D

[tardy stag]

oh whoops yeah do that

implicit differentaition is awesome

usually way simpler expressions

[bold panther]

oh i see

Thank you :)

.close

[lone heart]

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[opal sphinx]

A biologist recorded a count of 365 bacteria present in a culture after 5 minutes and 1100 bacteria present after 20 minutes.

[opal sphinx]

how do I find P(0) and r

I'm fucking begging you

[worn fox]

why close your last channel with helpful advice?

[buoyant storm]

What kind of growth is this?

in the number of bacteria?

[opal sphinx]

bacterial

[buoyant storm]

Not that term

[opal sphinx]

cause that

[buoyant storm]

Is it linear growth or..?

[opal sphinx]

idk what kind of growth

[buoyant storm]

Fill in the blank

[worn fox]

as someone literally begging you seem very unreceptive to help

[buoyant storm]

nvm

why are you studying this

Without knowing what kind of growth it is

[opal sphinx]

? that's the question I was given

[buoyant storm]

I’m saying

[left isle]

it helps to know what you're studying currently

[opal sphinx]

I'm assuming it's exponential

[buoyant storm]

Have you not learned this already?

[opal sphinx]

math

[buoyant storm]

Yes it is

Why didn’t you say that

Ok what’s the formula for exponential growth

[opal sphinx]

I'm assuming

[buoyant storm]

sub it in

[opal sphinx]

Pe^rt

[buoyant storm]

You’re supposed to make the assumption

[buoyant storm]

So? What do you do with the numbers?

[opal sphinx]

that's what I did

[velvet oar]

Can I see the question? Like a photo

[buoyant storm]

@velvet oar

[velvet oar]

Or is that everything given

Alr

Where did u find this?

[buoyant storm]

Exponential growth is assumed

[opal sphinx]

It's hw

[velvet oar]

We can assume the growth based on syllabus/subject

But alr

[left isle]

right

[opal sphinx]

math

[buoyant storm]

bacteria usually means exponential growth

[left isle]

which math tho

[opal sphinx]

logarithms and shit

[velvet oar]

Igsce? Ass maths? Alvl?

Add maths?

[opal sphinx]

wtf does any of that mean

[velvet oar]

If it's hwk from a specific subject/board they nearly always use the same formulas

Nvm

[opal sphinx]

Here's what I tried

it didn't work

[velvet oar]

Do you have the answer?

[opal sphinx]

no

[velvet oar]

It's 2.30am for me but

Set up simultaneous equations, as you did

And use logs to solve

If nobody helps you, in approx 7 hours ill do it

Sleeping is a priority though

[opal sphinx]

Gn

[velvet oar]

Thanks

This isnt urgent?

[opal sphinx]

no I've got until the 24th

[velvet oar]

Couldn't help but skim read some channels

This is important:

#help-8 message

Tmr i will explain

But with logs it isnt fifth degree

Its easier

Anyways gn

[lone heart]

@opal sphinx Has your question been resolved?

[potent steeple]

Alr assuming exponential growth:
365= ae^5n
1100=ae^20n
e^15n=1100/365=220/73
15n=ln(220/73)

n=ln(220/73)/15
a=365/e^ln(220/73)/3

I think

I’m not 100% sure and it’s almost 3 am but i think thats the answer

[left isle]

that's what i got as well for the value of r

[lone heart]

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[cursive badge]

im having a bit of trouble with these questions

for (a) im not sure where to start

(b) min nullity = 2 max nullity = 4 (min occurs when u have like ab^T have nonzero only in row 1, cd^T have nonzero only in row 2, etc) (max occurs if everything is ab^T cd^T and ef^T have nonzero only in row 1)

and (c)(d) im also not sure where to start

[lone heart]

@cursive badge Has your question been resolved?

[cursive badge]

<@&286206848099549185>

[lone heart]

@cursive badge Has your question been resolved?

[tacit arch]

Try #linear-algebra

[grand girder]

The range of the linear transformation $T_1(\mathbf{x})=\mathbf{A x}$ is the column space of $\mathbf{A}$, right? And just observe how the matrix multiplication $\mathbf{a}\mathbf{b}^T$ forms the columns of $\mathbf{A}$.

