help-0

[thorny solar]

the subject was related to pendulums, and harmonic waves.

sorry if this is not the correct way to ask for help for an issue like this.

.close

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[alpine sable]

Can i get some gelp for this question

Theres another way to solve this equation but i forgot

[warped verge]

I think if you have 100% of liquid with 15% of milk, so 85% will be a coffee. Next do the math.

[alpine sable]

How

[warped verge]

Sec, i need to write this down on paper

if i am not wrong this a answer

[alpine sable]

Yeah thats what I got from my other equation

What would be the equation for it though

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[errant hinge]

how r varies from -l/2 to +l/2

anyone please, i have exm trw please tell me

[tacit arch]

That's just the choice of coordinates. The middle of the rod is the origin

l is the length, so l/2 is half the length in each direction

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[glacial jasper]

im like raging rn this is really confusing

[marsh rapids]

a teacher decided to have pupils work in groups today. She put them in groups of 4 and had 3 groups work on activity A and the 7 remaining groups work on activity B. How many pupils are there ?

Is it easier that way ?

[glacial jasper]

no im sorry i cant really understand that :/

i appreciate the effort tho!

[marsh rapids]

can you tell me how many groups there are ?

and if so, can you use that to find how many students there are ?

[lone heart]

@glacial jasper Has your question been resolved?

[lament glen]

whatever you do to one side of the equality, you also have to do it to the other

e.g. we want to isolate x right?

we can first add 3 to both sides to get rid of the -3

but we also do it to the right

so we have x/4 = 10

then we multiply by 4 since we want to get rid of the /4

we also do it to the right, so we get x = 40

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[dusky basalt]

Howdy, Im trying to find the cartesian inequation

[dusky basalt]

Im stuck after converting z to x+iy form ;/

[alpine sable]

Hmm...

Ok so the Re operator will basically remove all the imaginary components of the z.

It only gets the real parts.

[dusky basalt]

Oh, thats what that is for, never seen that

[alpine sable]

So when you multiply z with the parentheses, you get 9z + 5iz.

And Re(9z + 5iz + 1) = 9z + 1

And you can then continue your inequality

[dusky basalt]

where does the 9z come on the otherside?

[alpine sable]

From distributing the z into (9+5i)

[dusky basalt]

im talking about the RHS

[alpine sable]

No that's just applying the properties of the Real operator

[dusky basalt]

Hmmm okay

[alpine sable]

The inequality turns from

$$\Re( (9+5i)z + 1) \le 0$$
$$ 9z + 1 \le 0$$

[ocean seal]

Ausaramun

[dusky basalt]

Okay but I cant solve that for x can I?

[lofty oriole]

But, $$\Re((9 + 5i)z + 1) = \Re((9 + 5i)(\Re(z) + i\Im(z)) + 1) = 9\Re(z) - 5\Im(z) + 1$$

[ocean seal]

pi over four

[lofty oriole]

Guess I need to divide it into lines, it can’t display the whole equation

[lofty oriole]

But, $$\begin{array}{rcl}\Re((9 + 5i)z + 1) &=& \Re((9 + 5i)(\Re(z) + i\Im(z)) + 1)\ &=& 9\Re(z) - 5\Im(z) + 1\end{array}$$

[ocean seal]

pi over four

[alpine sable]

Oh yea I forgot to account for the imaginary part of z

[dusky basalt]

so how do I find the cartesian inequation?

[lofty oriole]

I did the conversion part, now just note that if $z = x + iy$ (where $x$ and $y$ are real numbers), then $\Re(z) = x$ and $\Im(z) = y$. Replace $\Re(z)$ and $\Im(z)$ in the inequation I got, and you will have the answer.

[ocean seal]

pi over four

[dusky basalt]

but that would only leave 9x-5y + 1 right? I wouldnt be able to solve explicitly for x?

I've done other region questions with imaginary numbers and usually solve for x

[lofty oriole]

Yes

This is because the inequation represents a region on the Argand diagram

So you can’t really solve for x or y

[lone heart]

@dusky basalt Has your question been resolved?

[dusky basalt]

Sorry its not correct

that inequation represents the region

how do I find the cartesian equation

[lofty oriole]

But you can’t convert an inequality to an equation

[dusky basalt]

cartesian inequation*

[lofty oriole]

It really does look like a region above a straight line though

[dusky basalt]

right so how do I find where that line sits

Sorry ahaha

[lofty oriole]

That’s $9x – 5y + 1 = 0$. But if you want the region it’s $9x – 5y + 1 \leq 0$

[ocean seal]

pi over four

[dusky basalt]

Ok yeah I understand

Thankyou for your help @lofty oriole

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[dusky elk]

A sorceress has summoned a spirit and has contained it using a perfect 10 ft wide circle of salt on the floor of a rectangular room (the circle of salt is centered in the middle of the room). The sorceress stands in the north east corner of the room. The north wall is 15 ft away from the salt circle, and the sorceress is 30 ft away from the spirit when it appears in the center of the circle. What are the dimensions of the room?

