help-23

[cinder pagoda]

okie

ty

.close

[safe radish]

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[exotic nacelle]

How do i clean dust

[exotic nacelle]

In my bed

[primal granite]

this is for math help

[tall bough]

take the integral to determine the area

[exotic nacelle]

Ok then?

[tall bough]

buy a new bed

[exotic nacelle]

Im a bat

I want more of it

[silent narwhal]

or he could flip it along the x-axis

[exotic nacelle]

Those beds in the market suck

[primal granite]

ok, stop trolling.

[tall bough]

.close

[primal granite]

.close

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[wraith prism]

This is valid

[final halo]

if by A' you mean the complement of A, then that is not equal to A - B

your second equality is true

[wraith prism]

Why?

So A'is U-A?

[final halo]

A' is everything that is not in A, so it cant be equal to "everything in A but not in B"

if U is your universal set then yes

[wraith prism]

I see thanks

I guess third is incorrect because It should be B bar not B' right?

@final halo

Or intersection

So it's okay

[final halo]

what do you think the difference is between B bar and B', because they are usually two notations for complement

[safe radish]

@wraith prism Has your question been resolved?

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[keen turtle]

simplify the expression

[keen turtle]

i cubed it and got

but if i simplify it to 2 sqrt5 + 3x you go full circle

[sweet mica]

Have you tried the formuka for the diference of cubes?

a³-b³=(a-b)(a²+ab+b²)

[keen turtle]

no, that's prob what i needed

what would i apply that to though

[wraith prism]

2ab?

[keen turtle]

also it's ab

ye

[wraith prism]

Yes

[sweet mica]

Yes ab

[keen turtle]

what would i apply it to

also the hint tells me to cube the entire expression

[sweet mica]

a-b = (a³-b³)/(a²+ab+b²)

But, if the hint says that, do that

[safe radish]

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.

[wraith prism]

Sorry i deleted

[keen turtle]

i'm willing to use ur method but i just don't get how

[wraith prism]

Bro just put the value a,b and solve

[keen turtle]

oh wait

[wraith prism]

a=2+√5
b=2-√5

[keen turtle]

i'm dumb

ye

[wraith prism]

Not more than me

[keen turtle]

alr i'll come back to this but should i close this in the meantime

[wraith prism]

Yes ensure me

[keen turtle]

and start a new help channel

[wraith prism]

Answer is 38√5?

[keen turtle]

if i still need help

[sweet mica]

I might not work, bye.

[keen turtle]

oh ok

.close

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[rain quarry]

Can someone check my work pls

[rain quarry]

Also can someone help me isolate cosx

[safe radish]

@rain quarry Has your question been resolved?

[safe radish]

@rain quarry Has your question been resolved?

[rain quarry]

.close

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[wraith prism]

any other short cut for this question?

it is saying that 1 to 20 we need to pick 3 numbers but they should be numbering order so how many ways of probability

<@&286206848099549185> Is there any Hindi tag where hindi knowing people can see this question

[obsidian ginkgo]

Are you aware on how to find total number of possibilities?

[wraith prism]

I can solve the question by this explanation

I am here asking about any other method

Total number of possibility of picking 3 number is 20C3

@obsidian ginkgo

[obsidian ginkgo]

You dont need to manually write out all the cases

There are always going to be n - 2 number of cases, for this question where n is the upper limit

Or broadly

n - l - 1 [ Where n is the upper limit and l is the lower limit ]

@wraith prism

[grim plover]

whats kramagt?

[obsidian ginkgo]

in order ig

[hazy elbow]

the three numbers are in order

i.e. ascending

[grim plover]

ah I see

[grim plover]

no, theresno shortcut afaik

[hazy elbow]

well, instead of writing all favourable possibilities, you could have figured out how many of them would be there

so, the first favourable condition would be (1,2,3) and the last would be (18,19,20)

so see the change in the first number

from 1 to 18

so total = (18-1)+1=18

(+1 since 1 and 18 are included)

@wraith prism

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@wraith prism Has your question been resolved?

[safe radish]

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[little cipher]

how do i draw a graph likes this on paper

[little cipher]

$h(t)=-0.2t^2+4t$

i have to find the line of symmetry of this function

[flat frigate]

紅卫兵

[little cipher]

ax+bc+c?

$$\frac{-b}{2a}$$

[flat frigate]

紅卫兵

[little cipher]

and then use quadratic equation, where x = 1

i believe

[burnt notch]

You can draw a parabola in different ways

But maybe the most important thing is to know if it is convex or concave

Do you know how to find, from the equation, whether a parabola is concave up or concave down?

[little cipher]

i think this is concave down

like a 😦

anyone?