[ocean seal]

adzetto

[cursive badge]

Each column has like an element of a and all of b

So is it just b,d,f?

And the transpose a,c,e?

[grand girder]

indeed

[cursive badge]

What about the rank 1 condition

Ty sm btw!!

[grand girder]

I was talking about option a. For c you just have to think about "has rank 1 meaning that all its columns are scalar multiples of one vector"

[cursive badge]

Okay rhats what i figured so like c and e is scalar multiple of a OR b and d are scalar multiple of f (or some combination of thsoe)

[grand girder]

true

[cursive badge]

Okay thanks!

.close

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[humble phoenix]

can someone help

[gloomy saffron]

Oh sorry, Can you explain your problem more clearly

i cant understand Korean, sorry

[humble phoenix]

its the remainder

[gloomy saffron]

are you meaning insert x=-2/3 into the previous function to get the value of it?

[sour dove]

yeah I'm with Kown, lol. Can you post the original question?

[humble phoenix]

thats what the teacher gave me 💀

[gloomy saffron]

how, that's impossible

can you tell us the meaning of it?

[sour dove]

I think it says total?

not sure though

[sour dove]

oh nvm lol

it does look like total though lol

[humble phoenix]

lol

oh

[gloomy saffron]

polynomial division?

[frigid hatch]

he wants to find the remainder of
(6x^3 + 2x - 1) / (x+2/3)

without actually dividing but using the remainder theorem

[gloomy saffron]

OH, I understand

[humble phoenix]

yes

[gloomy saffron]

so

$\frac{6x^3 + 2x - 1}{3 \times (x+2/3)}$

[humble phoenix]

oh

[ocean seal]

kowngx

[gloomy saffron]

so you need insert -2/3 into

$\frac{2x^3 + \frac{2}{3}x - \frac{1}{3}}{x+2/3}$

[humble phoenix]

oh

[ocean seal]

kowngx

[gloomy saffron]

we get 2*(-2/3)^3+2/3*(-2/3)-1/3

also -16/27-4/9-1/3

we get -37/27

[humble phoenix]

oh

[gloomy saffron]

Oh, maybe o forgot sth

you need multiple -37/27 by 3

answer is -37/9

[gloomy saffron]

a/b division when both a and b were reduced by the same multiple, the value of quotient won't change, but the remainder of the a/b will also reduced by the same multiple.

[humble phoenix]

got it

[lone heart]

@humble phoenix Has your question been resolved?

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[wanton charm]

6-1

[wary stream]

Don't troll

[wanton charm]

i’m just testing how this works

bc idk how to use the bot

[wary stream]

$Are you talking this$?

[ocean seal]

dldh06

[wary stream]

Using #bots #latex-testing

[wanton charm]

ohh

[wary stream]

And read #latex-help

[wanton charm]

do i have to use that around my question

ok

[sour dove]

you can use Latex, but generally since it has a tiny learning curve to use we recommend clear, readable screenshots 🙂

[wanton charm]

wait i’m confused

do i just send a picture of my problem

[wary stream]

Yes

[wanton charm]

okok

ty

[sour dove]

sorry for the late reply

so the only difference between y = x^2 and x = y^2 is that x = y^2 is rotated 90 degrees to the right

like this

do you know how translations and stretches/squeezes work?

[wanton charm]

yea

i’m just confused on how to graph it

[sour dove]

in this case, we flip. h controls the vertical translation, k controls the vertical translation

[wanton charm]

wiat sorry let me be more specific

i have to graph the points of the parabola given that equation

i understand translations but i have to plug certain numbers in to find where the coordinates go

[sour dove]

oh you just plug and chug and then connect the dots. They do it here

[wanton charm]

but i’m just confused

bc when i do it myself i always get it wrong

this is a fresh problem

[wary stream]

You're probably messing up the algebra

You're just getting coordinate points

You plug in a few x values to get the cooresponding y value

Like you do something like x = 0

[wanton charm]

wait let me try and do it rn

and i’ll tell u if i get stuck or if it’s wrong

wait im so confused

i have a new problem now bc i keep getting them wrong

this si the new one

[wary stream]

https://www.youtube.com/watch?v=TxPDQfWeAUg&ab_channel=Mario'sMathTutoring
That might help

[wanton charm]

ok ty

[lone heart]

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[devout rapids]

How do you do q3 (c)

[devout rapids]

I think you have to diff it and then do second diff to show TP is min but I’m not sure how to/might be doing smth wrong

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@devout rapids Has your question been resolved?