[dusky elk]

I need help finding the equation

[fervent timber]

draw a picture

[last ether]

^

I was gonna say

Draw a diagram

Helps you visualize what is going on

[dawn birch]

goofy ahh question 💀

[last ether]

I mean

The sorceress could be in any diagonal from the center

It just depends on how long the East-west walls are

[heavy sun]

Lol would it be 50 x 10sqrt(11) ?

[last ether]

I mean

If we assume that the sorceress is in the corner

But like

The sorceress could be anywhere

She could be above the circle

[heavy sun]

Let's assume she can't fly ye

[dusky elk]

k

[dusky elk]

wait howd you get that?

[last ether]

Lame ass sorceress

[heavy sun]

Rest is obvious

[dusky elk]

ohh alr

tyvm

[heavy sun]

Np

[zealous dagger]

Anyone know how to get this? 🤔 intially I thought that all you have to do is divide the number then add 1002 but that is incorrect

"In a municipal election 39218 votes were cast for two candidates. The winner had 1002
votes more than the loser. How many votes did the winner receive?"

[heavy sun]

19104

[zealous dagger]

you sure? I was attempting it again and I think the winner gets 20110 votes

[heavy sun]

Oh wait

19104 is the loser

20106 is the winner

@zealous dagger

[zealous dagger]

thank you👍 I figured out how to do it lol

loser = 19108
winner = 20110

[dusky elk]

pythagerous right?

[heavy sun]

Yes

[dusky elk]

30^2-25^2=sqrt(275)

?

@heavy sun

[heavy sun]

x=sqrt(275) in the diagram I sent

[dusky elk]

so sqrt(275)+25^2 = 30^2

?

@heavy sun

[heavy sun]

Bro I think you should study pythagoras theorem again

[dusky elk]

lmao

[dusky elk]

pls just tell

[heavy sun]

Here x=sqrt(275) and the length of side of rectangle is 2x

[dusky elk]

ohh i understand

and then the height is 50

thx

[heavy sun]

Yes

[dusky elk]

it would be (2sqrt(275)) * 50

?

[heavy sun]

Yes

[dusky elk]

alr thx

[lone heart]

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[cinder stump]

Uh I got a question, so like how do I know the length of something from the perspective? Like I'm standing awy from something it appears to me to be 5cm but in reality it's like 10 so how do I found out it's 10? Is there a type of rule or what

[cinder stump]

Yes but the thing is

I'm trying to find the real side yk?

The angular size I'm seeing I got it and I got the distance so what do I do to get the real size?

@umbral dune

So I multiply?

?

Ight so I multiply angular size with the distance right?

But den it might like give me a big number lol

Hmm can you give an example cuz I'm a little stupid?

Hmm well I'm trying to do it irl yk? But I don't have the numbers right now

But let's say

I see something the size of 5cm

At a 100cm distance ok?

How do I get it's real size yk?

Cuz if we do 5x100 it would be 500

Which is too big yk

So do I still divide it?

No I'm giving an example the size I'm seeing is 5cm yk?

I'm standing away from it

And it appears to me 5cm

So look ill tell you the irl thing I'm using this for

So look something behind a glass

And I'm trying to find it's size yk?

So let's say I measure its size from the glass yk?like put a ruler or somin like that on it behind the glass

And let's say it gives me 5cm yk?

And there is like a 30cm distance

So how do i get the actual size? 💀

Well like I think it don't really matter since its like yk I'm measuring it from the glass yk?

It appears on the glass 5cm on the ruler

And like a 30cm distance whats the rule?

Hmmm

So like I put my eyes a little far from the glass right?

And then see how tall it is

Then what

@umbral dune

Then what 💀

Ik. What I'm saying is that the distance between the glass and the object is 30cm yk?

So I'm measuring from the glass

Haaaa

Hmmmmmmm

Then what's the answer yk?

Breh

Let's say we get the measurements right?

Now what I do

Knowing its size from this distance?

Well no cuz it's inside the glass yk?

Like a box

Bruh

Fine I'll see what I can do

Hmm

Hmmmmmmmm

Eh it kinda is

Need to read it like twice

And I'll get ot

It*

So ye thanks

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[zinc thunder]

Which operation, between 2 polynomials, multiplication, addition, subtraction or division will not always result in a polynomial? And why?

[fervent timber]

first of all what does a polynomial mean?

[zinc thunder]

An expression with multiple terms, I think

[fervent timber]

yes

what else

[zinc thunder]

Idk🐸

[fervent timber]

the exponents have to be positive integers

[tender dew]

division

because it will produce rational function

[zinc thunder]

.close

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[wraith bridge]

help

[tender dew]

first

negative coefficient

and odd degree

[wraith bridge]

.close

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[frozen matrix]

can someone explain the last part

[frozen matrix]

those numbers are 0 at the bottom

[clear stump]

no

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@frozen matrix Has your question been resolved?