$-4/-0.4$

[flat frigate]

紅卫兵

[little cipher]

$-10/1$

[flat frigate]

紅卫兵

[little cipher]

midpoint = $-10$

[flat frigate]

紅卫兵

[burnt notch]

Sorry, I'm back

Yes it's concave down, because the coefficient of t² is negative

[little cipher]

$\frac{-10}{1}\mp\frac{\sqrt{16-4(-0.2*0)}}{1}$

[little cipher]

what would c equal to?

[flat frigate]

紅卫兵

[little cipher]

4+(10)

-(4+10)

14 or 6

[burnt notch]

What do you mean by c? Are you talking about the form f(t) = at² + bt + c ?

[little cipher]

yes, but it would be equal to 0

[burnt notch]

Exactly, c = 0

And what do you mean with midpoint? Is it the vertex?

[little cipher]

that blue line

[burnt notch]

So it's not a point, it is called axis (of the parabola)

[little cipher]

oh

so x =10

[burnt notch]

An axis is a line, therefore it has an equation, which in this case is $x = 10$

[flat frigate]

Alberto Z.

[burnt notch]

Now, you may want to find the coordinates of the vertex, right? @little cipher

[little cipher]

what is vertex?

[safe radish]

@little cipher Has your question been resolved?

[burnt notch]

The minimum (or the maximum in this case) of the parabola

[safe radish]

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[cinder pagoda]

!status

[safe radish]

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

[cinder pagoda]

3

[obsidian ginkgo]

First of all
The second solution should be 180k - 45cuz otherwise you would miss solutions

[cinder pagoda]

why?

[obsidian ginkgo]

Do you agree that sin 225 is 1/root2

Yea mb

Do you agree that sin 135 is 1/root2

[cinder pagoda]

yes

[obsidian ginkgo]

How would you get it using 45 + 360k

[cinder pagoda]

answers are wrong?

and Im wrong?

[obsidian ginkgo]

They worked extra hard and wrote all the different cases in the different quadrants

180k +- 45 is equivalent

[cinder pagoda]

well I didnt get the 225 + 360K

[obsidian ginkgo]

Do you agree that sin 225 is - 1/root2

[cinder pagoda]

ya

[obsidian ginkgo]

Then

[cinder pagoda]

I need proof not Speculation

@obsidian ginkgo how did you get to 225?

[mossy fractal]

I think from the 180 - (-45)

[cinder pagoda]

Ohh ur right tnx

.close

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[cinder pagoda]

second answer is wrong?

[cinder pagoda]

Thats the answers

nvm

.close

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[lean otter]

Can anyone please help me with this question

[hazy elbow]

!status

[safe radish]

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

[sharp dome]

Make x+y the subject of the formula

[lean otter]

I

[lean otter]

Sorry i can’t understand what you mean.

[safe radish]

@lean otter Has your question been resolved?

[sweet mica]

You have to do the operations until you reach x+y

[wraith prism]

I got xy term in it

[lean otter]

I tried but i can’t get

Thank you everyone i will try asking my teacher.

.close

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[brazen helm]

How do i solve the differential equation

[brazen helm]

$y’-3y=0$

[flat frigate]

bigpufik

[dusty crescent]

This is a linear first order differential equation. Have you learnt how to solve these?

[lean otter]

What’s this is it y-3y=0

[dusty crescent]

Do you know any class of functions whose derivative is a constant times the value

[wet burrow]

No , it's y' - 3y = 0 ; y' is the first derivative of y wrt x

[brazen helm]

I mean

not really no

I mean i guess somethign with e?

[lean otter]

Are u doing trignomeryy

Never learned this I

Algebra 2

[brazen helm]

I dont know what you mean

[dusty crescent]

that's a great idea!

[brazen helm]

Ok but how do i prove that?

not just guess

[dusty crescent]

Oh, proving is harder

[brazen helm]

Yeah thats why i need to do

[dusty crescent]

oh

I would divide by y and integrate using the chain rule

[brazen helm]

right give me a second

so can i say

$\frac{y'}{y}=3$, then $\int \frac{dy}{y}=3$?

sorry i mean just three

[flat frigate]

bigpufik

[dusty crescent]

looks good

[brazen helm]

so $\ln{y}+C=3$

[flat frigate]

bigpufik

[dusty crescent]

hmmm

[brazen helm]

i mean abs value right

so $y=e^{3-c}$

[flat frigate]

bigpufik

[void glen]

👍

[dusty crescent]

no, you need to integrate 3 over y too

over x i mean

[brazen helm]

I FORGOT

you are so right

[brazen helm]

so just

$y=e^{3x-C}$

[dusty crescent]

Great!

[flat frigate]

bigpufik

[brazen helm]

so its basically all about isolating all the "ys" on one side, and constants on the other?

and the integrating

[dusty crescent]

in this case, yeah. There is no general way to solve DE:s

But thats what makes it interesting!