[lone heart]

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[coarse vale]

Help.

[tacit arch]

Use 1/(1*2) = 1/1 - 1/2

Then repeat for all terms

Then group and cancel

[vale wigeon]

riemann this series is alternating

are you sure this will work

[tacit arch]

Shit I can't read signs

[lone heart]

@coarse vale Has your question been resolved?

[austere lagoon]

can we somehow do that by telescopic method

[coarse vale]

I tried some stuff and reached till here.
The correct option is the 3rd one so pls help to correct the mistakes.

[coarse vale]

Nvm, figured out. ty.

.close

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[true pecan]

I have a question regarding effective annual interest rate

[copper temple]

dont ask to ask just do it

[true pecan]

How do they come up with this 23.22%

[lone heart]

@true pecan Has your question been resolved?

[true pecan]

I think I got it

.close

[lone heart]

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[neon cliff]

Let the function y=f(x) be continuous on the segment [0;7/2] with the graph of the function f(x) as shown below. The function y=f(x) reaches its maximum value on the segment [1/2;3] at which point x0 below?

[elder valve]

If that is the derivative that is graphed, the maximum point of f(x) should be between 2 and 3, but the maximum of the values allowed would probably be x=3

[neon cliff]

I'm hesitating between point 3 and point 1, but looking at the chart, I see that point 3 is lower, I don't know if it's right or wrong.

[elder valve]

While point 3 is lower, there seems to be just about the same area above the curve between 2 and 3 as there is below, and since there is also area above the curve between 1 and 2, that gives point 3 a higher value than point 1 would have

[neon cliff]

ok thank u

.close

[lone heart]

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[elder valve]

Np

[lone heart]

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[empty spade]

how to get B

[empty spade]

,rotate

[empty spade]

I got 20x = 22y

[young finch]

go through your steps

[empty spade]

,rotate

,rotate

[opal pendant]

your working is right

[empty spade]

idk how to get it in the form of x + y

or if u even need to get it in that form or not

[opal pendant]

i'm guessing because x and y are intergers you can just sub x=1

[empty spade]

if x = 1
22y = 20
y = 10/11
multiply x and y by 11
so x = 11, y = 10
x + y = 21

is that how u do

[opal pendant]

yes i think so

[empty spade]

ok

thx

.close

[lone heart]

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[alpine sable]

I don't understand where I went wrong

[near apex]

$\sqrt{a^{2} + b^{2}} \neq a+b$

[ocean seal]

.enemagneto

[young finch]

just isolate sigma

no need to do square root cause you have the value of mu

[alpine sable]

i see

this is what i found

is that correct

the one up there is what i started with

Oh it's correct, checked the solutions

[alpine sable]

ty for this, was helpful

.close

[lone heart]

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[vale wigeon]

!status

[lone heart]

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

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

[vale wigeon]

show current progress

$x - 0.4x = 0.5$, solve for $x$

[ocean seal]

Ann

[lucid ember]

0.6x = 0.5

x-0.4x

[modern sedge]

This is not right

you probably divided both sides by 0.4

[young finch]

1-0.4

1x

[ocean seal]

methisalwaysright

[modern sedge]

You divided it incorrectly

[young finch]

best not to do it that way though, further complexion

[modern sedge]

Yeah, use this to simplify x-0.4x

I was just showing what was their mistake

[young finch]

yeah just making sure they knew that

[lone heart]

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[vapid shuttle]

I am trying to write $xy^2\frac{dy}{dx}=y^3-x^3$ as $\frac{dy}{dx}=f(\frac{y}{x})$

[ocean seal]

austinu

[vapid shuttle]

but I get to

$\frac{dy}{dx}=\frac{y}{x}-(\frac{x}{y})^2$

[ocean seal]

austinu

[vapid shuttle]

and I don't see a way to get out of that

the point of rewriting is because it is a homogeneous diffeq

I want to solve it using substitution

and I am trying to write it good first

Any tips?

