help-13

[rare osprey]

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[cedar kiln]

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[edgy granite]

Hi, a small question, if we have improper integral in form of x^n, its converges if n is what?

[random shale]

if n < -1

[edgy granite]

So if n is 4/5, its diverges?

[tropic oxide]

improper integral over what interval?

[0,1]? [1, +∞)? something else?

[edgy granite]

[0,1]

Im now solving this, and using useful limits, i got $\frac{3x}{x^{\frac{1}{5}}}$

[wraith dagger]

$crooge MxDuck

[cedar kiln]

@edgy granite Has your question been resolved?

[edgy granite]

<@&286206848099549185> Maybe you will have some idea guys?

[tawny warren]

@edgy granite what does this represent?

[edgy granite]

I used useful limits and wanted to use LCT or DCT to understand its convergence

So, mostly, on lectures we did something in form of 1/x^p, which I know

But now I got the result above, and I dont really know how it will help to understand convergence

[tawny warren]

so this is as x->0?

[edgy granite]

Yes

[tawny warren]

i'm not sure if it's right

the denominator

[edgy granite]

0 is singular point cuz 5th root of 0 is 0, e^0 is 1, and 1-1 is 0

And in denominator we cant have zero and thats why we should use LCT or DCT if im not wrong

[tawny warren]

wait so u used lim x->0 (e^x-1)/x = 1?

[edgy granite]

Yes

[tawny warren]

so shdn't it be 3x/(x/5)??

ur limit

[edgy granite]

In my case, x is fifth root of x, and we should multiply and divide the denominator by fifth root of x, to use useful limit

So its 1 * fifth root of x

[tawny warren]

wait so it's e^(x/5) ryt?

5th root

[edgy granite]

Yes, e^(x^(1/5))

[tawny warren]

lim x->0 (e^(x/5-1)/(x/5) = 1 then?

since the standard x is replaced by x/5

am i right?

[edgy granite]

Yes, but to be able to divide it by x^1/5, we should also multiply it bt x^1/5, to keep the it same

[tawny warren]

nono i meant this

not x^(1/5)

oh waitt

my mistake really sorry for the confusion

misread some symbols

[edgy granite]

Its okay

[tawny warren]

so it wd just be 0 ryt?

[tawny warren]

this

[edgy granite]

And here, sin(3x)/3x tends to 1

Oh, sorry, not like this'

Here, and the second fraction also tends to 0, and we left with things that I showed before

[tawny warren]

yeah for some reason x/5 stuck in my head instead of x^(1/5)

[edgy granite]

I checked in calculator, its convergent, but idk how to prove it

[cedar kiln]

@edgy granite Has your question been resolved?

[cedar kiln]

@edgy granite Has your question been resolved?

[cedar kiln]

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• 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!

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[crimson sedge]

I understand the concept of spans

but I don't know how to start this question

[foggy merlin]

you can write (x, y, z) = (x, y, 2x)

try to find v and w

[crimson sedge]

how do you get to this step from

[crimson sedge]

this

[foggy merlin]

(x, y, 2x) = (x, 0, 2x) + (0, y, 0) = x(1, 0, 2) + y(0, 1, 0)

[crimson sedge]

took me a while to understand but i got it now

thanks

[cedar kiln]

@crimson sedge Has your question been resolved?

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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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[wintry mural]

How to get to know that when to put a zero between the numbers while dividing the numbers when you are cancelling them instead of dividing?

[shut reef]

What

example

[ember python]

??

[thick blaze]

🤔

[obsidian coral]

Is this even English?

[ember python]

Definitely not correct English

[steep meadow]

Haha I like how a bunch of people are confused

[shut reef]

Of course we are

[ember python]

We need some kind of translator or something

[steep meadow]

Facts since I've no clue what they mean either

[shut reef]

He probably invented a new type of math and is confused at what he has created

[ember python]

Dude that correction did NOT help

He just added more and made it worse

[steep meadow]

Cancellation is legit just division by itself anyway?

[wintry mural]

Here's an example

[thick blaze]

Whats wrong

[ember python]

Do you speak English

It’s okay if not I understand

I’m just curious

[wintry mural]

When I cancel them I didn't put the zero between the numbers so I'm confused how to get to know that when you put a zero

[shut reef]

How old are you

[wintry mural]

No I don't speak English

[ember python]

Right

What ‘zero’ between the numbers?

[shut reef]

Probably referring to the 1st 0 in 30250

[wintry mural]

Yeah

[ember python]

What’s the problem with it?

[shut reef]

You can cancel zeroes at the end of numbers as long as it's the same amount

[wintry mural]

I'm in middle school

[shut reef]

age?

[wintry mural]

Why do you want to know

[ember python]

I mean

[shut reef]

You should know division at a legal age of being in discord

what grade in middle class?

middle school

smh

[ember python]

I saw some guy asking us to help in order numbers in the thousands in increasing order

[shut reef]

what

[ember python]

Like you don’t want to potentially insult them but…

[shut reef]

true

so lets say we have $\frac{20}{30}$ @wintry mural

[wraith dagger]

.,..

