help-0

[short blaze]

3rd one

[remote heron]

they did like this

$2 \sqrt[5]{\frac 23} = 2 \sqrt[5]{\frac{2 \cdot 3^4}{3 \cdot 3^4 } }$

multiply by 1

under the radical

pretty sneaky

[short blaze]

im about to jump out of a window

[remote heron]

oop sorry

[short blaze]

ok so

wait what does that do?

[ocean seal]

janniku

[remote heron]

there we go

[short blaze]

oh

[remote heron]

so, you can combine in the numerator

under the root

[short blaze]

u get 3^5

[remote heron]

yup

to me this seems uhh

not better

but it is equivalent

[short blaze]

wait how did they get 4c

[remote heron]

c to the fourth?

[short blaze]

no

the 3rd answer

it has 4c

[remote heron]

oh, i didnt even notice those powers were the same

i was eyeing this one

[short blaze]

oh

[remote heron]

sorry i cant count to 3

but, if you were looking at the third answer

i think if you played around with it a bit, youd notice how hard it was to get rid of the 3 entirely

because there is no factor of 3 left at all

[short blaze]

ok

[remote heron]

(there is no factor of 3 in the number four, and there are no other numbers)

[short blaze]

yeah i see how what u did rearranges the answer to answer 4

cuz 3^4 times 3 is 3^5

[remote heron]

yes

[short blaze]

and 3^5 to the fifth root is just 3

but then

why is it 2c/3

why does the 3 still have to be dividing

[remote heron]

V

so we started here, with a 2c

[short blaze]

yes

[remote heron]

and then we played with the numbers

$2 \sqrt[5]{\frac 23} = 2 \sqrt[5]{\frac{2 \cdot 3^4}{3 \cdot 3^4 } } = 2\sqrt[5]{ \frac{ 2 \cdot 3^4 }{ 3^5 } } = \frac23 \sqrt[5]{2 \cdot 3^4 }$

[short blaze]

yeah so when we multiply by 3^4

we turn the denominator into 3^5

so when we simplify that into 3

how come its 2c/3 and not like 2c+3 or 2c times 3

[ocean seal]

janniku

[short blaze]

does the 3 have to stay in the denominator?

[remote heron]

its the denominator coming out

yea

[short blaze]

ok

[remote heron]

you could split it back into the quotient

if its helpful to you

i mean, with a root on the top and the bottom

[short blaze]

yeah that makes sense to me

so the answer was right i just tried it

ok thanks

[remote heron]

$2\sqrt[5]{ \frac{ 2 \cdot 3^4 }{ 3^5 } } = 2 \frac{ \sqrt[5]{2 \cdot 3^4} }{ \sqrt[5]{3^5} }$

[ocean seal]

janniku

[remote heron]

[short blaze]

so are we allowed to move the denominator from there to there

[remote heron]

yea, this is fraction properties

when everything is a product like this

with no plusses or minuses

you have a lot of freedom to rearrange things

[short blaze]

ok

yeah i need to check on my properties and laws

i forgot them

[remote heron]

exponent and fraction stuff for sure

but you can boil them down a good amount

it just takes time to get used to them and to see what people are doing

theyll always skip a step or two that is hard to track

youll get it

[short blaze]

thank u

bye

.close

[lone heart]

Channel closed

Closed by @short blaze

Use .reopen if this was a mistake.

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.

[lime sluice]

give me some hints to solve these types of questions within seconds

[young finch]

this is physics right

[lime sluice]

Nope

[young finch]

oh

[lime sluice]

Time speed work

[young finch]

cause centripetal and linear speed are different

[lime sluice]

I guess I should have posted it in competition maths

[young finch]

id start by finding their speeds in meters per second

[lime sluice]

Multiply with 5/18

[modern pelican]

Can anyone help me🥲

[young finch]

#❓how-to-get-help

[remote heron]

[modern pelican]

Thanks

[vale wigeon]

open your own channel lol

[young finch]

now you can use an equation to find distance in terms of time

d=vt

[lone heart]

@lime sluice Has your question been resolved?

[vale wigeon]

eh??? i think the marked answer is wrong too

hold on

,calc 27/3.6
45/3.6

[ocean seal]

Results:

7.5
12.5

[vale wigeon]

so these are X and Y's speeds resp in m/s

after 720 seconds, we have their distances travelled as:

,calc 7.5 * 720
12.5 * 720

[ocean seal]

Results:

5400
9000

[vale wigeon]

which differ by one lap, so they do meet

but they don't meet at the starting point

they meet diametrically opposite the start

since they've done 1.5 and 2.5 laps respectively by that point

[fossil latch]

since the two should meet at the starting point after time t(unit: hour, since the time is in kilometers per hour)

45km/h × t = 27km/h × t + 3.6km ×n, n is a positive interger(1)

Description: since the two meets, the total distance that y ran should be the total distance x ran + n times the length of the circular track.