[lucid ember]

what happens if you let u = y/x and substitute?

[vapid shuttle]

well that is the substitution I am making

I let $y=zx$ then $\frac{dy}{dx}=z'x+z$

[ocean seal]

austinu

[vapid shuttle]

then I perform my subs

and I get $z'x+z=z-(\frac{1}{z^2})$

[ocean seal]

austinu

[vapid shuttle]

then I get $z'x=\frac{-1}{z^2}$

[ocean seal]

austinu

[vapid shuttle]

oh and I guess this is just seperable?

I suppose that was the goal

hmm I just thought I always had to rewrite as f(y/x)

and the inverted one was throwing me off

[lucid ember]

this looks right

[vapid shuttle]

ty

.close

[lone heart]

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[vapid shuttle]

I’m wondering where I went wrong

Could anyone point it out?

[lucid ember]

it should be x*dz/dx

[vapid shuttle]

it is

oh

I see what you mean

I substituted it in wrong

ty

.close

[lone heart]

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[vapid shuttle]

is there a nice identity for simplifying $cos(x+y)sin(x+y)$?

[ocean seal]

austinu

[vale wigeon]

1/2 sin(2x+2y)

:trollface:

[vapid shuttle]

just so I am not xy probleming

I am solving a diffeq

I got to

$y+cos(x+y)sin(x+y)=x+c$

[ocean seal]

austinu

[vapid shuttle]

and I am just seeing if I can make it any simpler

or possibly explicit

doesn't look like I can do explicit

[vale wigeon]

where's the y'

is this a 0th order DE

[vapid shuttle]

this is the solution

[vale wigeon]

[vapid shuttle]

I will show original

or it is my solution

hopefully it is right

$\frac{dy}{dx}=\tan^{2}{(x+y)}$

[ocean seal]

austinu

[vale wigeon]

[vapid shuttle]

u=x+y, du/dx=1+dy/dx, dy/dx=du/dx-1

[vale wigeon]

,w implicit derivative y + 1/2 sin(2x+2y) = x

[ocean seal]

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Requested by ann_dec#0

[vale wigeon]

,w (1-cos(2t))/(1+cos(2t)) = tan^2(t)

[ocean seal]

Results provided by WolframAlpha

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

Requested by ann_dec#0

[vale wigeon]

[vapid shuttle]

TRUE

[vale wigeon]

yeah checks out

[vapid shuttle]

but as for the simplifying

it looks like it probably has to be implicit

do you agree?

gonna post another question here too

is $\arctan{(x+y+1)}=x+c$ as simple as it gets

[ocean seal]

austinu

[vapid shuttle]

just another thing about if I can write it implicit or not

I think not

because tan(arctan(u)) neq u

so I can't do that

and yah

unless I am missing something

Are both of these necessarily left in implicit form?

[vale wigeon]

definitely

[vale wigeon]

eq u

[vapid shuttle]

neq u

is it equal?

hmmm

doesn't arctan have a domain restriction

tan(arctan(u))=u but arctan(tan(u)) neq u

via google

that's tricky

[lone heart]

@vapid shuttle Has your question been resolved?

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[worn tapir]

could anyone please explain why in for all moments of A, why its 5cos(45) x 0? wouldnt it be x 9 as thats how far away the force is?

[iron swallow]

The force from Ax( would point directly into the point A hence not adding any moment. Ay on the other hand is 9m away. Just as the 10kN force is ignored.

[worn tapir]

right so only account for orthagonal forces found using trig?

[lone heart]

@worn tapir Has your question been resolved?

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[indigo anchor]

i don’t understand what it’s asking?

[near apex]

When you plot those graph, you'll see that they are symmetrical. You have to give equation of line about which two parts are mirror image of each other.

,w graph y=x^2

[ocean seal]

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[near apex]

@indigo anchor Look at this.

[indigo anchor]

oohh i see

how do i plot the graph again

[near apex]

I supposed you must have been taught that.