[shut reef]

what would that be

[wintry mural]

2/3

[shut reef]

correct

how about $\frac{200000}{30000}$

[wraith dagger]

.,..

[wintry mural]

20/3

[shut reef]

yeah so you understand how this works

[wintry mural]

Yeah I know

[shut reef]

Yeah so what did you need help with?

[wintry mural]

Actually, I don't know about when to put 0 between the numbers in the quotient while dividing

[shut reef]

so this is the problem you're working on $\frac{30250}{1089000}$?

[wraith dagger]

.,..

[wintry mural]

1089000/36

[shut reef]

ohh

so you put a 0 when you are dividing 0 by smth

[wintry mural]

While dividing 1089000 by 36, how to get to know when to put zero between numbers in the quotient

[shut reef]

Calculator

lol

[wintry mural]

While doing manually

[ember python]

Do you mean like long division?

[wintry mural]

Yeah

That includes putting zero between numbers in quotient

[ember python]

Then the 0 gets put there if the divisor doesn’t go into the number you’re considering

[wintry mural]

Can you please elaborate this with the help of a small example ?

[dusky hawk]

Try putting your numbers in here: https://www.calculatorsoup.com/calculators/math/longdivision.php

[wintry mural]

.close

[cedar kiln]

Channel closed

Closed by @wintry mural

Use .reopen if this was a mistake.

[wintry mural]

.reopen

[cedar kiln]

✅

[dusky hawk]

Notice that 36 doesn't go into 9. So we put a 0 in the quotient and drop the next digit in the dividend.

[ember python]

Exactly^

[cedar kiln]

@wintry mural Has your question been resolved?

[cedar kiln]

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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.

[crimson sedge]

I need help please

[cosmic steppe]

First principle is the limit definition

[crimson sedge]

This is what I did

Is it correct? I had no idea for part b

[cosmic steppe]

you did the derivative right

Now it asks for the tangent line

First, find f(-1)

Okay I gtg so

Do this:

find f(-1)
Find f'(-1)
Use point slope

[crimson sedge]

It is 7

[crimson sedge]

Okay, thank youu!

[glass blade]

f'(-1) ?

[crimson sedge]

no, f(-1)=7

[glass blade]

Ah ok

And what's f'(-1)

[crimson sedge]

-18

[glass blade]

Now you can write the equation of tangent

y- f(-1) = f'(-1)(x-1)

[crimson sedge]

y - 7 = -18 (-1-1)

[glass blade]

No no

The tangent is like this

Where it's slope is to f'(-1)

Oh wait it was written at x=-1

[crimson sedge]

the slope is found by the -1 for the both x and y1 = 7, y2 =-18

and to solve for b it is y - 7 = -18 (-1-1)

[glass blade]

It will be y-7 = -18(x-(-1))

Which becomes y-7 = -18(x+1)

The reason is the point slope form
We are given a point (x1, y1) and we have to find eqn of a line of slope "m"

The equation is y-y1 = m(x-x1)

Here your x1=-1 , y1=7 , m=-18

[crimson sedge]

wouldnt m be 25

[glass blade]

Nope m = f'(-1)

What you have found

[crimson sedge]

i did 7-(-18)/-1-(-1)

[glass blade]

How did you get this equation
Tell me your thought process

[crimson sedge]

i did rise over run to find the slope

y1-y2/x1 - x2

[glass blade]

Yes you aren't wrong

But the -18 you found is actually slope

So your eqn is
(y-y1)/(x-x1) = -18

[crimson sedge]

ohh that makes sense, mb

the derivative is always the slope of the tangent

[glass blade]

Yes

And your x1 is already given which is -1
And you found y1 which is 7

So just put the value

[crimson sedge]

to find x2?

[glass blade]

x2?

No no

[glass blade]

I mean put the value here lol

Sorry for being little confusing

Through this you shall get the equation of tangent

[strange ingot]

is this channel available for help?

[glass blade]

Ah currently little occupied

[strange ingot]

ah

[crimson sedge]

the format is Ax + By = c, A= -18 and B is the y intercept, right?

[crimson sedge]

x is -1, i got 25 for it

[glass blade]

Nope

When you speak of intercepts
x-intercept is (c/A) and y intercept is (c/B)

How to find
To find y-intercept you put x= 0
To find x-intercept you put y=0

Or write it in this form
x/a + y/b = 1

[crimson sedge]

where is -18 then, also once i find x intercept i can find c or a but how do i find any one of those

[glass blade]

y=mx + c right?

You agree?

For an equation of straight line

[crimson sedge]

yea but my class uses b instead of c

[glass blade]

Where m is slope

[glass blade]

Ok so y =mx+b

Now ok?

[crimson sedge]

yea m is slope and b is y intercept

[glass blade]

Let's now make Ax + By = C in the form of y=mx+b

By = C - Ax
y = (-A/B)*x + C/B

[glass blade]

Now compare this equation with y=mx + b

You shall see what the slope and y-intercept is

[crimson sedge]

c is the slope?

[glass blade]

y = mx + b

We all know that m is the slope right?