27km/h × t= 3.6km × p ,p is a positive interger (2)

We can use these two terms

I'd start by applying p= 1, 2, 3, and so on to find the value of t, on (2)

And then check if it doesn't contradict (1)

Do be careful though that I set the unit of t to be in hours and the track length is in meters instead of kilometers, and the speed is in km/h.

Hmm... if we change (1), 18km/h × t = 3.6km × n
my insticts tell me that for the minimum value of t, n=2 and p=3

But that's my instincts because I don't have a paper rn

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[cerulean herald]

im confused on how to solve this

"Classify each conic section adn write its equation in standard form"

is this an Ellipses

[tight locust]

To classify just ignore lower order terms

Like for instance the form of that first equation is just -x^2 + y = c, for some constant c which we don't care about yet. Then y = c + x², which is the form of a?

[cerulean herald]

so what do i do from here

[tight locust]

What shape is it?

[cerulean herald]

parabola?

[tight locust]

Yes

[cerulean herald]

because only one side is squared

[tight locust]

Yes

[cerulean herald]

so do I do + 75 to both sides

[tight locust]

Let's rewrite so that x² is positive

[cerulean herald]

so I multiply everything by -1

[tight locust]

y - 21 = x^2 - 10x

[cerulean herald]

ok

[tight locust]

Then complete the square on the right side

[cerulean herald]

so its

wait

what do i do from here

(x-5)(x-5) - 25?

[tight locust]

Yep

(x-5)^2 - 25 = x^2 - 10x

I agree

[cerulean herald]

ok

[tight locust]

Yep

[cerulean herald]

is that it

[tight locust]

Almost

Move the 21 to the right

[tight locust]

Yeah, that's good

[cerulean herald]

okay

can u help with one more

[tight locust]

Ok

[cerulean herald]

what should I do first?

x^2 isnt negative

[tight locust]

To classify just ignore lower order terms

[cerulean herald]

so ignore terms with no variable

[tight locust]

Do you understand what is meant by a lower order term?

[cerulean herald]

ignore terms with no variable?

[tight locust]

Not quite

Ignore terms with small exponents

Or rather of smaller algebraic degree

So the form of this equation is just

x^2 + y^2 = c

[cerulean herald]

ok

[tight locust]

For some constant c that we don't care about yet

Do you see what I did there?

[cerulean herald]

✅

[tight locust]

What does this mean physically

[cerulean herald]

Wdym

[tight locust]

If you were to draw this

[cerulean herald]

oh

erm

wait

circle?

[tight locust]

Yes

[cerulean herald]

Ok!

[tight locust]

Bonus points:

How can you already tell it's a circle, and not an ellipse

[cerulean herald]

its just x^2 and no thing

No letter nexst to it

[tight locust]

Not quite

You can tell because the squared terms have the same coefficient

[cerulean herald]

Hm Ok

[tight locust]

So we have equal scaling along the vertical and horizontal axes

[cerulean herald]

[tight locust]

Does that make sense?

[cerulean herald]

No

I mean

yeah

wait

[fossil latch]

4x²+4y²=1 is also an equation of a circle

[tight locust]

So something like
2x^2 + y^2 = c
Would be an ellipse
But something like
10x^2 + 10y^2 = c
Is a circle

[cerulean herald]

Okay

[fossil latch]

Because if you divide each side with 4, it becomes x²+y²= 1/4

[cerulean herald]

Ok

So what should i do

[tight locust]

We have
x^2 + y^2 + 6x - 2y + 9 = 0

Lets pretend the y terms aren't there

[cerulean herald]

Ok!

[tight locust]

What can we do with
x^2 + 6x

[cerulean herald]

Factor

complete square

[tight locust]

Yes, complete the square

[cerulean herald]

what do i do with 9

[tight locust]

The point is to create an equal expression

So you want to solve:
(x+3)² - k = x^2 + 6x

[cerulean herald]

Alright

is k =9

[tight locust]

Yes

So then verify this is true

Does:
(x+3)^2 - 9
Equal
x^2 + 6x

[cerulean herald]

Yes

so i replace

[tight locust]

Yes

[tight locust]

Yes

[fossil latch]

We can still factor y

[tight locust]

Now you can cancel the 9s

[cerulean herald]

✅

[fossil latch]

Same thing with what you did with x

[tight locust]

And then complete the square for the y terms by pretending the x terms aren't there

[cerulean herald]

Ok wait

Erm...

https://cdn.discordapp.com/attachments/714899075040018552/1026836319856500809/caption-2-2.gif

[tight locust]

Let's make it simple

[cerulean herald]

how do i factor this

[tight locust]

Don't factor

Complete the square

[cerulean herald]

oops

Yes

[tight locust]

What can you do with y² - 2y

[cerulean herald]

Idk

Wait what

[tight locust]

Let's back up

[cerulean herald]

(y-2)(y+1)

[tight locust]

No

Do you see where I got
y^2 - 2y
From

[cerulean herald]

Yes

[tight locust]

What did I do there?