[frozen matrix]

thank you very much

[lone heart]

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[vague iris]

Is this correct so far?

[tight locust]

Yea

[vague iris]

okay ty! I tried to solve it. Is this correct?

[tight locust]

Yeah looks good

[vague iris]

nice tysm!

.close

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[dusky elk]

is this right cuz the radius is not 10

[dusky elk]

?

anyone?

@last ether

[lone heart]

@dusky elk Has your question been resolved?

[dusky elk]

cmon man go find a diff channel

<@&286206848099549185>

[dusky elk]

.close

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[sly comet]

What is the max amount of x-intercepts of a polynomial with highest degree of 6?

[oak perch]

6

[sly comet]

Then how many turning points could it have?

[oak perch]

What is the definition of turning point?

Nvm I searched the definition

[oak perch]

5

[sly comet]

So any polynomial to power degree n

Means that the max turning points it could have are n-1?

[oak perch]

Yeah

[sly comet]

Is this always the case?

[oak perch]

Yeah

Turning points are real roots of the derivative of the polynomial

Which is of degree n-1

[sly comet]

ok thanks

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[granite zealot]

So I’m need some help with using matrices to solve system of equations there was something like that on my math final and I didn’t know what to do

[granite zealot]

And maybe some other general algebra 2 stuffs

And then solving the system of equations

<@&286206848099549185>

I found one from homework

<@&286206848099549185>

I generally don’t understand what to do or where to start

.close

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[quick oyster]

Need help with numbers 3 5 6 and 10

[meager pagoda]

Hi

For #3 what do you think the first step would be

You need to find the area and the formula for area of a circle is πr²

[quick oyster]

6 2 x 3.14

[meager pagoda]

6 is the diameter

The formula asks for the radius

[quick oyster]

So 3?

[meager pagoda]

To find the radius you would just divide by 2

Yes

[quick oyster]

28.26 is the answer?

[meager pagoda]

Yes

[quick oyster]

Thank you

[meager pagoda]

Do you know how to start #5

[quick oyster]

Nope

[meager pagoda]

Okay so for #5 I would start by finding the circumference of the whole circle

C=2πr

Then I would divide by 2 to find the length of half the circle

Then I would add 18

[quick oyster]

I’m confused on this part

[meager pagoda]

Okay so we are given that the diameter is 18

So the radius is 9

So in your calculator

Type in 2 x 3.14 x 9

When you get that answer, that is the circumference of the whole circle

[quick oyster]

Alr

56.52

[meager pagoda]

Yeah, now divide by 2

Then add 18

And that would give you the perimeter of half the circle

[quick oyster]

46.26

[meager pagoda]

Yes

Do you want to try #6

It’s similar to #5

[quick oyster]

Sure

[meager pagoda]

Okay, let me know when you get an answer

[quick oyster]

226.08?

[meager pagoda]

Okay, how did you start this question

[quick oyster]

18 x 2 x 3.14

[meager pagoda]

This question asks for the area

And the formula for area is πr^2

We are given that the diameter is 18, and the formula asks for the radius

Don’t forget to divide by 2

So the correct equation you would set up is 3.14 x 9^2

Do you understand?

[quick oyster]

Oh alr

Same answer as before? 56.52

[meager pagoda]

No, the question above asked for the perimeter which is basically the distance around the circle

This question asks for the area

[meager pagoda]

Use this equation

And then divide by 2

[quick oyster]

28.26

That’s the area?

[meager pagoda]

No

9^2

Is 9 squared

Not 9x2

So do 9x9

3.14 x 9 x 9

[quick oyster]

254.34?

[meager pagoda]

That’s the area of the WHOLE circle

Now you need to divide by 2

Are you understanding more now?

[quick oyster]

127.17

[quick oyster]

Yeah

[meager pagoda]

Yes

Your answer for #10 is incorrect

Do you think you may know how to start it?

[quick oyster]

10^2 5^2?

[meager pagoda]

What’s the formula for the area of a circle

[quick oyster]

A = pi r^2

[meager pagoda]

Yes okay

Find the area of each circle

Then divide the area of circle 1 by circle 2

Then you should get your answer

Try solving it, if you have any questions let me know

[quick oyster]

Alr

First one is 314.16

And 2nd one is 78.5

@meager pagoda

[meager pagoda]

Yes!

Now divide 314/78.5

And you should get an answer!

[quick oyster]

4

[meager pagoda]

Yea

[quick oyster]

Thank u so much I really needed this help.

.close

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[kindred path]

does anyone know the answer to this?

[lone heart]

@kindred path Has your question been resolved?

[kindred path]

is this correct?

<@&286206848099549185>

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@kindred path Has your question been resolved?

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[alpine sable]

How do i know the original function of this?

[shell widget]

Which question are you talking about?

[alpine sable]

Q36

Terrible screenshot

[shell widget]

Well if you put x=0 in 5/(2x+10), what do you get?