Anyway, in general, you take a few points and plot them to find outline of graph.
Of course, for checking if you have drawn it correctly, you can make use of online graphers.

[indigo anchor]

yeah i was, just forgot haha

ah yeah you find the x and y intercepts right?

i completely forgot thank you for reminding'

.close

[lone heart]

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[tired drum]

How do we choose

[tired drum]

How do we choose to which graph to minus

[lone heart]

@tired drum Has your question been resolved?

[tired drum]

<@&286206848099549185>

[dense acorn]

I assume you're aware how to find the area already

[tired drum]

Yeah

[dense acorn]

if you have your areas, just think about which area you need to remove to leave the area you're interested in

[tired drum]

Yeah?

Ik which area I want

how do I know which area to remove tho?

[dense acorn]

if you removed the area under the line from the area under the exponential, what would be left

it'd be the area that's under the exponential, but not under the line; since we subtracted the area under the line

does that make sense, and do you see what you should subtract instead?

I can draw out both real quick to make this easier

[tired drum]

Yes please

From the way I see it, which ever area you remove you don’t get the area in between

[tired drum]

Because which ever one you subtract your loosing the area in between

[dense acorn]

it helps to consider the combined area first (their sum)

we have each value on its own, the area under g and the area under f

[tired drum]

Mhm

[dense acorn]

I've drawn the red area a bit too far there, but hopefully you see how subtracting the red area from the pink area would leave just the pink area without the overlap

the red area should stop where the pink area does

I'll correct that actually thats confusing

[dense acorn]

the red area is exactly this

[tired drum]

Mhm

[old cedar]

Anyone from India?

[tired drum]

Yeah I see

[old cedar]

Class 8 maths chapter 1.2 please

[tired drum]

But we’re trying to find the over lap area right?

[tired drum]

This channel is occupied

[old cedar]

Oh

[tired drum]

there’s available channels

[tired drum]

^

@dense acorn

[dense acorn]

yes, sorry I just realised I should have mentioned something else first.

so we have the areas, if we want to remove the overlap I think it's easiest to split up the region we're considering

what we want is to only subtract overlapping area, but right now some red overlaps with pink, and some pink overlaps with red

[tired drum]

Yeah

We’re trying to find the over lapping areas

Like the middle bit

[dense acorn]

yes, but if we just subtract our two areas over the entire region, we'd be subtracting red area that isn't overlapping

so we need to split it up first

do you see that there's a region where the red area is entirely inside of pink area, and a region where pink area is entirely in red area

[tired drum]

Yeah

[dense acorn]

by region I mean interval sorry that wasn't clear

oh wow there's a much easier approach to this I'm so sorry

[tired drum]

Yeah outside the overlapping region

Lol all g

What’s the easier approach

[dense acorn]

I'll draw it since explaining in words is confusing even me

[tired drum]

Alright

[dense acorn]

you want to look at the overlapping region more like this

since if you compare this with what we had before, over these intervals the area we're looking for is enclosed by whatever function is on the bottom

[tired drum]

Ah ok makes a lot more sense

Thank you very much

[dense acorn]

sorry if the writing was overcomplicating it I should rely more on drawing

[tired drum]

All good dude thanks

[lone heart]

@tired drum Has your question been resolved?

[lone heart]

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[lone heart]

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[bleak mulch]

how many 6-digit number can be built with 1 0 0 4 2 1?

[vale wigeon]

!status

[lone heart]

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

[bleak mulch]

1

[vale wigeon]

if the digits were all different, and none of them was zero, would you be able to answer the question?

[bleak mulch]

yes

6! would be answer

[alpine sable]

okay now

001132 isnt a valid number

neither is 012324

having 0 in the first two positions makes the number invalid

you have to discount the cases where there are 0's in the first two digits

[alpine sable]

apply the product rule that you did here again while discounting the 0's in the first two digits

although assume 00 as a block here

[vale wigeon]

also after you do that, account for the fact that you have 2 ones and 2 zeros so you will overcount

[bleak mulch]

ok

[alpine sable]

i say this because you don't want to remove the cases where you have something like 102342

[bleak mulch]

what is the problem with 102342?