[glass blade]

What did I write in place of m here

Just focus on
y= (-A/B)*x + C/B

[crimson sedge]

u wrote -A/B

[glass blade]

Yes

So what is the slope

[crimson sedge]

-A/B is the slope

[glass blade]

Yes

And what's the y-intercept

[glass blade]

Here b is the y-intercept

[glass blade]

What did I write in place of b here?

[crimson sedge]

u write c/b

[glass blade]

So C/B is our y-intercept right?

[crimson sedge]

yea

[glass blade]

Nice

So now you know how to find x and y intercept of Ax + By = C

Anyways coming on this equation

Ok let's go simple so that you can understand easily

We take the general equation of the line ok @crimson sedge ?

Your favorite y=mx+b

Where m = slope and b= y-intercept

[crimson sedge]

yea, my favorite cause it the most simple one

[glass blade]

Yeah

Now (-1 , 7) is the point that lies on the tangent

[glass blade]

Assume this is the equation of the tangent

[glass blade]

So what do you think
If I put y=7 and x=-1 here

Will it be wrong?

Remember (-1, 7) is in the tangent

[crimson sedge]

no it wont

[glass blade]

Nice

So 7 = m(-1) + b

Right?

What's m
m is the slope of tangent which is -18

[crimson sedge]

b is 26

[glass blade]

Actually it's 25

18+7

18+8 = 26

[crimson sedge]

-18(-1) = -19

[glass blade]

Nani

[crimson sedge]

wait i did plus

[glass blade]

[crimson sedge]

mb

[glass blade]

Yes it's product

y = m*x + b

So it was 7 = (-18) *(-1) + b

[crimson sedge]

c/B = 25 a/B= -18

[glass blade]

Yes

So if we just see it in terms of y=mx + b

Then b = 25 and m=-18 right?

[glass blade]

.

[crimson sedge]

YEA

[glass blade]

Nice

[crimson sedge]

oops sorry all cap

[glass blade]

Now plug the value of b and m in
y= mx + b

But dont replace x, y with anything

y = -18x + 25 right?

[crimson sedge]

yea

i was gonna right it but i type slow

[glass blade]

There you go
That's your equation of tangent

[glass blade]

That means you understood

[crimson sedge]

yea but how to i make it standard now

[glass blade]

Standard like Ax + By = C?

[crimson sedge]

yea

[glass blade]

Just shift the -18x from RHS to LHS

18x + y = 25

And it became in the standard form

Understood?

[crimson sedge]

so B is 0?

[glass blade]

Ax + By = C

Compare the A, B, C with 18x + y = 25

And you tell me what's the value of A, B, C

@crimson sedge

[crimson sedge]

C is y intercept

A is the slope, 18

[glass blade]

What's the value of B after you compare?

@crimson sedge

Agree with me?

[crimson sedge]

it is 1 because C/b is 1

[crimson sedge]

yea i agree

[glass blade]

B is 1 right?

[crimson sedge]

yea

[glass blade]

Nice

[crimson sedge]

thank youu so much

[glass blade]

Let me give you a question from my side

You give me the answer this time

Just for revision

[crimson sedge]

okay bring it on

[glass blade]

Don't worry stay calm

Ok

Just a second

Let f(x) = x³+3x²+2x+1 , find the equation of tangent to the curve y=f(x) at x=1

[crimson sedge]

not afk, just doing it rn

[glass blade]

Np take your time

[crimson sedge]

-11 + -y = -4

right?

[glass blade]

Yes

Nice

Job

[crimson sedge]

u teach better than my teacher

[glass blade]

Wait a second lol

Your every step is correct

But look at the last step

[crimson sedge]

is the y incorrect?

b was -1 so i made it -y

[glass blade]

It's -11x + y = -4

[crimson sedge]

i got -1 tho

11/(-11) makes it a negative

[glass blade]

y= 11x - 4 is correct

Then after that when you shift 11x to the left side of the equality it becomes -11x
So it is -11x + y = - 4 @crimson sedge

It's just simple calculation mistake

You understood?

[crimson sedge]

yea i understood, ugh i always make tiny mistakes like those

cause i was rushing

[glass blade]

Np

Best thing is

You did everything correctly

[crimson sedge]

yea i feel so good 😅

[glass blade]

it's just minor calculation mistake that comes due to tension and rushing

Don't rush
Keep cool and solve it

You can do it

[crimson sedge]

can u also please help me on part c too

[glass blade]

Sure

Let me check where is the question

[crimson sedge]

it in pinned

[glass blade]

Ok let's do it @crimson sedge

Whats the condition for the slopes of perpendicular lines?

[crimson sedge]

it had to go across by 90 degrees

[glass blade]

I mean that's ok
But ok you can remember this condition

If m1 is the slope of line 1
And m2 is the slope of line2

And line 1 and line 2 are perpendicular to each other

Then m1*m2 = -1

[crimson sedge]

so the slope would be 1/18

[glass blade]

And if line 1 and line 2 is parallel to each other then m1 = m2

[glass blade]

Why 1/8 ?

[crimson sedge]

does 6b relate with 6c?