And you can write the denominator as x - 0

And you'll get your desired form

[shell widget]

Yes.

[alpine sable]

I was doing x = 1/2

😩

[shell widget]

Can you do it now?

[alpine sable]

I get f(c)) 1/2

[shell widget]

Yes, f(0) = 1/2.

[alpine sable]

I don't get how it's C though

Wouldn't i have to derivative f(x)

[shell widget]

Can you tell me what f(x) is?

[alpine sable]

5/2x+10

[shell widget]

5/(2x+10), yes.

And we know that the limit given is just f'(0)

Differentiate 5/(2x+10) and plug in x=0.

[alpine sable]

-1/10

[shell widget]

Yes.

[alpine sable]

@shell widget

This would be C right

Since (2)^3 = 8

Without the minus

[shell widget]

Yes, answer is C.

Cause x^3 - 2^3 = (x-2)(x^2 + 2x + 4)

[alpine sable]

I don't get why i don't derivative x^3

[shell widget]

Because there is no limit here

[alpine sable]

But I do with the multiple choices?

[shell widget]

What do you mean?

[alpine sable]

I mean i should be getting the derivatives of the multiple choices?

[shell widget]

No no

There is no derivative involved in this question

[alpine sable]

Because its missing the limit

[shell widget]

Yes.

[alpine sable]

?

Then I was getting the answer by luck

So f(x) = 8

[shell widget]

f(x) = x^3, that is given.

f(2) = 2^3 = 8

f(x) - f(2) = x^3 - 8 = x^3 - 2^3

You should know that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

So x^3 - 2^3 = (x - 2)(x^2 + 2x + 4)

[f(x) - f(2)] / [x - 2] = (x - 2)(x^2 + 2x + 4)/(x - 2) = x^2 + 2x + 4

[alpine sable]

I get it now..

After being given the answer though

[shell widget]

No derivative involved here.

However, if lim x--> 2 is given with the question

Then you just plug in x=2 in x^2 + 2x + 4

And you will get f'(2), where f(x) = x^3

[alpine sable]

Wouldn't it be 12

[shell widget]

Yes.

[alpine sable]

Alright thanks for the help

Really appreciate it

[shell widget]

Np!

[alpine sable]

.close

[lone heart]

Channel closed

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[vocal tapir]

x^2-x-30=0

[iron swallow]

Hello

[vocal tapir]

how do I find the roots?

[iron swallow]

My channel

But I can help you

[vocal tapir]

ok

[iron swallow]

Like square roots

[vocal tapir]

ya

[iron swallow]

Just click this button

[vocal tapir]

hmm

[iron swallow]

Oh do you generally want to understand the concept

[vocal tapir]

I understand the concept, BUT

I suck at squaring

meaning factoring

these ones

(a-b)^2

if that's the case

[iron swallow]

Can I have a question

[vocal tapir]

ya

[iron swallow]

This

Ok

So what do you think squared means

@vocal tapir

[vocal tapir]

can we get straight to the point?

sorry

I know the other stuff

but

[iron swallow]

Basically a number times a number

[vocal tapir]

yea

[iron swallow]

So a times a

Is

[vocal tapir]

dying inside

[iron swallow]

We can write that a squared

[vocal tapir]

dude I know that

[iron swallow]

-b times -b

[vocal tapir]

how do I factor (a-b)^2

[iron swallow]

=+b

What factor you can’t factor that

That not a factoring question

You can expand

Not factor it

[vocal tapir]

.close

[lone heart]

Channel closed

Closed by @vocal tapir

Use .reopen if this was a mistake.

[iron swallow]

It is probably expand

[jolly notch]

what

i can solve your qs

[iron swallow]

Hey

[jolly notch]

x^2-x-30=0

right?

[vocal tapir]

yea

I just had enough

sorry

[jolly notch]

reopen

[vocal tapir]

.reopen

[lone heart]

✅

[jolly notch]

Okay so do you know how to break up the middle term?

[vocal tapir]

I know it's x(x-6)+5(x-6) BUT

I only get to that via trial & error

[jolly notch]

Hmm

Alright

[iron swallow]

Where is the question

[jolly notch]

So there's multiple ways of solving quadratic equations

[jolly notch]

pinned

[jolly notch]

1. breaking up middle term
2. quadratic formula
3. completing square

which one would you use

[iron swallow]

May bad I never saw your question

[iron swallow]

I thought you meant this

[jolly notch]

@vocal tapir

are you there?

[vocal tapir]

definitely not completing the square here I think

but breaking up middle term

would suffice

ig

[jolly notch]

yes that's unnecessary unless the question commands you to

[vocal tapir]

into -6x+5x

[jolly notch]

yes so how do you break up the middle term

what do you think is the first step

[jolly notch]

how do you get those values OTHER THAN trial and error

[iron swallow]

Find to number that times to 30

[vocal tapir]

that's a very good question to which I do not have the answer

[jolly notch]

he opened the ticket.