[alpine sable]

nothing

[topaz pendant]

no need to assume it

[vale wigeon]

it's made from the wrong digit set

[alpine sable]

oh yeah sorry, i forgot about the set

but yes

[topaz pendant]

just make sure that the 1st digit is not zero rest all is accepted so the answer would be 5*5!

[bleak mulch]

thats not the answer because there is also double 1 is the set

[topaz pendant]

so 5*5!/4

[bleak mulch]

the answer is 150

[alpine sable]

you still have the two other 0's

divide by 2 again

[bleak mulch]

oh ok

[topaz pendant]

so here is the think see the 1st digit cant be zero but there are 2 1s so it will be 5/2 similarly the rest 5 digits have 2 zeroes so it will be 5!/2

[bleak mulch]

yes

[steel olive]

can you repeat the numbers in the above question?

or u cant repeat

[bleak mulch]

there are six digits

and u have to build 6 digit numbers

[steel olive]

can i repeat digits i.e. from 0,0,1,1,2,4 can i make 111111 as a number or not

[bleak mulch]

no

[steel olive]

then the answer will be 120

number of ways to arrange 0,0,1,1,4,2 = 6!/2! x 2! = 720/4 = 180
in these 6 numbers,there are 2 zeroes,i.e. 2/6 of the numbers in total combinations will begin with 0,so 2/3 of the numbers wont begin with zero,
so 180 x 2/3 = 120

[topaz pendant]

you have to build a six digit no so there cannot be zero in 1st place

[lone heart]

@bleak mulch Has your question been resolved?

[lone heart]

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[shadow verge]

!help

[teal bronze]

do you know the binomial theorem?

[abstract tiger]

expand using the binomial formulae of positive power

[shadow verge]

yuh

but im getting my answer in positive

😦

[teal bronze]

you can get the coefficients of (x + y)^n from the pascals triangle. the kth term will have the kth element from the nth row in the pascal's triangle (starting counting with k = 0 and n = 0)

[shadow verge]

wait 1 min let me send u what i done

[wintry whale]

!help

[lone heart]

Please read #❓how-to-get-help

[teal bronze]

another channel

[wintry whale]

where

[teal bronze]

use a free channel

like help-1

[abstract tiger]

-3

[shadow verge]

where did i go wrong?

[bright stag]

the anser is -24

[shadow verge]

na

[abstract tiger]

answer is -216

[shadow verge]

yup

but where did i go wrong?

[abstract tiger]

4* 27x^3 (-2/x)

[bright stag]

no u get x^2 when its 4c1

[shadow verge]

how is it one?

shouldn't it be 4C2?

[abstract tiger]

x power 3 divided by x is x squared

[bright stag]

because in ur answer the x^2 in the denominator and numersator gets canceled

[shadow verge]

yes

but it will be 216

which is wrong

[bright stag]

yes thats what i was trying to say

[shadow verge]

it should be -216

[abstract tiger]

its neagative

let me send answer in written

[shadow verge]

ok thx

[bright stag]

yes it would be -216

4

427(-2)

[ornate ginkgo]

Should be 0

No?

[shadow verge]

no

its -216

[ornate ginkgo]

Hmmm

[abstract tiger]

@shadow verge

[shadow verge]

mmmm ur not using binomial method are u

like the formulae

[abstract tiger]

its binomial

[shadow verge]

Cr

[abstract tiger]

i just expand the C

[shadow verge]

oh ok

cool

i understand

[ornate ginkgo]

Ohh wait ik what you did wrong

Btw

@shadow verge

[shadow verge]

r=3?

[ornate ginkgo]

r = 1

[shadow verge]

oh

[ornate ginkgo]

We are looking for power of x to be 2

4 - 2r = 2

[shadow verge]

ok

[ornate ginkgo]

Yeah sorry

Should be 3^3

Instead of 3^4

Aaaaaaa im so sloppy today

[shadow verge]

😭

[lone heart]

@shadow verge Has your question been resolved?

[lone heart]

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• Be polite and have a nice day!

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[dapper lynx]

Hey all!

[dapper lynx]

Could I get a sanity check?