[glass blade]

Our equation was x - 6y + 18 = 0 right

Now make it in the form of y= mx + b

Where m is the slope and b is y-intercept

[crimson sedge]

y= 1x +0

[glass blade]

-6y = -x - 18
y = (1/6)*x - (18)/(-6)
Which becomes

y = (-1/6) *x + 3

Agree?

[glass blade]

[crimson sedge]

yes i understood

[glass blade]

How did you arrive at this I wanna know first
There shouldn't be any confusion within you

[crimson sedge]

cause in the standard form, A was not there meaning A is just 1

[glass blade]

Yes

But slope was -A/B remember

Our B is -6

Let me take you back there

[glass blade]

.

[crimson sedge]

saving that formula cause i already forgot

[glass blade]

You don't need to remember that @crimson sedge
You can just derive it

[crimson sedge]

takes time rearrange it, easier for me to memorize

[glass blade]

Ah ok

Anyways

So our A was 1 right

[crimson sedge]

yea

[glass blade]

Let me paste the question here

So that you don't have to check pins continuously

[crimson sedge]

okay

[glass blade]

For solving

https://media.discordapp.net/attachments/903430334681608232/962782188347199488/IMG_7984.jpg

Ok

And our B is?

[crimson sedge]

6

[glass blade]

Ax + By = C
x + (-6)y = -18

B is?

[crimson sedge]

-6

[glass blade]

Nice

[crimson sedge]

mb mixed it with the other equation

[glass blade]

So what's our slope
-A/B = ?

[crimson sedge]

-1/6

[glass blade]

Np xD

[glass blade]

No no place the value of A and B

• (1)/(-6)

It becomes 1/6

[crimson sedge]

why isnt the 1 negative

[glass blade]

Because A = 1 you yourself said it

I just put the values of A and B
In -(A/B)

Which is -(1/-6)

Which becomes 1/6

Agree?

[crimson sedge]

yes i agree

[glass blade]

Nice so we got the slope of the line
x + 6y = - 18 right?

[crimson sedge]

yep

the slope is 1/6

[glass blade]

Yes

Now the slope of the line perpendicular to x + 6y = - 18 is?

[glass blade]

Use this

[crimson sedge]

-6/1

[glass blade]

Nice

You are doing great

[crimson sedge]

thank youu

[glass blade]

Ok so our question said that

The line perpendicular to x+6y = -18
Is actually the tangent to the curve y=f(x)

So what did we actually found out?

[glass blade]

I mean the slope that you found out here is the slope of?

[crimson sedge]

the slope of the tangent to the curve

[glass blade]

Awesome

Now
Find the equation of the tangent

y = mx + b

Put the slope

[crimson sedge]

is b the same as the one in the standard equation

[glass blade]

We only know the value of m

[glass blade]

Yes

I mean b = C/B

Where Ax + By = C
y = -(A/B)*x + C/B

[crimson sedge]

its -3

[glass blade]

If you compare that with y = mx + b
We get b = C/B

[glass blade]

-3 ?

Where you got that?

[crimson sedge]

-18 / 6

[glass blade]

No no

Forget the previous tangent

That's nothing to do it with it

The reason is
If you read the question carefully

A curve can have multiple tangents

Also remember
Our previous tangent had slope -18
And this tangent has slope -6 @crimson sedge

So do you think that they are the same tangent?

[crimson sedge]

no they are differant

[glass blade]

Nice so let's focus on here

[crimson sedge]

C is zero

so there no b?

[glass blade]

Oh wait did you find the value of b?

From that x-6y = - 18 ?

[crimson sedge]

yea

[glass blade]

Don't do that xD
That's different equation

Wait let me try to draw a picture for you

This is what it kinda looks like

You can only find the relation between the slopes of the perpendicular lines
The y- intercepts and others are different

You get my point?

See the diagram

By the way since you are very passionate about Ax + By = C

There is a relation with that which can be used as a shortcut

But imma tell that later to you

Anyways you understood
Why it's wrong to do like that?

[crimson sedge]

yea because they only cross one point so they ant have the same slope

cant*

[glass blade]

Yes their slopes are in relation of m1.m2 = -1

But the other parts like y-intercepts and all aren't same

Ok?

[crimson sedge]

yea they only the same in one x and y

[glass blade]

Yes

But anyways

Since you are passionate about Ax + By + C
More than y = mx + b

I can roll with that

Ok so for x - 6y = -18 I wrote Ax + By = C right? @crimson sedge

For this line which is the tangent I shall write it as A°x + B°y = C°

[crimson sedge]

yep thats right

[glass blade]

A° is another constant

[crimson sedge]

°?

ohh

[glass blade]

Just a constant

You can take it as A1 too

(A1)x + (B1)y = C1

[haughty axle]

The plane has a marker (0:1).

In each of the following cases, determine if points A, B, and C are aligned.

1. A(5; B(8; 2) and C(-1;-10);

2. A(-3; -3), B(8:0) and C(12; 1)

[glass blade]

Now

y = -(A1/B1)*x + (C1/B1)

[glass blade]

This channel is occupied lol

[haughty axle]

Ok excuse

[glass blade]

So -(A1/B1) represents our new slope ( slope of the tangent) and C1/B1
Represents y-intercept of the tangent

Agree?