[iron swallow]

You can use this method

[jolly notch]

alright
so the general eq is

ax^2+bx+c

so you multiply a and c

[vocal tapir]

yup 🙂

[jolly notch]

in this case 1 and 30

[iron swallow]

Yup

[jolly notch]

(note if it was -1 and 30 you would take -1 and multiply them)

[iron swallow]

He is a lot better at explaining then me

[jolly notch]

and multiply them to get a number (this case 30)

and find out its factors

1x30
2x15
3x10
5x6

[iron swallow]

6 and 5

[jolly notch]

and see which pair adds up to the middle term

oh wait

i messed up

[iron swallow]

Lol

[vocal tapir]

no worries

[jolly notch]

the numbers are 1 and -30

so you take the -

and you get -30

[iron swallow]

And the if they ask to solve for c

It become plus 30

[jolly notch]

-1x30
-2x15
-3x10
-5x6
1x-30
2x-15
3x-10
5x-6

These are the possible pairs.

are you following?

do you understand till here @vocal tapir

[iron swallow]

Are they asking you to solve to @vocal tapir

[jolly notch]

yes

[iron swallow]

Ok so then I’m this case it is the opposite

[jolly notch]

what are these pairs of? the product of a and c.

[iron swallow]

So plus 30 and

[jolly notch]

it's -30 and 1

x^2-x-30

[iron swallow]

Ya

@jolly notch

[jolly notch]

he literally went off

[iron swallow]

Could you help me after

[jolly notch]

question?

im bad at math

[iron swallow]

I know it is linear but how do I explain it

[jolly notch]

is that PHYSICS???

[iron swallow]

No

Linear graphs

Really easy

It like and a question

[jolly notch]

on a graph it makes a straight line?

um

i dont know

google it

[iron swallow]

But do I just write that

I have to write what makes it linear

Ok I got another question then

[woven crane]

,rotate ccw 90

[ocean seal]

Couldn't find an attached image in the last 10 messages.

May 26, 2022, 7:20 AM

[iron swallow]

Hey

Here

[woven crane]

,rotate ccw 90

[iron swallow]

I just wana know what to write

[jolly notch]

you do understand this server is meant for homework HELP, not solve my homeword for me no offense

[iron swallow]

And how to word it

Na

[woven crane]

how did you determine its linear?

[iron swallow]

This is a practice test dude

[jolly notch]

ima leave then

[iron swallow]

I’ll

Kk

@woven crane could you help

Ik it linear

But I dot. How to explain it

[woven crane]

.

[woven crane]

.

[iron swallow]

I don’t honk I can just draw a graph

To prove it

[vocal tapir]

sorry had to do some stuff

im back

[woven crane]

@iron swallow

[iron swallow]

I am using this channel know

[vocal tapir]

sorry had to do some stuff im back

[iron swallow]

Please find another one

[vocal tapir]

yes

[vocal tapir]

there's free channels currently

feel free to take advantage

[iron swallow]

No you left

This is mine now

[vocal tapir]

channel hasn't been close

up until it isn't closed

either due to inactivity

[iron swallow]

You just closed it

[vocal tapir]

or manually closing

no

[iron swallow]

.close

[vocal tapir]

I don't see your username here

there's 2 channels

absolutely more than enough for you

[iron swallow]

Can I just help you

Your doing like really easy stuff how are you struggling

[woven crane]

rude

[iron swallow]

Sorry

I liek explained the question to him above but he think I am wrong

X=30,-1

@woven crane

Help me

[woven crane]

??

[naive valley]

what is the actual question in this channel?

i scrolled back like 10 pages and couldn't find it

[vale wigeon]

OP seems to want to know how to solve x^2 - x - 30 = 0 by factoring without trial and error

as far as i can tell

[lone heart]

@vocal tapir Has your question been resolved?

[naive valley]

hmm, well the coefficient of -30 on the constant term tells you that the roots have opposite signs, and the coefficient of -1 on the x term tells you that they must differ in absolute value by 1.. quickly checking the integer factors of 30, only +/-5 and +/-6 are plausible, then you can easily check that (x+5)(x-6) works

[vocal tapir]

yeah I'm sorry at this point

but I'm at work

💀

let me read up

[vocal tapir]

all right I'll give you an evil problem and see how you'll do? since you're so tough

I've read so much and solved like 60 problems for a day different ways

being cocky only complicates your own life

[vocal tapir]

yup here?