[cerulean herald]

u got y

[tight locust]

Where did I get y^2 - 2y

[tight locust]

Yes. So just like we ignore y terms to complete the square for x

We ignore x terms to complete the square for y

[cerulean herald]

?

[tight locust]

Be careful with signs

[cerulean herald]

Wdym

[tight locust]

The box method isn't bad, but you're ignoring signs

Notice how we have -2y

Not 2y

[cerulean herald]

Oops

[tight locust]

Don't even think about x yet

We haven't even gotten to the constant term

[cerulean herald]

Ok

Wdym

[tight locust]

We have to again solve:
(y-1)^2 - k = y^2 - 2y

And make sure this is a true statement

[tight locust]

Right. So you've added 1 by making it a square. Now you must subtract 1

[tight locust]

Yes

[cerulean herald]

Is this good

[tight locust]

Yes

[cerulean herald]

my wifi shuts down in 14

Ok

[tight locust]

Remember

[cerulean herald]

Thank you

[tight locust]

You have the = 0

[cerulean herald]

Oh ye

[tight locust]

(x+3)^2 + (y-1)^2 - 1 = 0

[cerulean herald]

wait

why doesnt this graph

on desmos

[tight locust]

Zoom in

Lol

Its a very small circle

[fossil latch]

With a radius of 1

[cerulean herald]

Thank you

@fossil latch @tight locust

Have a good rest of your day

.close

[lone heart]

Channel closed

Closed by @cerulean herald

Use .reopen if this was a mistake.

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.

[alpine sable]

Hello

[alpine sable]

f:R+->R continuous and bounded

If x integral from x to x+1 f(t) dt = integral from 0 to x f(t) dt for every x in R+

Show f constant

Let F be a primitive of f with F(0)=0

So we havs x(F(x+1)-F(x))=F(x)

And from here

I have two options

To use lagrange or to see that F(x+1)/(x+1)=F(x)/x

I know the second solution

But what if we use lagrange

So we can say f(c_x)=f(d_x) with c_x in (x,x+1) and d_x in (0,x) for fixed x

I guess the Lagrange idea is harder

[quartz oxide]

Let me provide another approach

Let G(x) = (integrate f(t) dt, t from 0 to x)/x

(which is the average value of f(t) from 0 to x)

We can rewrite the condition as G(x+1)=G(x)

[alpine sable]

Yes I did it

Like that

[quartz oxide]

Then G must be constant because if not (suppose G(a) - G(b) = d > 0) we can assume that a and b is arbitrarily large, then produce arbitrary large f(x) contradicting the fact that f is bounded

Maybe?

[alpine sable]

Hmm

[quartz oxide]

Is this how you did it

[alpine sable]

I took g(x)=F(x)/x, again g(x+1)=g(x), g is differentiable g'(x)=(f(x)x-F(x))/x^2 so f(x)=g(x)+xg'(x). From g(x)=g(x+1) we jave g'(x)=g'(x+1) so g' is periodic with T=1 as g. By induction f(x+n)=g(x+n)+(x+n)g'(x+n).

Suppose there is x0>0 with g'(x0)≠0

So we get f(x0+n) when n tends infinity is {+-inf}

So we have a contradiction

so g is constant and we get f is constant

But I want to know if the Lagrange idea works somehow

[quartz oxide]

Which theorem of Lagrange are you referring to?

there are a lot

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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.

[last shale]

A research had found that 40% of people in a particular small city hate having pineapple on a
pizza. Fifty people of the city were taken randomly. Find the probability that from twelve to
twenty-one people hate having pineapple on a pizza.

[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

@last shale Has your question been resolved?

[native cave]

i don't know how English maths denotes probability but it's a binomial distribution as far as I can see

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[young finch]

whats row echelon form

[potent flame]

idk

[young finch]

compared to reduced row echelon form

[potent flame]

im confused

its like smth with the leading coefficient of each row

[young finch]

yea

[potent flame]

but i wasnt sure so i put it here

[young finch]

REF means there a leading coefficient in each row

RREF means there are only the pivot points in the matrix

no

thats not true

its when there are 0s above and below each pivot point as well

[potent flame]

so this would be REF

[young finch]

right

since the entry above the 2nd rows pivot point is 3 not 0

[potent flame]

oh i see

[potent flame]

how would we do smth like this then

[young finch]

each column represents a variable right

[potent flame]

yea

[young finch]

column 1 is x_1

[potent flame]

is the last column the solutions

[young finch]

col 2 is x_2 and so on

[young finch]

yes

since its in RREF the answers are right there

[potent flame]

oh so x=4?