[glass blade]

From here

[crimson sedge]

I combine y=-6/1c + b and y=-1/6x + 3 to find b?

[glass blade]

No no it won't be that easy

I shall come into that process

There is a tough road ahead in this question

[glass blade]

So -(A1/B1) represents our new slope ( slope of the tangent) and C1/B1
Represents y-intercept of the tangent @crimson sedge

Agree ?

[crimson sedge]

yep, i agree

[glass blade]

Nice so we can place the value of
-A1/B1 = -6 right?

[crimson sedge]

yea

[glass blade]

So our equation becomes
y = -6x + (C1/B1)

Agree?

[crimson sedge]

understood

[glass blade]

Let me assume C1/B1 as k
Ok?

[crimson sedge]

okay

y = -6x + k

[glass blade]

Yes

So our equation of tangent becomes
6x + y = k right?

[crimson sedge]

yea

[glass blade]

Now to your question

How shall we find "k"

[crimson sedge]

if we have x and y

[glass blade]

Yes we shall be solving that

Ok now need your full attention

Lemme prepare everything in hand

Ok you understand this diagram?

[crimson sedge]

0 = x-6y + 18 = 6x + y

[crimson sedge]

yea i understand

l, m is what we need to find

[glass blade]

So the point (l,m) lies in 6x+y= k , x-6y=-18 and y=f(x) curve

[glass blade]

Yes

[glass blade]

Agree?

[crimson sedge]

yes i agree

[glass blade]

Now since they lie on them
So let's satisfy (l,m) in them.

6l + m = k
l - 6m = -18

We can calculate k from here

[crimson sedge]

huh i am confused

is k = 385/6

64

[glass blade]

I just placed l and m in place of x and y in x-2y = -18 and 6x + y = k

[crimson sedge]

l is 3.405

m is 2.432

right?

[glass blade]

Oh I haven't calculated it

Wait a sec

I got two choices for l
Either 1 or -1/2

[crimson sedge]

i think it is -1/2

brb in 3 minutes

I am back

Sorry that took longer than I intended

@glass blade

[glass blade]

Anyways let's actually now try to solve it

So our tangent had a slope of -6 right?

[crimson sedge]

okay'

yea

[glass blade]

So if we differentiate the curve at
point (l,m) we shall get the slope of the tangent?

6l - 12l² = -6
Which leaves l = 1 or -1/2

Now find m for both cases by putting 1 and -1/2 in the equation of the curve
m = 3l² - 4l³

[crimson sedge]

where did the 12 came from

[glass blade]

Differentiation of 3x² - 4x³

Which was our equation of the curve

[crimson sedge]

oh yeaa

[glass blade]

You shall find two different values of l and m
See what satisfies the curve x + 6y = -18

[crimson sedge]

its -2 and -6

[glass blade]

The value of m?

[crimson sedge]

wait no

it is -15 and -1/2

[glass blade]

-15 @@

[crimson sedge]

(-15) + 6(-1/2) = -18

[glass blade]

No no

Look we differentiated the curve
f(x) = 3x² - 4x ³

Right?

And we got f'(x) = 6x - 12x²

Agree?

[crimson sedge]

6L - 12L² = -6 = 1 or -1/2 3(-1/2)^2 - 4(-1/2)^3, m= 5/4 3(1)^2 - 4(1)^3 = -3.88

[crimson sedge]

yep, understood

[glass blade]

So m= 5/4 or m=-1 right?

[crimson sedge]

yea

[glass blade]

And l = 1 or -1/2 right?

[crimson sedge]

yep, is it both or only one I

cause it isnt a quadratic

[glass blade]

So we have two sets for (l,m)

(1 , -1) or (-1/2 , 5/4)

Agree?

[crimson sedge]

yep i agree

[glass blade]

We need to check what values for l and m can actually be taken

We have that equation remember
x - 6y = -18

?

[crimson sedge]

yea so we plug it in to see if it matches with the other equation

[glass blade]

Yes

Just plug in the sets of (l, m) and see if it's satisfies

I am pretty sure there is a mistake in this question lol

[crimson sedge]

what other equation

cause i tried every and they all didnt match

[glass blade]

Yes I know it won't match

Lol

You know the reason?

Misprint in the question

The equation which was given to us
Will be x-6y = -8
And not x-6y = -18

[crimson sedge]

oh i see, it okay cause i know know how to do these type of questions thank to you

[glass blade]

Wait I have a proof tho

To show you that it was wrong

See the graph

If I took x - 6y = -18

Then no wonder 6x + y = k (k=-7/4) btw

Was tangent

But the 3 of them never intersected

While

[crimson sedge]

i think the teacher accidentally pressed the 1 in 18

[crimson sedge]

make sense why none of our answers matched

[glass blade]

Yes

And even to prove myself wrong

I took the intersection point of x-6y=-18 and the curve

Yet the 3 of them didn't intersect

[crimson sedge]

thank you so much, I really appreciated it. you really made me understand so much in just one day

[glass blade]

@crimson sedge i was talking about this

[glass blade]

.