[vocal tapir]

yes

I know breaking up the middle term into -6x+5x

but

I forgot how to do it without trial & error

[vale wigeon]

thing is, factoring things directly kind of implies some degree of trial and error and/or just being lucky and spotting it

[vocal tapir]

damn I was always insecure and thought it shouldn't be like that

[iron swallow]

Are you done

[vocal tapir]

no

[iron swallow]

If you are @vale wigeon could you please help after

[naive valley]

due what the hell, you already have two channels of your own

[iron swallow]

I can’t find them

They just go aaay

Away

[vocal tapir]

this guy has been here as soon as I took the channel

[naive valley]

oh

[vocal tapir]

he's capping btw

[vale wigeon]

they have your name on them

[vocal tapir]

2 active

💀

[iron swallow]

Ya I can’t see them

[vocal tapir]

dawg

DWAG

[iron swallow]

How do I go to them

[vale wigeon]

#help-10

[vocal tapir]

stop the cap

[vale wigeon]

click this

[naive valley]

see this little arrow to the left of "MATH HELP" - that is clickable, make sure it is pointing down

otherwise channels that you have read get hidden

[iron swallow]

My channel ain’t there

[vocal tapir]

we can see your channel

it is mf

[naive valley]

the "MATH HELP (OCCUPIED)" one, I can see your arrow points right, click it to make it point down

[iron swallow]

But I can’t

[vocal tapir]

I can't with this guy

[iron swallow]

Oh

[vocal tapir]

anyhow

ok so I got one more complicated problem

(3x-2)^2=16

[iron swallow]

Thank but could one of you come and help after

[vocal tapir]

open it, leave your problem

if in 15 minutes no one has responded

ping helpers

[iron swallow]

Kk

[vocal tapir]

or use /r/learnmath/ in reddit @iron swallow

[naive valley]

one approach is to expand out the square and rearrange into the usual quadratic form

[vocal tapir]

yeah so it breaks up into:

[naive valley]

another approach is to square root both sides (but keep in mind there will be a + and - version)

[vocal tapir]

3x-2=4 and 3x-2=-4

but I don't understand why

[naive valley]

well more generally if you have a^2 = b^2

then a = +b or -b

[vocal tapir]

hmmm

[naive valley]

like a^2 = 4

a can be 2 or -2 right?

[vocal tapir]

oh

I see it

yea

[naive valley]

same deal here

[vocal tapir]

if it's -a^2 then it shouldn't be a real number

right?

if put under a radical

[naive valley]

you mean if it was -a^2 = 4?

yeah there would be no real solution

[vocal tapir]

I see tysm

I'll close this one for now

.close

[lone heart]

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[fossil sundial]

<@&286206848099549185>

[lone heart]

@fossil sundial Has your question been resolved?

[stuck grail]

From your sketch in (b), you should be able to see that the only way the line y=k could intersect the curve C at 3 distinct points is if the value of k lies somewhere strictly between the two critical values of C. If k is greater or less than both of those values, the line can only intersect once, and if k equals one of the critical values it only intersects C at two distinct points.

So use calculus to find the critical points of C, then plug in those points to find the critical values of C.

@fossil sundial

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[true fossil]

Give a definition for the range of a linear transformation T. Suppose that the matrix A represents the transformation T. What is the
range equivalent to in terms of A?

[true fossil]

I am confused about the second part

Suppose that the matrix A represents the transformation T. What is the
range equivalent to in terms of A?

Would it be the coloums of A?

We have to write defintions for school

[stuck grail]

Close. It's the column space of A (the space spanned by the columns of A)

[true fossil]

So would this be more right: Simple the range of a linear transformation: T: V- > W is a subspace W. Give a definition for an eigenvalue and eigenvector. What is an
eigenspace

[lone heart]

@true fossil Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[sinful tiger]

Hello, I was calculating the derivative of this first function, and I did get the right development. However I don't exactly understand how you should simplify it to get the (x-1)^2*(4x+2)...

[lofty oriole]

You take the common factor out.

$$\begin{array}{rcl}f'(x) &=& 3(x - 1)^2(x + 1)+ (x - 1)^3\&=& (x - 1)^2 \left(3(x + 1) + (x - 1)\right)\end{array}$$

[ocean seal]

pi over four

[lofty oriole]

If you continue to simplify the second bracket, you should get what they got.

[sinful tiger]

Thank you! It was quite dumb T_T

[lofty oriole]

It's okay, next time you will see it 🙂

[dusky blaze]

please show working

[sinful tiger]

.close

[lone heart]

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[scenic wren]

Help

How?

How do I reduce to the same denominator?

You mean taking the LCM?

How would that help?

[vague coral]

i dont think it will

[scenic wren]

It's an inequality here. I think AM GM typeofshit

Maybe jensen's idk i don't know what function to assume

[vague coral]

try comparing the numerator and the denominator in each fraction

[scenic wren]

This is something i came up with

A quadrilateral whose diagonals are b+d and a+c and they intersect at right angles. So i got a relationship in angles and sides but idk I'm stuck

[lone heart]

@scenic wren Has your question been resolved?

[scenic wren]

Yep i did that

Took a² out of the denominator and stuff

Didn't understand what to do next

what's a'?

Yes

What next?

I'm confused af

[lone heart]

@scenic wren Has your question been resolved?