[young finch]

x_1=4

but x itself will be a vector of x_1,x_2,x_3

[potent flame]

but if the last column is the solutions since its in RREF wouldnt it be x=4 y=-10 and z=-8?

therefore making the correct option x=4?

[young finch]

it says solution of x

oh

x,y,z

[potent flame]

yea

[young finch]

sure

[potent flame]

so x=4?

[young finch]

usually I see it as x_1 x_2 and x_3

yea

[potent flame]

yea because u take system of equations with x y and z

[potent flame]

this would be correct right

just like the last question

[young finch]

yes cause z=0

[potent flame]

so that makes y=20

[young finch]

yup

[potent flame]

but what if there are 4 values in the last column

like rn we only see 3

but what if there are 4

[young finch]

wdym

[potent flame]

4 solutions

lemme send rq

[young finch]

thats not how matrices work

[potent flame]

like this

look how there are 4 in the last column

[young finch]

yeah its the same thing

[potent flame]

and they ask for x1

[young finch]

just 4 dimensionsal

[potent flame]

so x1 x2 x3 and x4?

[young finch]

x_1=0 cause x_4=0

[potent flame]

then x2 = -7 and x3 = 10?

[young finch]

since x+4=0 every entry in the 4th column should be 0

[young finch]

yep

[potent flame]

but x1 is also 0 but not everything in the 1st column is 0

[young finch]

thats only cause the rightmost column is 0 in the first row

[potent flame]

oh

[potent flame]

so x1 in this case would still be 0?

like for the question x1 = 0?

[young finch]

ye

[potent flame]

alr thanks

[potent flame]

also so RREF always has the solutions on the right sides while REF doesnt?

like this would be RREF?

[young finch]

yeah thats RREF but you see how x_2 doesnt equal 0

x_1=-5x_4

[potent flame]

but the solution set on the right has 0 for x_2

[young finch]

wait

no that isnt RREF

cause the entry above the second pivot point is 4 not 0

[potent flame]

it has to be 0?

[young finch]

yep

[potent flame]

so this is just REF

[young finch]

yea

[potent flame]

ok ok thanks

[potent flame]

What about smth like this where they ask for x4 but there isnt even an x4

[young finch]

x_4 is the 4th column

[potent flame]

oh

so is it just 0?

or is it written as inconsistent

because there is no x4 in the solution column

[young finch]

no its a free variable

[potent flame]

so we just write 0 for x4=?

[young finch]

i think so

[potent flame]

aight ill check it out once more but thanks for all the help

.close

[lone heart]

Channel closed

Closed by @potent flame

Use .reopen if this was a mistake.

[young finch]

np

[lone heart]

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.

[warped topaz]

https://i.imgur.com/Zgbw363.png

[warped topaz]

x(t) = 80t^3 + 144t^2 + 36t
y(t) = 60t^3 +102t^2 + 18t +1
and
x'(t) = (12)(20t^2 + 24t + 3)
y'(t) = (60t)(3t+4)

I dont really know what to do next though...

[alpine sable]

The question is the tangent line at the origin

So x=0 and y=0

Now what do you think you have to calculate?

[warped topaz]

So x'(t) and y'(t) = 0?

[alpine sable]

No those are the derivatives. Its good that you already calculate them but you will need them for the slope of the tangent

The origin is just x(t)=0 and y(t)=0

[warped topaz]

And calculate t?

[alpine sable]

Exactly

[warped topaz]

okok

Btw what are we actually doing by finding t here?

[alpine sable]

You need to find the t so you can use the derivative to find the slope in the origing

[warped topaz]

ok

1 moment I will get the values

[alpine sable]

Do you know how to find the t?

[warped topaz]

For x(t) the values of t = 0 and -3/2 and -3/10
For y(t) the values of t = (-6-√21)/10 and (-6+√21)/10

[alpine sable]

For x you did it correct. How did you do it for y? Because they are incorrect

[warped topaz]

Oh

Just used the quadratic formula

I probably made a mistake those were some annoying numbers haha

[alpine sable]

And how did you do it for x?

[warped topaz]

I dont see my mistake 😓

[warped topaz]

Just factored out t and then factorized

[alpine sable]

Its already a hint in how the equations are given. Because they are both already factored for you

[warped topaz]

Oh

[alpine sable]

So that makes it much easier because you dont have to factor them yourself

Do you see how you can get the values for t for the y(t)=0?

[warped topaz]

1/3, -3/2 and -1/5

Damn couldve saved myself so much time hahaha

[alpine sable]

Exactly

So now for what t does x=y=0?