[brazen helm]

the next one is $y'=yx^2$

[flat frigate]

bigpufik

[brazen helm]

give me a second

but i think i know how to solve it

so just

$y=e^{\frac{x^3}{3}-C}$

[flat frigate]

bigpufik

[dusty crescent]

That's correct

[brazen helm]

okay great

thanks

.close

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[keen turtle]

From the system

x+2y=5
y+2z=8
z+2u=11
u+2x=6

find each of the values

[keen turtle]

the sum of each would be 10

and im pretty much stuck there

[quasi bison]

"sum of each"?

also the last two equations can be used to find u and z.

[keen turtle]

misprint

x+y+z+u=10

[quasi bison]

substitute one of your variables away

like u for example

u = 6-2x

[keen turtle]

oh

the teacher did it like 1 + 3 gets x+2y+z+2u=16

and then subtract from the sum to get y+u=6

and x+z=4

still substition ig?

[quasi bison]

i mean there's no obligation lol

[keen turtle]

wonder why he did it like that

[safe radish]

@keen turtle Has your question been resolved?

[keen turtle]

might've it just been to demonstrate the symmetrical nature of the equation or smth

[safe radish]

@keen turtle Has your question been resolved?

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[safe radish]

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Remember:
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[glass girder]

bruh this is like yr 2 work

[daring lily]

!status

[safe radish]

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

[wraith prism]

1

[glass girder]

lol

[wraith prism]

I just need hints I'll solve it further

[glass girder]

drop back a year

[thin bridge]

derviatives and slopes

[wraith prism]

Ohh got it

[glass girder]

wasnt that hard

[wraith prism]

Y'=4x-4

[wraith prism]

It is not hard but I may be in a confusing state right now

[glass girder]

alr well drink prime

[thin bridge]

NOT APPROPRIATE

[wraith prism]

@glass girder get lost

Leave the channel

[thin bridge]

lowercase y, but yes

[wraith prism]

What next so any parallel line will be 2x+k

[glass girder]

sorry guys that was my friend when i went to the bathroom

Im really sorry

[thin bridge]

what's the slope of
y = 2x + k

[glass girder]

Sorry again

[wraith prism]

m=2

[thin bridge]

and what's the slope of a line parallel to that?

[wraith prism]

Same

[thin bridge]

yes

can you continue from here

[wraith prism]

That's why i wrote this

Line of equation which we are finding

I will say...4x-4
2x-2
So k =-2

[sly field]

what

you have 2 equation just make slopes of two equal

[quasi bison]

sounds like a very flimsy excuse tbh

[thin bridge]

I will say...4x-4
2x-2
So k =-2

your thought process is unclear

[wraith prism]

y+2=2(x-1)

I got the point from putting y'=0 then put in the equation

(1,-2)

I guess this is correct. I remembered the process

[thin bridge]

why are you setting y' = 0

[wraith prism]

To make it tangent

[thin bridge]

no

y' gives the expression for slope at certain x

[sly field]

tangent = slope

[thin bridge]

you don't want your slope to be 0

[grim plover]

u do that when u want critical point

[thin bridge]

you want you slope to be the same as the desired line

hence my leading questions

[wraith prism]

I guess this is correct

[wraith prism]

Slope is same m=2

[thin bridge]

hence what should you be setting y' equal to?

[wraith prism]

To find the point of inflection

And then passes through the line

[thin bridge]

also NOT answering my question

[peak hemlock]

4x-4=2
x=3/2
let the tangent line is y=2x+a
f(3/2)=2(3/2)+a
a=-9/2
y=2x-9/2
is it correct?

[thin bridge]

!nosols

[safe radish]

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.

[sly field]

y' should be equal to slope of line

[wraith prism]

But why?

[thin bridge]

y' gives the slope at certain x

[lean otter]

hi everyon

can someone help me with one que.?

[thin bridge]

you interested at when the slope of your function is the same as y = 2x + 5 (which had a slope of 2)

[sly field]

make new channel

[lean otter]

If tan x = b/a Then find the value of sqrt((a + b)/(a - b)) + sqrt((a - b)/(a + b)) *

[thin bridge]

thus you should be setting
y' = equal to that slope

and NOT something else

[sly field]

i think divide by a

[wraith prism]

I am confusing what is this now?

[quasi bison]

please open your own channel. read #❓how-to-get-help for instructions.

[wraith prism]

Slope of the function= slope of the line

[wraith prism]

Wtf

[brave wolf]

Read what Ann told you

[wraith prism]

@lean otter get lost from here

.close

[thin bridge]

please read #rules #❓how-to-get-help

[safe radish]

Channel closed

Closed by @wraith prism

Use .reopen if this was a mistake.