[fossil sundial]

<@&286206848099549185>

[oak perch]

Got it. First f(a,b,c,d)=f(ta,tb,tc,td) in other words it’s homogeneous therefore we only need to consider it on part of a sphere. Aka, we assume that a^2+b^2+c^2+d^2=1, a,b,c,d>0

Next use Cauchy–Schwarz inequality

That sum $\leq \sqrt{a^{2}+b^{2}+c^{2}+d^{2}} \sqrt{\frac{1}{a^{2}+b^{2}}+\frac{1}{b^{2}+c^{2}}+ \frac{1}{c^{2}+d^{2}}+ \frac{1}{d^{2}+a^{2}}}$

[ocean seal]

Cogwheels of the mind

[oak perch]

$=\sqrt{\frac{1}{(a^{2}+b^{2})(c^{2}+d^{2})}+\frac{1}{(a^{2}+d^{2})(b^{2}+c^{2})}} \leq \sqrt{8} <3$

[ocean seal]

Cogwheels of the mind

[oak perch]

The last inequality comes from 1/x(1-x)<=4

QED. We even found a less upper bound 2sqrt(2)

Take a=b=c=d=1/2 we see that 2sqrt(2) is actually the maximal value

[lone heart]

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[fickle owl]

simple checking my work

[fickle owl]

\frac{2+x}{1-d}\ge 3 + \frac{(2+x)}{1-d}d^2... d=1/4

$frac{2+x}{1-d}\ge 3 + \frac{(2+x)}{1-d}d^2... d=1/4$

$\frac{2+x}{1-d}\ge 3 + \frac{(2+x)}{1-d}d^2... d=1/4$

[ocean seal]

! matthewzz

[harsh girder]

solve the inequality for x?

[fickle owl]

yes

[harsh girder]

What have you tried?

$$\begin{align}&(2+x) \frac{1-d^2}{1-d} \ge 3 \
&(2+x) (1+d) \ge 3 \
&(2+x)\frac{5}{4} \ge 3\
&2+x \ge \frac{12}{5}\
&x \ge \frac{2}{5}
\end{align}
$$

[ocean seal]