[warped topaz]

-3/2

[alpine sable]

👍

[warped topaz]

Why were we looking for this

Its the only real solution?

[alpine sable]

Because you are looking for the t for which it goed through the origin so x=0 and y=0

[alpine sable]

Yes

[warped topaz]

okok I get you

Wait is that just the answer?

[alpine sable]

No now you have to use the derivative

[warped topaz]

Oh I replace t with 3/2 right?

[alpine sable]

Exactly, just dont forget the minus

[warped topaz]

Oh ye haha

[warped topaz]

With both? Or just 1?

Like will I get the same answer if I put it in either?

[alpine sable]

No you have to do it in both

[warped topaz]

Ok and then what do I do with them

Set them equal to eachother?

[alpine sable]

The slope is deltay/deltax right?

[warped topaz]

yeye

[alpine sable]

So you divide the y value by the x value

[warped topaz]

Ah ok

[rotund laurel]

I need help with maths problem please help it's urgent

[warped topaz]

Then go to #❓how-to-get-help

[rotund laurel]

Tried it but don't even know how to do it

[warped topaz]

Go to #help-12 and type your question

When youre finished type .close

[warped topaz]

https://i.imgur.com/VNvZQSW.png

What did I do wrong

[alpine sable]

If this is the slope you have to put it in the formula of the form y=ax+b

[warped topaz]

ooooooooh yeye

[warped topaz]

https://i.imgur.com/ebBvOyS.png

What did I do wrong now haha

[alpine sable]

And if my calculations are right x’(-3/2)=144 and not 155

And you also dont need to put the +0 because +0 is nothing

[alpine sable]

I dont know if this matters

[warped topaz]

ohhhhhh I misstyped haha

Hmmm still incorrect

Did I make a mistake somewhere else?

I dont think so...

Not sure what im doing wrong

[alpine sable]

Im going to check the derivatives

[warped topaz]

I mean we got -3/2 for both right? so they should be correct no?

unless it was a coincidence

https://i.imgur.com/EclJwzd.png

I checked the solution ^^ apparently I did make a mistake with my calculations somewhere haha

But its fine cause I think I understand the method now 😄

[warped topaz]

I will some more examples haha

But I think I know how to do it!

Thank you for your help, you explained it really well!!

❤️

.close

[lone heart]

Channel closed

Closed by @warped topaz

Use .reopen if this was a mistake.

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.

[strange fractal]

how do i know

[strange fractal]

what the fraction is

[near apex]

Try making use of points you know from graph.

Like you must have used point (-3,8) to find the constant term.

Similarly, do you know any other point on the graph whose value you can plug in to find the coefficient of first term?

[strange fractal]

im confused

it looks as fat as like

-1/3 ig

[near apex]

Wait... You need the find the value inside that box before (x+3)^2 term. Right?

[strange fractal]

ummm no

i just found the turning point (vertex)

and put it in

hello...

[near apex]

yes.

I'm sorry. I'm not sure of what's it that you are having issue with.

[strange fractal]

like how do u find the fraction bit

the 2 boxes

[strange fractal]

OHHHY ES

YES

SORYR

yes

also if this says 0 is greater than h doesnt that mean h is a negative number

[native cave]

yes

[strange fractal]

and when it is negative it goes to da right?

[near apex]

Yes. It does.

[native cave]

is the formula (x-h)²

[strange fractal]

Yes

[native cave]

if h<0 then you get (x+...)² which would make it to the left

if h = - 2 you'd get (x-(-2))² = (x+2)²

maybe @near apex needs to confirm because I'm not very sure

[fiery salmon]

it will go to right

it is (x+k)^2 where k is positive

[near apex]

No. It's left only.

[native cave]

wait i said it was left

[near apex]

yes. Think now. The value which was earlier achieved at x = 2 will now be achieved at x = 2-k. So, graph shifts by k unit to the left.

[near apex]

yes. Sorry. I meant to reply to him.

[native cave]

no worries 👍

[fiery salmon]

yea

silly mistake

sorry

[near apex]

It's okay. It happens.

[strange fractal]

U GUYS ARE CONFUSING

[near apex]

@strange fractal Did you get it ?

[near apex]

Wait. I'll explain from the start.

[strange fractal]

wdym i thought it now means h is negative so we get (x -...)^2

[near apex]

So you have (x - h)^2, where h is negative.

[strange fractal]

bc 0 is greater than h

oh.... cuz if we sub it in...

its positive?

[native cave]

yeah

[near apex]

Yes.