[sly field]

yes you will get x from this

[lean otter]

Ok

Sorry

[wraith prism]

.reopen

[safe radish]

✅

[wraith prism]

So let me first write what i did...i found y' then =0 which gives a point of inflection and we find a point (1,-2) and we pass a line through it which has the same tangent and you said slope of the line 2 =slop of the function
4x-4=2
X=3/2
Now our line equation line will be y=2x+k what should I put at y to get value of k even x =3/2 is not sufficient

should I put 3/2 into equation

[sly field]

why are you finding point of inflation

[quasi bison]

your line must pass through (3/2, f(3/2) ) in order to be tangent

[thin bridge]

..i found y' then =0 which gives a point of inflection
firstly doesn't necessarily give you the point of inflection and in this case it doesn't, (it gives locations of stationary points which could potentially also be inflection points)
and as mentioned earlier setting y'=0 is pointless for this question

[wraith prism]

Y=2(3/2)^2-4(3/2) ?

[quasi bison]

btw y'=0 is for turning points and not inflection points

[wraith prism]

This is helpful to give y point

[sly field]

what is parallel to line y= mx +b

[wraith prism]

This is correct @sly field

y=2x-3/2

I got this

[thin bridge]

Y=2(3/2)^2-4(3/2) ?
that'll give you the y-coord at the point of tangency which you'll need

[wraith prism]

I got the difference what i was doing and now what i did

[sly field]

-9/2

[wraith prism]

Nope

-3/2 is correct

[thin bridge]

who's telling you its correct

[wraith prism]

Now i found why it was correct

I put -3/2 directly in the equation

[grim plover]

*inflection

[wraith prism]

(3/2,-3/2)

First i need to find and now i got it

Y=2x-9/2

Finding line equations by y-y1=2(x-x1) is not an actual problem to me

even first the line which i got by critical point where y'=0 also has the same slope

I meant we can draw many lines where it has m=2 means parallel to the line

[calm bridge]

those are not tangents

[wraith prism]

Yes exactly

[calm bridge]

there will be only 1 tangent to the curve with that slope

others are chords

[wraith prism]

The line which i found first by point (1,-2) is tangent to the curve

And have the same slope

[sly field]

i can't understand why are making it so complicated

[calm bridge]

how?

at x = 1, slope is 0

[wraith prism]

My doubt is genuine and i am refining it. Just imagine it by graph not by equations

[calm bridge]

so the tangent is horizontal

[wraith prism]

As we give m=2

[calm bridge]

not having a slope of 2

f'(x) = 4x - 4

try substituting x = 1

[wraith prism]

Now i understand what is the main mistake...slope/tangent

The line passing through (1,-2) also has same slope to the line y=2x+5 but it is not tangent to the curve

Here we want a line which has same slop as the line has and it should be tangent to the curve not intersecting the curve...we can get many lines parallel but they cut the curve

So here we just get slope value from the given line which is simply 2...now we need a point at the curve...we know every point on a curve has tangent(except critical points like 1,-2 here)

[calm bridge]

critical point also has a tangent

[thin bridge]

there can be tangents to critical points too

[wraith prism]

So we find the slope of the curve by Differntiation first then put it equal to the line slope so it gives x point and by curve equation we can get y point

[calm bridge]

the slope is just 0

[thin bridge]

you just don't care about the tangent to this one critical point that you unnecessarily found

[calm bridge]

horizontal tangents

[wraith prism]

Ohh so (1,-2) is the special point on the curve where slope of tangent doesn't exist right?

[calm bridge]

it does exist

0 exists

[thin bridge]

its the point on the curve where derivative is 0,
that's how you obtained that to begin with, by setting derivative to 0

[wraith prism]

Maybe i should say...slope is zero at only (1,-2) in this curve

[sly field]

yes

[wraith prism]

Tangent on any curve has slope 0 it will be parallel to x axis and tangents which have slope infinite will be vertical tangent to x axis

[thin bridge]

tangents which have slope infinite will be vertical tangent to x axis

horrid wording

firstly undefined slope
and they'll be parallel to y-axis or perpendicular to the x-axis

[wraith prism]

Big sorry

RIP my English

Now i differentiate slope and tangent

I was mixing these words equally

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[lean otter]

Can someone please explain me the red underlined part?

[lean otter]

it just means they're odd functions i.e. f(-x) = -f(x) for all x

[dim solstice]

Odd functions have origin symmetry and what’s above the x axis right of 0 is below when you’re left of 0 (and vice versa) so you can exploit symmetry to make them zeros if you’ve got an interval that’s symmetric around the y axis.

[wraith prism]

I guess in the integration they can set the limit -a to a?

As 2 times if even function

[lean otter]

over R means an improper integral from -inf to inf, which evaluates to 0 as Alti said (we have a symmetric interval)

[wraith prism]

Amd odd function then 0

[lean otter]

yes

that's correct

keep in mind that the lower bound changes when you do that

Thank you, folks!

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[placid oak]

1. no, because the rationals are dense in the reals; if f was a bijection, a_n and a_(n+1) would have to be "adjacent" rationals, but there are rationals between every pair of rationals, so a monotonic bijection cannot exist
   (not sure on 2) though)

[safe radish]

@lilac totem Has your question been resolved?