I think I've done this right

[nimble fern]

looks good to me

[lone heart]

@dapper lynx Has your question been resolved?

[dapper lynx]

Thanks Biscuity!

[lone heart]

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[wintry whale]

!help

[wintry whale]

and

Some can u just send the answer with the explaintion

and this

[gloomy saffron]

R U testing?

[wintry whale]

no I have a assigenment

I need the questions tho

[gloomy saffron]

only solution?

[wintry whale]

can u show the work too

[vale wigeon]

!nosols

[wintry whale]

pls

[lone heart]

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

[vale wigeon]

no we don't do that here

[wintry whale]

then can u help me get the answers atleast

[cold pumice]

The intersection of the line with the other line is at y=6 or with the y axis at y=6?

[gloomy saffron]

hey, I DIDN'T SAID THAT I WOULD GIVE HIM SOLUTIONS

[worn fox]

Didn't need to shout, heard you all the way from another channel

[wintry whale]

can someone please help me

[tacit arch]

attempt the problem yourself first

[dense acorn]

for this one you just need to draw the lines on the axes given

[dense acorn]

^ it's better to be able to show what you're stuck on

[wintry whale]

riemann I did

the teacher didn't give an explainion

[tacit arch]

show

[vale wigeon]

WHY ARE YOU SHOUTING?

[gloomy saffron]

I may have overreacted a bit. I'm afraid of being warned.

😭

[wintry whale]

.close

[lone heart]

Channel closed

Closed by @wintry whale

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[wintry whale]

I didn't even get help

[dense acorn]

you said you attempted the problems, if you don't have work done to show that's fine but there's not much to go off otherwise

[tacit arch]

you were asked to show work

[lone heart]

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[frail kelp]

| A U B \ A | = | A U B \ B |

[blazing charm]

someone please help i'm lost on this question

sorry bro 💀

[frail kelp]

f

[blazing charm]

.rotate

[tacit arch]

,rotate

[blazing charm]

im just confused by the wording and also the context

[native cave]

uh, me too

[blazing charm]

lol

if anyone can help 🙏

[lone heart]

@blazing charm Has your question been resolved?

[cold pumice]

Holyshit these questions are so annoying

So many words

But let me try to understand wtf they want from you

[blazing charm]

lmaoo yeah

[cold pumice]

Ok I got it

Ok em

A problem

The dog is connected to something with a leash

Now,

You know what

This is a drawing of your wonderful problem

[torn elk]

Not sure if asking total arean inside or at all.

I'm guessing he is asking for this area.

[cold pumice]

I do not think so

1. It's stated that the dog dug a hole, so it can go outside the yard

And you didn't even colored the yard

[torn elk]

I might understand wrong but

the hole was in B, right?

from H to B, there are 12 feet, and the leash is 15, so he has 3 ft more from inside

[cold pumice]

2. Think about this logically, can really a dog with a 15ft go that deep into the house? Point C I mean

[torn elk]

which is already inside red

[cold pumice]

You didn't understand

Because the leash is limiting the movement of the dog, I am pretty sure the question is impossible, because different leashes will allow different movement

But

Stupid questions --> Stupid answers

[torn elk]

Let me think for a moment, I'll re-read this ton of words

[cold pumice]

I will draw it in geogebra for more accurate drawing

[blazing charm]

hmm

im confused

ping me if you figured it out

[torn elk]

this is the area is being asked

[cold pumice]

An accurate drawing with a circle with radius of 15

[torn elk]

yeah, with the accuracy of geogebra

[cold pumice]

Oh wait

I think I got it

[cold pumice]

Is that a sarcasm?

[torn elk]

no sarcasm

[cold pumice]

In just a sec

That's the area they want

@blazing charm

[blazing charm]

let me check this out

[cold pumice]

Logic:
The dog can ran in all of the yard
After going under the fence on the yard, he got 3 ft of leash left (15-12), so a semi circle with a radius of 3
After going into the garage, he got 9 ft of leash left (15-6), so 3/4 of a circle with a radius of 9

Which in total is:

[blazing charm]

how can the dog run in all of the yard if hes stuck to a 15 ft leash on point H?

that means the area in which he can run in the yard is a semi-circle with a radius of 15 ft

[cold pumice]

Yard: 18 * 9=162
The semi circle: pi * 3^2 * 0.5=4.5pi
The 3/4 of a circle: pi * 9^2 * 0.75=60.75pi
In total: 65.25pi+162 which is roughly 357.56 ft^2

[cold pumice]

Look at this drawing

That's the 15ft from point H

As you can see, the yard fits perfectly here

[blazing charm]

what?