So it has to be x-6y = -8
Or else the curve, the tangent and the given line will never intersect

[crimson sedge]

1.33 is the m value?

[glass blade]

Nope

[crimson sedge]

i mean 2.88

[glass blade]

Yes

Oh wait

I mean I took that for the test lol

The real (l,m) values are (-1/2 , 5/4)
And it satisfies and 3 of them get intersected there

If and only if x-6y= -8

[glass blade]

@crimson sedge

Just remember that if we write
x-6y = - 18
The tangent, the line and the curve will never intersect

At a single point

[crimson sedge]

so our answer was correct, the only problem was in the page it should b 8 not 18 since our is the only only that intersected all three

[glass blade]

Yes

Because in question they said that all 3 should intersect

So it has to be 8 and not 18

And our answers for those intersection points are correct

Aka (-1/2 , 5/4)

[crimson sedge]

i have 2 last question, can u please help me on

so sorry 😅

[glass blade]

Ok send i can be awake for 1 hour more ig

[crimson sedge]

I just need help on 3 and 4

I did 2 already

[glass blade]

Oh

[crimson sedge]

What I did for 3 so far

/rotate

[glass blade]

The point of discontinuity shall be on 0 and 3

[crimson sedge]

i know, cause of the graph but how do i explain

do i say cause the limit arent the same

[glass blade]

Wait nvm lol

Zero won't be the point of discontinuity

I just calculated

[glass blade]

Yes

Check limits at 0- and 0+

And 3- and 3+

[crimson sedge]

on 2x+4 or x^2+2

2x+4 3- = -2

x^2+2 3- = -7

[glass blade]

Suppose
g(x) , x≤a
f(x) = { h(x) , x>a

And i tell you to check limit at a- and a+
Then for a- you have to consider value of x which is less than a
Clearly here x≤a but function has value g(x) at that time
So you shall write lim(x->a-) g(x)

And for a+ you have to check value for >a
Here x>a but function gives h(x)
lim(x->a-)h(x)

Like that

Got it?

[crimson sedge]

yes, i understood

[glass blade]

So for 0- and 0+ evaluate

[crimson sedge]

they both 2

[glass blade]

Nice

And what's the value at 0

[crimson sedge]

its 2

[glass blade]

So what do you think it's continuous right

[crimson sedge]

yea cause limf(x) is defined

[glass blade]

Since x->0- , 0+ and at 0 it gives out the same value

[glass blade]

Nice

Now check at 3- and 3+

[crimson sedge]

they are differant

so its a discountintity

[glass blade]

So what's the point of discontinuity?

[glass blade]

Yes

So only 3 is the point of discontinuity right?

[crimson sedge]

yea

[glass blade]

Nice

So your 3 is over

Now for the last

[crimson sedge]

faster and easier than i expected xd

i hope question 4 would be the same

[glass blade]

Yes

Let me do the 4 for you

'rotate

[crimson sedge]

damn ur handwriting is so good

[glass blade]

,rotate

[glass blade]

Ah nice lol

[glass blade]

Ah it's bad when I write fast lol

[glass blade]

Oh that interminate actually will be indeterminate

There is no word named as interminate form

It's indeterminate form

[crimson sedge]

okay, i see

thank you for clafirying that

[glass blade]

Also let me share something with you

I told you imma share some shortcuts

[crimson sedge]

sure

[glass blade]

Lemme write and ss it for you

[crimson sedge]

yes please!

[glass blade]

Ok done

Some jist of what we had discussed today

And some shortcuts and tips

[crimson sedge]

saved! thank you so much for this omg

[glass blade]

Take care and ask in case of any confusions
Good luck haha

[crimson sedge]

https://tenor.com/view/catthankyou-cat-gif-24824893

[glass blade]

Oh btw close the channel if we are done for today
Only you can close it lol

Just in case someone else needs help

Just write
.close

[crimson sedge]

.close

[cedar kiln]

Channel closed

Closed by @ember lark

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
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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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[hard jetty]

Can you transpose any matrix?

[vagrant breach]

as far as i'm aware

it just switches the rows and columns

[hard jetty]

Do matrices need to be square to add?

[vagrant breach]

you can transpose non square matrices

[flint plinth]

no, they just need to have the same number of rows and same number of cols

[vagrant breach]

^^

[hard jetty]

Isn’t that a square matrix? What is a square matrix if not?

[flint plinth]

no, i mean matrix A and matrix B must both have the same size, e.g. both must be m x n

it is not necessary that m=n (square matrix)

[hard jetty]

Thank you all

[hard jetty]

Thank you

What is the right answer?

[umbral jackal]

do you know what linear means

[hard jetty]

Straight

[umbral jackal]

algebraically?

degree

firstly

2x^2+y definitely isn't linear

(cot 5) is a constant

therefore (cot 5)x+2y=1 is linear to both x and y

[hard jetty]

What about 5xy-y=2?

[umbral jackal]

uh idk

[hard jetty]

Thanks

Anyone else know?

<@&286206848099549185>

Is x+y+z=sin (pi/4) linear

I go with yes

What of x +1/y + z =5?