[quasi bison]

do you mean whether there exists a bijection with BOTH these properties at once?

or are you asking about each property one by one

also

Just X

Helpers don't know what you still need help with if you only respond with ❌.
Please tell us what is still troubling you.

right

well

for convergence, suppose f(n) -> a ∈ [0,1]

pick ε s.t. (a-ε, a+ε) is a proper subset of [0,1]

then there exists N such that f(n) ∈ (a-ε, a+ε) for all n ≥ N

and thus you have to cover the entirety of ( [0,1] \ (a-ε, a+ε) ) ∩ Q, an infinite set, with only N-1 elements at your disposal.

which you cannot do.

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[wraith prism]

i want to think more about a intresection b

[harsh parcel]

uh

the q wants when either fail

and not when when both fail

so they used inclusion exclusion

thats why the intersection

because thats the probability both fail

[quasi bison]

what do you doubt about it?

A and B's exam outcomes are independent of each other.

or assumed as such. it won't be the case if, for example, A and B happen to be close friends who studied everything together and so are more likely to make the exact same mistakes.

but such circumstances would have been mentioned.

[wraith prism]

In this question we can use
P(A U B) = P(A)+P(B)

Why did we not use this?

[quasi bison]

no, we cannot.

P(A ∪ B) = P(A) + P(B) is only true if A and B are disjoint, i.e. if it is known A and B cannot happen simultaneously.

[wraith prism]

Any example Ann

[quasi bison]

sure

[wraith prism]

Two numbers at one time

On a dice

[quasi bison]

that was the example i was going to give, yes

you could also give examples with cards

[wraith prism]

Yes

[quasi bison]

it is very easy to come up with examples of disjoint events

[wraith prism]

I understand the meaning

Thanks

[safe radish]

@wraith prism Has your question been resolved?

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[coarse kelp]

What's the difference of this

[coarse kelp]

and this

why use this one ^

[minor goblet]

i believe the bottom is just the top one but written out fully

[coarse kelp]

no

its not

[minor goblet]

can you give more context?

[coarse kelp]

alright I just realized what it is now by answering your question

[minor goblet]

glad to help!

[coarse kelp]

the first one is when you're given a surface like this: R(u,v)

in that form

and the second one is for when you're given something like z=f(x,y)

ok thanks

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[coarse kelp]

.reopen

[safe radish]

✅

[coarse kelp]

what does this notation mean

[minor goblet]

R(u,v) would be a vector no?

so you just apply f to the vector

[coarse kelp]

can you give example

[minor goblet]

i.e. $\vec{R}(u,v) = (R_x(u,v), R_y(u,v), R_x(u,v))$ so $f(\vec{R}(u,v)) = f(R_x, R_y, R_z)$

[flat frigate]

nadav

[coarse kelp]

🤨

ok let's say

\begin{align*}
\vec{R} &= \langle u, v, u + v \rangle\\
f(x,y,z) &= x + y + z
\end{align*}

[minor goblet]

if for example $\vec{R}(u,v) = (uv, u+3v, 3)$ and $f(x,y,z) = x+y+z$ then $f(\vec{R}(u,v)) = uv+u+3v+3$

[flat frigate]

nadav

LeGM

[minor goblet]

yep exactly

2u+2v

[coarse kelp]

huh

ohhh

bro that's easy

so like

x=u

y=v

z=u+v

that's it?

u+v+(u+v)

[safe radish]

@coarse kelp Has your question been resolved?

[minor goblet]

yeah sorry

[safe radish]

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[halcyon torrent]

How to answer all 3 parts

I attempted doing some divisions and ratios but no result

[fathom lava]

For part v) can you find an angles to calculate, I think that will help

[halcyon torrent]

But all we know is 90 degrees which is give

[fathom lava]

You have two sides for the smaller triangle on the right

I'm assuming as you have been set this problem you've done trigonometry?

[halcyon torrent]

Calm

So will 1.5 be adjacent 😭

[fathom lava]

Yep :)

[halcyon torrent]

Tyx

Oke more question

One

[icy linden]

Pretty sure you don’t need trig for these

All possible with similar triangles

[halcyon torrent]

How do yk if it’s adjacent or opposite

Ik hypotenuse but the other 2 are confusing

[fathom lava]

Interesting

[halcyon torrent]

?

[fathom lava]

So if you look at the actual angle you want to find, the adjacent side will be "touching" your angle, and the opposite will be the side opposite the angle

[halcyon torrent]

So for vii

If I want to look for angle 0

The adjacent will be 7

Correct?

[fathom lava]

If the triangle isnt a right angle the rules don't really apply

[halcyon torrent]

Oh so how do I begin doing it

[fathom lava]

I will need to have another look at it

Maybe we should ask the person who had the soln with similar triangles

Ah okay so because the two triangles have the same angles they are similar

So you can do it with ratios

[halcyon torrent]

So I devide 7 by 4?