秋水

$$\begin{align}&(2+x) \frac{1-d^2}{1-d} \ge 3 \\
&(2+x) (1+d) \ge 3 \\
&(2+x)\frac{5}{4} \ge 3\\
&2+x \ge \frac{12}{5}\\
&x \ge \frac{2}{5}
\end{align}
$$
```Compilation error:```! Package amsmath Error: Erroneous nesting of equation structures;
(amsmath)                trying to recover with `aligned'.

See the amsmath package documentation for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.62 \end{align}
                
Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.```

[lone heart]

@fickle owl Has your question been resolved?

[lone heart]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[meager fossil]

What does the arrow mean in this?

[vague coral]

imply

[oak perch]

Φ(10)=4, as long as n is coprime to 10 we always have n^4=1 mod 10

Oh my bad, yeah imply…

[meager fossil]

okay... soooo

I still don't get it

[vague coral]

@oak perch you are so into solving all the exercises in this server

[meager fossil]

so basically any prime number greater than 5, when raised to the power of 4 has a final digit 1?

[oak perch]

Yeah… I am bored…

[oak perch]

Yeah, since this tells you n and 10 are coprime

[meager fossil]

idk what coprime is

[oak perch]

Relatively prime?

gcd(n,10)=1

[meager fossil]

never heard of it

so what's gcd

[oak perch]

Greatest common divisor

[meager fossil]

okay so what does that mean

[oak perch]

? You asked a elementary number theory question without knowing what being relatively prime or gcd means…?

[meager fossil]

Yeahhh

[oak perch]

greatest common divisor of two integers m,n, denote gcd(m,n) is a positive integer d such that

d divides m, d divides n and

Any integer d’ such that d’ divides both m and n, we have d’ divides d

[meager fossil]

This seems very advanced

[oak perch]

It isn’t

[meager fossil]

So what's d'

I've never done elementary theory

just basics proofs

[oak perch]

Any integer such that …

[mortal trellis]

well you can also do it by calculating (10n+x)^4 for x=1,3,7,9 (why is that enough?). you don't need what cogwheels is doing

[oak perch]

this question doesn’t make much sense to you… if you don’t know what Euler function φ means and why a^φ(n)=1 mod n for any a coprime to n

[meager fossil]

why 10n+x?

[mortal trellis]

so x is the last digit of the number

[oak perch]

Yeah, works better for him.

[mortal trellis]

10 times anything always has a 0 at the end

[meager fossil]

and would it be for x=7,11,13 etc since n is greater than 5

[mortal trellis]

no

x=1,3,7,9. we are going through the possible last digits of all primes greater than 5

[meager fossil]

okay

[mortal trellis]

in general, if you have any number k with the last digit x, then m can be written as 10n+x for some other number n

so to prove your claim you need to show that every p^4, p>5 prime, is of the form 10m+1 for some m

and a way to do that is to see that every such p can be written as 10n+x for x either 1, 3, 7 or 9 and then calculating (10n+x)^4 and trying to write it as 10m+1 for some m

[meager fossil]

alright thanks, I'll do what I can with this

.close

[lone heart]

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[lone heart]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[alpine sable]

No clue what i should be doing here

Q10

[lethal stump]

ur trying to solve for when the tangent line to f(x) is horizontal

so when f'(x) = 0

[fossil sundial]

yh

it is stationary

gradient is 0

meaning it is horizontal

[alpine sable]

That's what I've done here

[lethal stump]

you've simplified to that poinyt

[alpine sable]

Derivative, then = 0

[lethal stump]

but you can still factor further

x^2 - 12x -16

[fossil sundial]

-4x^2+12x^2+16x=0

facor by 4

4(-x^2+3x^2+4x)

[lethal stump]

oh yea also you've factored it wrong

[fossil sundial]

x^3

mb

[lethal stump]

yea ur good

[fossil sundial]

-x^3

[lethal stump]

you could factor a -4x instead

so smth like

[fossil sundial]

mhm

[lethal stump]

-4x(x^2 - 3x + 4)

[fossil sundial]

more easier

to factorise

[alpine sable]

That's stupid

Look at how I've factored

😂 😂 😂 😂

[lethal stump]

😭 factoring mistakes fkn suck

because you only see them after like 10 mins of staring at ur working

[alpine sable]

Yeah that's embarrassing I've been solving too many questions tbf

Anyway thanks for the help i don't think I would've realised the mistake for hours

.close

[lone heart]

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[humble remnant]

Do you know what they mean by A, O, and H?

[lone heart]

@pale heron Has your question been resolved?

[pale heron]

nope

wait i think i do

[humble remnant]

What do you think they are

[pale heron]

adjacent opposite and hypotenuse

?

[humble remnant]

Yes

[pale heron]

alr im good now

ill just label them

[humble remnant]

👍

[pale heron]

.close

[lone heart]

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• 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.

[empty kindle]

how to prove this

[empty kindle]

also f is continuous on ab

and n = 1, 2, 3, ...

[marsh rapids]

I know no simple proof of that. The only one I ever saw used Bernstein polynomials to quite a significant extent

[empty kindle]

it is

something with weierstrass theorem

[marsh rapids]

Stone-Weierstrass

[empty kindle]

yeah

but i dont know how to approximate

[marsh rapids]

Do you know the Bernstein polynomials ?

[empty kindle]

this?

[marsh rapids]

Yes

We defined Bnk without the binomial coefficient, so Bn(f) = sum of (Bnk f(k/n)

The end of question 12 is the Stone-Weierstrass theorem

It is not a trivial question, but you can use the fact that Bn(f) -> f to show that f is 0

[empty kindle]

hm

[marsh rapids]

Using the fact that the integral is 0 for every n

Hint: || by linear combination, the integral of P(x) f(x) is 0 for any polynomial, try to find a useful polynomial||

[empty kindle]

ok

it is

0 for every polynomial

if f is also polynomial

then P=f

f^2 = 0

[marsh rapids]

f is not a polynomial, f is any function

Use the theorem Stone-Weierstrass theorem

With a bit of rigor, it can be made to work

[empty kindle]

we have to show that

[marsh rapids]

Show what ?

[empty kindle]

wait

we can

approximate P with another function

so for any function

or idk

[marsh rapids]

I thought you considered that theorem known ? So then we know that Bn(f) -> f

Where Bn(f) is a polynomial

[empty kindle]

wait

i was trying with trigonometric functions 😄

if Bn(f) - > f

Bn(f) is polynomial

then integral of P * Bn(f) is 0

or Bn(f) is 0

but Bn(f) - >f

so f=0

😄

im not comfortable with bernstein polynomials

😦

[marsh rapids]

What is P ? You only integral integral of P * f = 0 for any P. There's no f here, so that looks wrong.

[empty kindle]

P is any polynomial

[marsh rapids]

Then the integral of P Bn(f) != 0

That's not the correct approach

Reread the hint

[marsh rapids]

At least not the one I had in mind

[empty kindle]

can we pick

the polynomial that -> f?

[marsh rapids]

That is a polynomial

[empty kindle]

Bn(f) * f

?

[marsh rapids]

Yes

[empty kindle]

so this is 0

[marsh rapids]

What does that tell you about f ?

[empty kindle]

it is 0?

[marsh rapids]

Why

You can't just state the result you're trying to prove

[empty kindle]

Bn(f) ->f

its like f^2

[marsh rapids]

Rigorously provable. Go on

Almost there

[empty kindle]

is it something with Bnf sum of (Bnk f(k/n)

[marsh rapids]

Let's take for granted (rather than rigorously proving it) for now that this sequence of integrals goes to the integral of f^2. What can you conclude ? There's no hard math in this last step

Should be known property

Elementary property about integrals

[empty kindle]

idk

😐

[marsh rapids]

Sorry about the delay, was busy in another channel. What can you say of a function that's continuous, positive and whose integral is 0 ?

[empty kindle]

positive?

if it is always positive

its 0 for all x

if its never negative