[cold pumice]

That would be true, if the distance between point H and the other end was greater than 15, but it's 9, so he can run in all of it

[blazing charm]

it says that a leash is tied to point H

[cold pumice]

Yes

[blazing charm]

if the length of the leash is 15

[cold pumice]

Yes

[blazing charm]

that means that the dog can only go a maximum of 15 feet in each direction, forming a semicircle. the width of the yard is 18, since 40-22 is 18.

[cold pumice]

But the leash isn't on one of the end of the yard

It's stated clearly

Point H is 12 ft from point B on the segment GB

[blazing charm]

i agree

[blazing charm]

okay

[cold pumice]

And again

[cold pumice]

This is an accurate drawing of the garage+yard

The radius of the circle is 15

Of course he is limited when he exists the yard and when he enters the house as I explained before

But in the yard he can run freely

[blazing charm]

he can run freely in the yard because the his leash is 15ft long right? so from point H he can go 12 feet to B and 6 feet to G

[cold pumice]

Yes

[blazing charm]

okay i get that part now

now he says there is a small door for ginger to go inside the garage at point G

so if HG is 6,

and his leash is 15,

that means that he can go in the garage with 3/4 of a circle with a radius of 9 right?

or wait

[cold pumice]

Indeed

[blazing charm]

okay

and then it says

he also a dug a hole under the fence at point B

so that means

that he can go outside with a semicircle of radius 3

[cold pumice]

Indeed

[cold pumice]

Exactly like in this drawing

[blazing charm]

i get it now

thank you sir 🙏

[cold pumice]

Np :)

[blazing charm]

.close

[lone heart]

Channel closed

Closed by @blazing charm

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[tender anchor]

I'm having trouble w this problem so first i did dy/dx i got

6t/((t^(2)-243)+2t^2)

so for a i think that means its horizontal when derivative is = to 0 but im kinda confused how to solve for that

[tacit arch]

show your work?

oh you used (dy/dt) / (dx/dt) = dy/dx?

[tender anchor]

okay 1 sec i think i messed up

yes

[sharp sail]

Are you sure that's right?

[tender anchor]

i shoulve distributed t

[tacit arch]

but like you used product rule instead of multiplying?

[tender anchor]

yeah lol

[sharp sail]

you could've just substituted y/3 for t²-243

in the first equation

that makes it a lot more easier

[tender anchor]

should be 6t/(3t^2-243)

[sharp sail]

dy/dx?

[tender anchor]

yeah

[sharp sail]

that isn't quite right though

[tender anchor]

oh

[sharp sail]

try again

are u using ( dy/dt )/(dx/dt)

?

[tender anchor]

yeah

i did it again got the same thing

[sharp sail]

what did your dy/dt come out?

[tender anchor]

for dy/dt i first distributed the 3 and then its 3t^2-729 and the derivative of that is 6t

[sharp sail]

yea

[tender anchor]

and for t(t^2-243) i distributed the t made it t^3-243t which goes to 3t^2-243

[sharp sail]

wait that's right too

But originally, if you substitute y/3 for (t²-243) you get
x = t (y/3)
or y =3x/t
then dy/dx should come out to be 3/t

I wonder why isn't that so

[tender anchor]

what's y/3?

[sharp sail]

t²-243

from the second equation

[tender anchor]

oh

ok i think i got part b

[sharp sail]

oh wait now I got it

[tender anchor]

part a i still dont understand

is it just 0

ok ya it was that makes sense

i got it all right

[sharp sail]

if y = 3x/t
then if you calculate dy/dx then you also gotta multiply it with dt/dx, as per the chain rule, so sorry I was wrong you're right here