Divide*

[fathom lava]

Yes

[halcyon torrent]

Then multiply 1.75 to 5

[fathom lava]

Yes

[halcyon torrent]

Ok

But as for vi

Do I approach ratios or trig

[fathom lava]

Uhh let me have a think

Okay I believe each smaller triangle is similar to the big one

But I'm on a walk rn so don't have any paper to write things down

[halcyon torrent]

Or do I do that the hypotenuse is 9 then do trig

It’s ok I’ll let you enjoy your walk

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[wraith swift]

i have a question

[wraith swift]

why is extra written stuff useful for gauss jordan ?

wouldnt the elementary raw transformation give me value of x y z? why should i know what's written in the second slide?

[icy linden]

I did all with similar

[wraith swift]

<@&286206848099549185>

[lean otter]

Hola

[wraith swift]

yo mind helping me

[wraith swift]

^

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

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[languid moth]

hi i have a problem in which i have to say if the value of the problem (0,5 + 1/3 - 2/27 + 4/135) * 270/213 is the notation of a decimal number and im stuck on the procedure of the problem

[quasi bison]

??

are you just asked to solve that arithmetic problem?

or something else

[languid moth]

i have to solve it and then say if the value is the notation of a decimal number

which i forgot how

[quasi bison]

that's a little confusing the way you're wording it.

the same value can be represented in multiple ways, including but not limited to decimal notation.

[languid moth]

yea sorry english isnt my 1st language

[quasi bison]

what language was the problem written in?

[languid moth]

serbian

cyrillic

[quasi bison]

ok can you show me

[languid moth]

ok the question goes

[quasi bison]

(i can read cyrillic just fine, if that's what worries you.)

[languid moth]

o

wait

lemme send u an image

since i cant type fractions

[quasi bison]

yes do that

[languid moth]

h

whys it flipped

[quasi bison]

,rotate 180

[quasi bison]

ah!

i see it says "konačan"

that means finite, doesn't it?

[languid moth]

uhh

konacan means final

im p sure

[quasi bison]

it means something that has an end.

[languid moth]

yea

[quasi bison]

right

ok, that clears it up 100%

you just need to calculate this

and see if you can write it as a decimal without any infinite repeating part

(like for example if you got 1/3 as your answer, that would be 0.333333.... as a decimal and you would say no)

[languid moth]

i know the answer to it is 1 i just dont know the procedure

so yea

[quasi bison]

wdym procedure?

you calculated it somehow, yes?

that's your procedure

and just to double-check:

[languid moth]

yea in the back of the book

theres the answers

just

i need a procedure

[quasi bison]

,w (0.5 + 1/3 - 2/27 + 4/135) * 270/213

[flat frigate]

Results provided by WolframAlpha

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

Requested by ann_dec

[quasi bison]

...oh ok so you just looked in the back

[languid moth]

like the order in which i do it and that

[quasi bison]

alright...

[languid moth]

yea since i was stuck

[quasi bison]

do you know how to work with fractions?

[languid moth]

yeh

[quasi bison]

right

so then... just do it lmao

1/2 + 1/3 - 2/27 + 4/135

can make your own life easier by adding all four of these together all at once (with the same common denominator for all of them)

[languid moth]

o

ok tysm

i just gotta finish like

30 problems today

probably gonna stay up almost the whole night

i gotta finish all 75 problems my maths teacher gave me or else i cant go to the movies with my sister

and even tho theres 17 days to school

my parents are making me do it all now

so yea

[quasi bison]

that sucks but also isn't really our problem 💀

[languid moth]

lol yea

alr

ty

cya

.close

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[quasi bison]

np

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[lean otter]

I was finding this integral in the picture (on the top left corner). I am getting the final answer as shown in this working

[lean otter]

But, my answer key says it is $\frac{\sqrt{2}}{5}(tan^2(x) + 5)\sqrt{tan(x)} + C$

[flat frigate]

- Miles12345

[lean otter]

I have rechecked my working 5 times, but I cannot find where I have made a mistake

[calm bridge]

from -5/2

I am yet to check whole solution

oh wait no

mb

[lean otter]

And differentiation of cosx yields -sinx which makes overall expression positive

Slight mistake here (corrected in red)

[calm bridge]

yeah saw that

but in next step it was correct

last step

when you took t^1/4 common

inside will just be t

[lean otter]

Ohh

[calm bridge]

not t^5

[lean otter]

Yeah

Thank you very much

[calm bridge]

np

[lean otter]

.close

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[steady bane]

should i use bayes' theorem

[sweet mica]

No, because you don't want to invert a condition

[steady bane]

then how can decide which balls go into the second urn

[sweet mica]

Total probability, you have to consider every posibility

[steady bane]

like all balls black all balls white and so on

[sweet mica]