[native cave]

and positive is to the left

[strange fractal]

the question is worded badly yeah

[native cave]

yup, kinda theoretical and useless imo

[near apex]

So, did you get it? @strange fractal

[fiery salmon]

think of it like

where origin originally was

it is now at x=h

and h=negative

so it goes to left

[native cave]

true

[strange fractal]

yh

[native cave]

@strange fractal type .close

[strange fractal]

.close

[lone heart]

Channel closed

Closed by @strange fractal

Use .reopen if this was a mistake.

[lone heart]

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.

[trim sail]

question 14

nevermind i just got it

.close

[lone heart]

Channel closed

Closed by @trim sail

Use .reopen if this was a mistake.

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.

[warped topaz]

is -2^(1/2) = -√2? Or DNE?

[fiery salmon]

not defined

[tawny condor]

$-2^{\frac{1}{2}} = -\sqrt{2}$

[ocean seal]

redstoneplayz09

[tawny condor]

it is defined

[fiery salmon]

wait

its not (-2)

[tawny condor]

as you wrote it, the exponentiation is only applied on the 2

[fiery salmon]

or is it?

[tawny condor]

it's not on (-2), no

if you wanted it to be, you'd have to put parenthesis around it

[warped topaz]

Ah oke

Thx guys

❤️

.close

[lone heart]

Channel closed

Closed by @warped topaz

Use .reopen if this was a mistake.

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.

[strange fractal]

Hi

[strange fractal]

Can i simplify

The final answer to 12 +/- root 540?

[fiery salmon]

my answer is coming x=12(plus minus ) root(5/3)

[strange fractal]

Oh

I need to simplify the root before?

[fiery salmon]

i did 9/15(x-12)^2=1

[native cave]

no you can write it as 12 ± (root 540)/2

(root 540)= root(135*4) = 2 root(135)

so it can be simplified as 12 ± root(135)

[strange fractal]

.close

[lone heart]

Channel closed

Closed by @strange fractal

Use .reopen if this was a mistake.

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.

[formal tide]

Hi I need some help, i've been given a few details of a parabola and i must determine its equation. Could I have some help as to explain how to get its equation?

[vale wigeon]

depends on the details

[formal tide]

the details ive been given are that it has a turning point at (-3, 5)

and the parabola passes through the point (1, 13)

[vale wigeon]

may i suggest vertex form then

[formal tide]

no idea what that is but sure

oh by the way in case thats a bit complicated

im currently in year 10

in case theres another wya to do it thats way more advanced

@vale wigeon uhhhhh you there?

[vale wigeon]

$y = a(x-h)^2 + k$

[ocean seal]

Ann

[vale wigeon]

ring any bells?

this form

[formal tide]

yep

does ring bells

uh hello>

?

i just got ghosted

[fickle sentinel]

turning point is the deepest / highest point right?

[formal tide]

yep

[fickle sentinel]

you need to know that h is -3 and k = 5

[formal tide]

ah ok

so h is the x and k is the height>

so so far

[fickle sentinel]

yes

[formal tide]

would the equation

be y = a ( x +3 ) ^2 +5

[vale wigeon]

5 min delay is not ghosting come on

[fickle sentinel]

mhm

[vale wigeon]

yes now find a using the other point

[formal tide]

hmmmm

[fickle sentinel]

simultaneous equation if im not wrong

[formal tide]

so do i insert

OHHHH

OH MY GOD

I GET IT

SO I JUST PUT

13 = A ( 1 + 3) ^ 2 + 5

is that right

[fickle sentinel]

yes

you got it

[formal tide]

wait a minute

13 is not 21

[fickle sentinel]

which means A is not 1

[formal tide]

oh

[fickle sentinel]

did you forget a exists

[formal tide]

yeah

can i ask

what does a stand for

does it stand for any thing

or is it just a variable

like how h and k stand for x and y

[fickle sentinel]

a is multiplied by the square

a(x-3)^2 = ax2 - 6ax + 9a

think of it like this

now a(1+3)^2 should equal 13-5

should be an easy solve afterwards

[formal tide]

ok thanks

wait

• 3 ^ 2?

wouldnt it be

• 3

because its originally - 3

[fickle sentinel]

no

[formal tide]

so it would become +

cause theres two negatives

[fickle sentinel]

because h is -3 right?

formula a(x-h)......

x - (-3) = x + 3

[formal tide]

but its like

(x- h

[vale wigeon]

you kind of are

[formal tide]

( x - (-3)

[fickle sentinel]

yes

[formal tide]

so wouldnt it be x + 3

[fickle sentinel]

yes

[vale wigeon]

always has been

[fickle sentinel]

idk what changed your mind

[formal tide]

then why did you put x -3

[fickle sentinel]

it was an example

you asked what a meant

a(x+3)^2 is then ax^2 + 6ax + 9a

[formal tide]

so a = 1 half?

so is the entire thing

y = 1/2 (1 + 3)^2 + 5?