I go with no

Hello

@umbral jackal you there?

[umbral jackal]

hi

I have a help channel of my own

where I need help quick

[umbral jackal]

this isn't linear

it isn't even a polynomial

it contains y to the -1 power

[hard jetty]

Oh ok. Thanks, are polynomials linear!

[umbral jackal]

well those which are not polynomials definitely aren't linear

because they'd have like negative powers, non-integral powers, etc

,w polynomials

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by hellblaze_skyfire#2497

[cedar kiln]

@hard jetty Has your question been resolved?

Channel closed

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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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[split pier]

pls help

[cedar kiln]

Channel closed

Closed due to the original message being deleted

[split pier]

pls help

im very bad at algebra fraction

i need to submit my work by tdy

still have a lot

but i'll try them first

[split pier]

but this is the first question and idk how to do

[weak hazel]

https://www.mathway.com/Algebra // photomath app (which will prolly give you a step by step answer

[cedar kiln]

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[cunning kelp]

could someone help me with this math question

<@&286206848099549185>

[weak hazel]

#❓how-to-get-help

you ping after 15mins

[cunning kelp]

oh ok

[cedar kiln]

@cunning kelp Has your question been resolved?

[cedar kiln]

Channel closed

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[dense prism]

A student must take 6 courses to complete their degree, and they can be taken from 5 different faculties. In how many ways can the courses be distributed amongst the faculties?

[dense prism]

.close

[cedar kiln]

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[heavy finch]

Hey, so i'm in grade 10 doing Quadratic Expressions and just need help on this question.

[heavy finch]

I just want to know how to form the algebraic expression and I will try to understand from there.

[copper bane]

I'm math dumb myself but isn't question a is just, well a big rectangle - small rectangle

[heavy finch]

???

[copper bane]

i mean you can view the highlighted region

as full rectangle

but with a hole in size of white rectangle

[heavy finch]

So how would I word it? 4x . 2x . 12y . 6y?

Idk if that makes sense

the dots are multiply

[copper bane]

well if you want to drill a hole in somethings in math it's a minus

you find the area of big rectangle first

[heavy finch]

Ohh okay so would I write 4x - 2x?

[modern compass]

The shaded area is the large rectangle with the smaller rectangle removed. To find that area, find the area of the large rectangle, the area of the small rectangle, and subtract the two

[heavy finch]

Alright let me try this

Give me a second

[copper bane]

take ya time

[heavy finch]

So wouldn't the area be 72y Squared?

72y^2

Then do we factor it?

Sorry I came back from vacation while I was in the middle of doing this unit and she expects me to understand everything in 2 days.

[modern compass]

That's the area of the large rectangle, yes.

[heavy finch]

So 72^2y - 6x?

Is that okay

Or good

[modern compass]

???

what happened to the y?

[heavy finch]

Oops sorry

I thought I added it

[modern compass]

72y^2

[heavy finch]

Oh right, again, sorry.

[modern compass]

and how do you find the area of the smaller rectangle?

[honest stag]

Total area of rectangle will be 72y^2
And area of unshaded part will be 8x^2
So area of shaded part is 72y^2-8x^2

[modern compass]

don't just give out answers.

[heavy finch]

The same as the bigger one, 4x times 2x?

[modern compass]

yes, so what 4x times 2x?

[heavy finch]

8x^2

[modern compass]

right

[honest stag]

Area of unshaded part(white reactangle)

[modern compass]

so that's what should be subtracted, not 6x

[honest stag]

Yeah

[heavy finch]

Yeah, I don't know how I got 6.

Thank you, I understand.

For real.

[copper bane]

wait finished?

lol

sorry

[heavy finch]

I mean, I might have another question, but I will just make another ticket.

[copper bane]

don't forget to close this one

• .close

[heavy finch]

.close

[cedar kiln]

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[icy narwhal]

hello, not really a math question but

[icy narwhal]

wait nvm

.close

[cedar kiln]

Channel closed

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[icy narwhal]

.reopen

[cedar kiln]

✅

[icy narwhal]

is there an app like photomath thats offline?

I'm not really going for the picture scan feature

its just that their calculator is so simple and understandable to use

the problem is that you can't use it offline

I try to learn how to use scientific calculator apps but I absolutely just don't know how to use it

<@&286206848099549185>

[cedar kiln]

@icy narwhal Has your question been resolved?

[cedar kiln]

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[left hound]

Can someone guild me on how to solve this?

[kindred storm]

@left hound Zero product property.

If you multiply some things together and get zero, one or more have to be zero.

What things are multiplied together to give zero there?

[left hound]

x=0?

because whatever is multiplied by 0 = 0

[kindred storm]

Well, -9x(6x - 7) = 0.

[left hound]

oh

[kindred storm]

You have some things multiplied together on the left.

[left hound]

hmm

[kindred storm]

What's multiplied together?

[left hound]

-54x^2 + 63 = 0

[kindred storm]

No, don't multiply it.

Look at it.

[left hound]

oops

[kindred storm]

What things are multiplied together in -9x(6x - 7)?