Yes

[steady bane]

and then multiply each with probability of drawing a white ball

[sweet mica]

Subject to the condition, yes

$P(B)=P(B|A_1)P(A_1)+\cdots +P(B|A_4)P(A_4)$

[flat frigate]

Categorist

[sweet mica]

I think there are only four posibilities

[steady bane]

not three

[sweet mica]

Oh, yes, three

But well, you can take 4 and the fourth being imposible

Hahaa

[steady bane]

yeah

so p(B/A) means probability of drawing a black given one of the possibilities

[sweet mica]

Yes

You suppose the condition holds and you calculate the probability

For example you throw a dice
A= result 2
B = result even

P(A) = ⅙
P(A|B) = ⅓
P(B|A) = 1

[steady bane]

yeah

[sweet mica]

¿De dónde eres?

[steady bane]

india

[sweet mica]

Good

I asked bc your name is las_sombras which means the shadows or the shades.

[steady bane]

learned a bit of spanish from duolingo

but only remember basic words now

eres de espanã?

ok then thank you so much

.close

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[brazen helm]

Can i say that if

[brazen helm]

a is congurent to b mod n

then a is congurent to b + nk mod n

where k is any integer

[split ether]

Yes

[brazen helm]

so $a\equiv b (\mod n) \implies a\equiv b+nk (\mod n)$

[split ether]

Use \equiv

[brazen helm]

how do i make that symbol

[flat frigate]

bigpufik

[split ether]

Yes, that is true indeed

Might as well argue using the definition of congruency mod n

[brazen helm]

Yeah ok cause i just wanted to make sure

anyway thanks so yeah it all makes sense math didnt destroy the world

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[split ether]

Insufficient information

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@edgy pier Has your question been resolved?

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[wraith prism]

(0,2,3) and (2,-2,1) what is the path from equal distance help

[safe radish]

@wraith prism Has your question been resolved?

[wraith prism]

<@&286206848099549185>

[wraith prism]

Mclose

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[dire fjord]

Wdym by path from equal distance

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@dire fjord Has your question been resolved?

[wraith prism]

The line path

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[hallow kiln]

i feel like i can answer this but i would love some confirmation

[solar hazel]

sure, show what ya got so far or are thinking

[hallow kiln]

okay so for στ i got (147365)

but that doesnt seem right

[solar hazel]

i didn't do it yet but what doesn't seem right?

[hallow kiln]

my method for these questions doesnt seem right

[solar hazel]

hmm yes i think it's wrong

[hallow kiln]

i thought so

i havent done one with 2 different cycles

[solar hazel]

why is 4 mapping to 7?

[hallow kiln]

plus i havent really been taught the method

ermm

good point

let me try again

it doesnt matter what order theyre in does it?

[solar hazel]

very unclear question

[hallow kiln]

soz

[solar hazel]

orders of some things will matter here, for others it will not

[hallow kiln]

what method should i be using to find στ?

i was doing στ(1) = σ(3) = 4

[solar hazel]

you can start with whatever element you want and compute where it maps to

yes

that's a good start

now see what 4 maps to

[hallow kiln]

i did that for all the elements and got this

[solar hazel]

while doing that, you can start writing a cycle beginning with (1 4 ...

[hallow kiln]

but i did miss a number i just noticed

[solar hazel]

but 4 shouldn't be mapping to 7

tau sends 4 to 6 and no other 6s show up anywhere in sigma or tau

[hallow kiln]

okay

so i have στ(3) = σ(7) = 7

is that right?

[solar hazel]

yea

but

[hallow kiln]

so i should write that as (1437...)

[solar hazel]

nono

[hallow kiln]

oh

[solar hazel]

don't jump to random elements

(1 4 ...

what does 4 get mapped to?

[hallow kiln]

6

[solar hazel]

write that down

and then 6 goes to?

[hallow kiln]

8

[solar hazel]

gr8

[hallow kiln]

then 8 to 5

then 5 doesnt go anywhere so do i start a new cycle?

[solar hazel]

wdym 5 doesn't go anywhere

[hallow kiln]

theres no 5 in tau

[solar hazel]

so what

tau(5) = 5

so what's sigma(tau(5))?

[hallow kiln]

2

[solar hazel]

yes

[hallow kiln]

then 2 maps to 1

[solar hazel]

yes

[hallow kiln]

then is there a new cycle

for 3 and 7?

[solar hazel]

hold up, write down the cycle we just found

in here

[hallow kiln]

done ✔️

[solar hazel]

in discord i mean

[hallow kiln]

oop

lol

(146852)

[solar hazel]

ok perfect

yes, now how about 3 and 7?

[hallow kiln]

they would have a seperate cycle?

so (146852)(37)

[solar hazel]

yep

[hallow kiln]

awesome news

okay

so for τ σ it would be

one moment...