[fickle sentinel]

correct

[formal tide]

wait

where would i put x

in this

like as an equation

how would i write i

[fickle sentinel]

think back: a(x-h)^2+k

where will x be?

[formal tide]

so would it just be

a ( x + 3 ) ^2 + 5

?

well 1/2

[fickle sentinel]

where's a?

[formal tide]

in the front

[fickle sentinel]

yeah then you got it

[formal tide]

ok thanks a lot man

[fickle sentinel]

include y = in front btw

if not its an expression

[formal tide]

ok

btw

how do i solve this one

its just a photo

[fickle sentinel]

ok

[formal tide]

but i can tell you what details i have

[fickle sentinel]

sure

[formal tide]

but really the nonly details i can give you

is a point where its passing and its x intercepts

it has no y intercept

[fickle sentinel]

ok no problem ill see what i can do

[formal tide]

tp and AOS are unknown

[fickle sentinel]

aos?

[formal tide]

x intercepts are (2, 0) and (5, 0)

axis of symmetry

[fickle sentinel]

oh ok

[formal tide]

oiginally i thought i could do

y = (x-2) ( x -5)

but doesnt work

cause theres a y intercept

[fickle sentinel]

axis of symmetry, what does symmetry mean?

[formal tide]

its just the x of the turning point

its like cutting it in half

[fickle sentinel]

exactly

[formal tide]

and its the same on both sides

like a mirror

ohhhhhh

if im correct

[fickle sentinel]

midpoint

[formal tide]

AOS is directly in between

[formal tide]

the x intercepts

yep

so would it be like

3.5

?

[fickle sentinel]

mhm

[formal tide]

hold on a sec lemme erase soem stuff

[fickle sentinel]

is there any other info given

[formal tide]

none that i can see

[fickle sentinel]

then idk how you're supposed to solve for y

oh wait you can

[formal tide]

if i remember correctly

we learnt that the axis of symmetry is

-b/2a

and also

y = ( x - h) ^ 2 + k

or something like that

[fickle sentinel]

ignore the a(x-3.5)

no dont think about conpleting the square

all line points are relative to their initial equation

[formal tide]

ok

so uh

anythign else

[fickle sentinel]

did they ask for an equation?

[formal tide]

yep

[fickle sentinel]

ok what info do you have so far

[formal tide]

"Determine the equation of the following parabolas"

x intercepts

and the axis of symmetry

[fickle sentinel]

isnt the equation (x-2)(x-5)

[formal tide]

i mean is it?

because

if you expanded it

it would be

my og answer

[fickle sentinel]

you said it yourself unless they wanted you to complete the square

[formal tide]

but that would have a y intercept

[formal tide]

i mean we did learn that

we cna try

[fickle sentinel]

but here's the thing

you could have found the minimum point by just expanding (x-2)(x-5) and completing the square

in a(x-h)^2 + k, (h,k) is the min point.

[formal tide]

uh huh

so i expand

then complete the square

and through that

i can find the turning point

gotcha

[fickle sentinel]

you get the min point

yes

any other questions?

[formal tide]

quick question though

[fickle sentinel]

shoot

[formal tide]

x^2 - 7x + 10

[fickle sentinel]

uh huh

[formal tide]

seems a bit weird to square it

well to complete

the square

lemme try first

[fickle sentinel]

not really, they love decimals

[formal tide]

btw would that be

• ( 3 1/2)

like in there

idk why it became point

but that was a minus smbol

or would.i put it in as

( x + 3 1/2) ( x - 3 1/2

[fickle sentinel]

heres a guide on completing squares

[formal tide]

btw

[fickle sentinel]

see the 3.5? that number sounds familiar to another answer we just had

[formal tide]

would the - 3. 5 squared

be minus or postivie

like on the outside

where it adds together witht he 10

[fickle sentinel]

10 - constant^2

you know that constant^2 = positive

[formal tide]

yep

[fickle sentinel]

hence -(constant^2) is negative

the negative is not inside

[formal tide]

oh ok

[fickle sentinel]

its more complicated when i use b/2a, im simplifying

[formal tide]

so is the entire equation just

[fickle sentinel]

but it has something to do with it

[formal tide]

y = ( x- 3.5) squared - 2.25?

[fickle sentinel]

Yes

[formal tide]

thanks man

[fickle sentinel]

np

[formal tide]

oh uh

i also kinda forgot this

transformations

[fickle sentinel]

okay

[formal tide]

like translations

reflections

i kinda forgot how they look like in equations

ok so the question is

"Describe the transformations required to ahcieve the following when starting from y = x^2"

[fickle sentinel]

okay

[formal tide]

first one is

y = -2 ( x + 1) ^2

if im correct

[fickle sentinel]

the following hen?

[formal tide]

the + 1 means its moving to the left one?

when*

[fickle sentinel]

oh

the objective of the question is...?