[left hound]

not really sure

what you mean

[kindred storm]

Well, 5x is 5 times x, right?

[left hound]

yes

[kindred storm]

And x(y + 6) is x times y + 6, right?

[left hound]

yes

[kindred storm]

So, what's multiplied together in -9x(6x - 7)?

[left hound]

-3*3x= -9x

[kindred storm]

Close.

You have -9 times x times 6x - 7.

-9 x (6x - 7)

Do you see how I got the things multiplied together because they're written next to each other to multiply them?

Like -9 is written next to x, which is written next to 6x - 7?

[left hound]

not reallyy

I see what you mean

I just don't know how to solve the next step

[kindred storm]

OK, but let's make sure you got this step.

What's multiplied together in 6(x + 6)(x - 7)?

[left hound]

Question

can I solve this question using the
Line ac =
Line b=

method?

[kindred storm]

No.

[left hound]

alr

[kindred storm]

Let's go over some algebra.

[left hound]

k

[kindred storm]

Like if I write xyz, that means x times y times z, right?

[left hound]

ye

[kindred storm]

So, x, y, and z are multiplied together there.

[left hound]

ye

[kindred storm]

What about abc? What's multiplied together there?

[left hound]

abc

multiplied together

[kindred storm]

Well, separate them.

a, b, and c.

[left hound]

a, b, c

[kindred storm]

Right.

So, parentheses right next to something means multiplication as well.

[left hound]

ye

[kindred storm]

ab(c - 2) is a times b times c - 2.

So, a, b, and c - 2 are all multiplied together.

So, what's multiplied together in x(y - 2)z?

[left hound]

xy and x2

[kindred storm]

No, remember that parentheses right next to something means to multiply them together.

x(y - 2)z is x next to y - 2 in parentheses next to z.

So, it's x times y - 2 times z.

Does that make sense?

[left hound]

alr

got that

[kindred storm]

What about ab(c - 2)d?

[left hound]

a times b (c -2) times d

[kindred storm]

Almost.

a times b times c - 2 times d.

So, a and b and c - 2 and d.

Does that make sense?

[left hound]

ye

[kindred storm]

OK, and then there's nonvariable numbers.

Like 9.

So, if I have 50a, that's 50 times a.

So, what's multiplied together with 70x?

[left hound]

70 times x

70 times x = 70x

[kindred storm]

Right, 70 is written right next to x, so they're multiplied together.

[left hound]

ye

[kindred storm]

Negatives work the same way.

-9x(y - 2)z is -9 times x times y - 2 times z.

Does that make sense?

[left hound]

yes

-9 times x timex 6x-7 = 0

[kindred storm]

Right!

So, zero product property says that if you multiply together some things and you get 0 from that, at least one of those things you multiplied together has to be 0.

Like if I have abc = 0, I'm multiplying together a, b, and c.

So, a = 0 or b = 0 or c = 0.

Since they multiply together to give zero, one or more have to be zero.

Does that make sense?

[left hound]

ye

[kindred storm]

-9 times x times 6x - 7 comes out to zero.

[left hound]

alr

[kindred storm]

So, if they multiply together to give zero, which they do, at least one has to be zero.

So, write that out.

What do you get?

[left hound]

-9x(6x-7)0?

[kindred storm]

Nope.

Let's try with 8x(y - 7).

So, 8x(y - 7) = 0.

[left hound]

alr

[kindred storm]

So, we multiply together three things and get zero.

So, at least one of those multiplied things has to be zero.

The three things are:

8
x
y - 7.

[left hound]

ye

[kindred storm]

So,

8 = 0 or
x = 0 or
y - 7 = 0

At least one of those things you multiplied together has to be zero.

[left hound]

y-7

[kindred storm]

Well, we don't know which one.

The zero product property doesn't tell us which one.

So it might be any of them.

[left hound]

true

[kindred storm]

It could even be more than one of them.

Like abc = 0 when a = 0 and b = 0 and c = 2.

Two of them are zero there.

And that's at least one of them.

Does that make sense?

[left hound]

ye

[kindred storm]

OK, so let's go back to your problem.

-9x(6x - 7) = 0

What three things are multiplied together?

[left hound]

-9=0
x=0
6x-7=0

[kindred storm]

And they might be zero, so write = 0 on all of them.

And we don't know which one, so we put or between them.

Or between things means at least one of these in math.

[left hound]

alr

[kindred storm]

Like I went to the store or I'm at home means at least one of those is right.

Could be both.

Could be only one of them.

[left hound]

alr so how I figure out

[kindred storm]

OK, so we have:

-9 = 0 or x = 0 or 6x - 7 = 0

Can -9 = 0 ever?

[left hound]

yes

[kindred storm]

Well, let's go over what = means.

= means you have two numbers.

One on the left.

One on the right.

= means they're the exact same number.

-9 is exactly the same number as 0.

Is that right?

[left hound]

nope

[kindred storm]

Right, so -9 = 0 is wrong.

So, on the next line, you can leave that off:

-9 = 0 or x = 0 or 6x - 7 = 0
x = 0 or 6x - 7 = 0

With me so far?

[left hound]

ye