[solar hazel]

for my sake:
(137)(2468)(134)(25)

[hallow kiln]

what is that??

okay so

[solar hazel]

just writing what tau sigma looks like

[hallow kiln]

i have τ σ(1) = τ (3) = 7

[hallow kiln]

is mine the same?

[solar hazel]

your what?

[hallow kiln]

my answer

[solar hazel]

oh that's from the earlier part of the problem

[hallow kiln]

theyre both right?

oh wait

ik what you mean

apologies

so i have something for tau sigma but it definitely isnt right

i split it up idk if youre allowed to do that or not

wait

so τ σ(1) = τ (3) = 7, τ σ(3) = 6, τ σ(4) =

oops

but ive done that for all the numbers in sigma

is it (24368)(17)

[solar hazel]

hmm

2 should map to 5?

[hallow kiln]

oh yeah

[safe radish]

@hallow kiln Has your question been resolved?

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[trim vine]

$$If:I:=:\begin{pmatrix}1&0\ 0&1\end{pmatrix},:J:=:\begin{pmatrix}0&1\ -1&0\end{pmatrix}:and:B:=:\begin{pmatrix}cos\theta &sin\theta :\ -sin\theta :&cos\theta :\end{pmatrix},:then:B:equals$$

[flat frigate]

Krishiv

[trim vine]

Yeah how do I do this

Do I just square I and J or what

Oh shoot forgot to give the options one sec

[obsidian oracle]

You mean B = cos(theta)I + sin(theta)J ? It's cut off

[trim vine]

nah that's what the question says

[devout shale]

B is given to you

without anymore more information this isn't much of a question

[trim vine]

wait dude that's literally one of the options what 💀

[trim vine]

aight

[obsidian oracle]

Bruv

[trim vine]

how'd you come to that anyway

[obsidian oracle]

So look at which coefficients are equal to cos(theta)

[trim vine]

okay

oh so are we equating I and J with B

[obsidian oracle]

Basically, the coefficients on the diagonal are the ones equal to cos(theta)

[trim vine]

mhm

[obsidian oracle]

Then, sin(theta) and -sin(theta) represent the other two coefficients

So we want to separate B into a sum of a "cos matrix" and a "sin matrix"

[trim vine]

oh yeah and the coefficients correspong to that of J

[obsidian oracle]

Yep

[trim vine]

aight that makes a ton of sense

gotcha

thanks

.close

[safe radish]

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[jade charm]

I need to find derivatives. I got the first one fine. but i cant figure out why my 2nd is wrong

[plucky elk]

lots of places where algebra mistakes can happen

try simplifying y' first

[jade charm]

i figured it out! I messed up doing the derivative of sin x and changed signs when I wasnt supposed to

thank you!

last part of this problem needs me to turn these to a differential equation that equals 0. hmm

got it now after a bit of thinking. done now. thank you for guiding me a tad to finding my error!

.close

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[burnt notch]

!status

[safe radish]

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

[tired goblet]

1

[burnt notch]

Do you have to solve that equation? @tired goblet

[tired goblet]

I wanna find out what x is

I've basically put everything from pi/6 to 11pi/6 as x

On both sides and see what matches?

But I didnt get anything?

[burnt notch]

No, that's not how you solve an equation

Do you agree that $\sin^2x + \cos^2x = 1$

[flat frigate]

Alberto Z.

[tired goblet]

Yes? I remember seeing that before

[burnt notch]

That is a thing you should know very well, not only remembering but not being sure

Anyway, can you write, from that equation, sin²x in terms of cos²x?

[tired goblet]

Ooohhh

I fhink I get it now

Okay

Thank you lmao

It's one of those problems

[burnt notch]

You should get a 2nd degree equation

[tired goblet]

I can't believe I forgot how to do it

Yup

It makes it a lot easier

Thank you

I'm so glad I kept my notes...

.close

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[royal rune]

I have to order in ascending order x,y and z. My answer was x,y,z but the solution at the end of the book is y,z,x

[safe radish]

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

@royal rune Has your question been resolved?

[calm bridge]

this is directly A.M. >= G.M. >= H.M.

[royal rune]

wdym

what do those stand for

[calm bridge]

arithmetic mean, geometric mean and harmonic mean

[royal rune]

oh

so x is am y is gm and z hm?

nvm I just checked

thanks

close.

.close

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[frail rapids]

help me pls

[frail rapids]

<@&286206848099549185>

[safe radish]

@frail rapids Has your question been resolved?

[frail rapids]

how i check the answer to wuestion

[safe radish]

@frail rapids Has your question been resolved?

[plucky elk]

!show

[safe radish]

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

[dark apex]

Well, do the question you want. If u can't, seek help

[safe radish]

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[scenic swallow]

how to differentiate x log x-x

[calm bridge]

apply chain rule on xlogx

[scenic swallow]

then do d/dx of -x seperate?

[calm bridge]

yup