[formal tide]

describe the transformations

like show what transformations occured

for example reflected by 2

[fickle sentinel]

to get to what

[formal tide]

scaled by -2

[formal tide]

nothing

just show what happened

like what transformations happened

if the original thing

is just

y = x^ 2

[fickle sentinel]

this is what i understand

[formal tide]

do you know what a transofrmation is

[fickle sentinel]

you bracket x

square symbol remains outside

add one inside the bracket (x+1)^2

scale by -2

[formal tide]

uh huh

does the + 1 mean

translate to the left by 1 unit?

[fickle sentinel]

no, thats the constant

wait my mistake, yes

the constant affects y-intercept

it translates to the left

[formal tide]

ohhhh

[fickle sentinel]

y-intercept is 1, and since the coefficient of x^2 is unchanged, the curve's translation left/right corresponds to the y-intercept

(For (x+1)^2)

is that all?

[formal tide]

wait

[fickle sentinel]

looks like someone has ghosted me

[formal tide]

no i havent

i was trying

to set up my airpods

wouldnt connect

but uh wait

can you tell me how horizontal translations vertical dilation scale factor reflections in the x axis and vertical translation look like in an equation

like how to find them

[fickle sentinel]

side note my country doesnt teach transformation, im just using what i know

[formal tide]

because i didnt write it down

oh

[fickle sentinel]

oh im doomed

[formal tide]

ohhh

[fickle sentinel]

i think desmos . com solves everything you need for translation

do 3 equations with different factors changing and how it relates to horizontal/vertical translation

@formal tide uh i think you should look at #help-14

[formal tide]

ok

[fickle sentinel]

did you find what you needed?

[formal tide]

nope

i might have to open up another channel

[fickle sentinel]

no just ping another helper

[formal tide]

uh

how do i see

who are helpers

[fickle sentinel]

<@&286206848099549185> transformation help for shibe

ok sit tight

[formal tide]

while we wait

another bit of the revision i have

circles

[fickle sentinel]

equation of circle?

[formal tide]

im very confident about this one

but ima just make sure

Determine the centre and radisu for each of the following circles, then graph

(x -3) ^ 2 + (y + 1) ^2 = 9

if im correct

[fickle sentinel]

im 100% not graphing but ok lets see

[formal tide]

centre is (3, -1) radius is 3?

from what i remember

[fickle sentinel]

yes

because (x-a)^2 + (y-b)^2 = r^2

hence you get the point

and since r > 0, reject negatives obviously

[formal tide]

ok

thanks

@fickle sentinel

yo for the axes intercepts

how do i solve them

if i had to guess

if i remember correctly

you can input the numbers from the original formula

into another

to create a normal one

but i forgot how it should normally look like

.close

[lone heart]

Channel closed

Closed by @formal tide

Use .reopen if this was a mistake.

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.

[wanton pebble]

can anyone explain what to do

[alpine sable]

I would try a few easy values for A like 0 or 1

What happens when A=0?

[wanton pebble]

i can't find weather it is convegent at A=0

[alpine sable]

What does a_n become when A=0?

[lilac brook]

Hi! Solution : ||You have to take the limit as n goes to infinity to check for convergence or divergence of a sequence. In this case you have an infinity - infinity kind of indeterminate form. To deal with this we can multiply and divide by [sqrt (A^2n^2+n+1)+n], thus obtaining an infinity/infinity indeterminate form, which is easier to deal with, because we only need to care about the terms with the highest exponent. So we get n^2(A^2+1)/(n(|A|+1)), which we can simplify and get n(|A|-1). So we understand that as n goes to infinity, we get infinity * (|A|-1), and we can only hope it doesn't diverge when A is either 1 or -1, because we'd get an indeterminate form of the kind infinity * 0. And after checking with the value for A = -1 or 1, we get that the sequence converges to 1/2. Thus the sequence is convergent for exactly two real values of A, which are 1 or -1.||

[alpine sable]

!nosols

[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.

[lilac brook]

Oh sorry, I'm super new here

Should I delete the solution?

[alpine sable]

I also made that mistake when I was new

I thunk you can give the solution but you should say that you are giving the solution and censor it

So people can decide for themselves if they want to read it or not

[lilac brook]

Done.

[lone heart]

@wanton pebble Has your question been resolved?

Channel closed

Closed by @wanton pebble

Use .reopen if this was a mistake.

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.

[ashen niche]

2x/5 = 10

[broken raft]

hey @ashen niche

u multiply the 5 on both sides

u get 2 x = 50

and then u devide by 2 on both sides

to get x = 25

[buoyant storm]

!nosols

[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.

[broken raft]

got it

[lone heart]

@ashen niche Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[tiny aspen]

i need help