help-33

[deep grail]

You mean the smallest y value?

[grizzled sonnet]

yes. thats what range is.

if we cared abt x, we can plug in literally anything for x

might as well say -inf

by your logic, 1/x is infinity when x = infinity

[deep grail]

No, if x approaches infinity y should be -infinity

[grizzled sonnet]

no.

1/10 is what?
1/100 is what?
1/1000 is what?
where is it going?

[deep grail]

0

[grizzled sonnet]

yes

so the minimum value of 1/x is?

[deep grail]

0

[grizzled sonnet]

yes

do you see why its specifically 0; why it cant be, say, -1?

well

excuse me

1/x can

i mean in our original problem

$\frac{1}{ln(1-2x^2)}$

[elfin berry]

Karma

[grizzled sonnet]

1/x at x = -infinity is -infinity, i was caught up in the original problem. the minimum of 1/x is -infinity, not 0

but still, 1/x at +infinity is not -infinity, as you said.

[grizzled sonnet]

in any case, do you see why this is 0, instead of -infinity?

[deep grail]

I am lost

[grizzled sonnet]

where? my bad for the mixup earlier

[deep grail]

No worries, you told me the range is all of the y values of a function

And for that we need to gather the minimum and the maximum values

Tho get the range

For the min value we found the limit as x approaches 0 and got infinite

Am I right?

[grizzled sonnet]

this is where your wrong

What transformation of $u$ makes $\frac{1}{u}$ get smaller?

If $u = \frac{1}{\ln(1-2x^2)}$, how can we get the same behavior from the $\ln(1-2x^2)$ term, to shrink $\frac{1}{\ln(1-2x^2)}$?

[elfin berry]

Karma

[grizzled sonnet]

@deep grail

Note, there are two answers to the first question. One is not applicable, which is how we know to use the second one.

[deep grail]

When u approach 0

[grizzled sonnet]

when $u$ approaches 0?

[elfin berry]

Karma

[grizzled sonnet]

what happens

[deep grail]

1/u approaches - infinity

@grizzled sonnet

[grizzled sonnet]

are you sure?

[deep grail]

Yes

If u = 1000000000 1/u would be 0.000000000001

[grizzled sonnet]

thats not $u$ approaching 0.

[elfin berry]

Karma

[grizzled sonnet]

also, thats not -infinity.

you said "when u approaches 0, 1/u approaches -infinity"

and then gave an example of u, not close to 0, approaching not -infinity

[deep grail]

So it’s approaching 0?

Bro I am dumb

[grizzled sonnet]

._., are you guessing, or trying to figure it out?

[deep grail]

This is when u is approaching infinity

We need when u is 0

[grizzled sonnet]

do we?

we want the minimum value of just $1/u$

[elfin berry]

Karma

[deep grail]

Well I remember the graph of 1/x

It should be -infinity?

[grizzled sonnet]

dont think about that, this is important mathematical intuition.

it is

but when?

what causes $\frac{1}{u}$ to tend towards negative infinity?

[elfin berry]

Karma

[deep grail]

Wait it does from the left but from the right is positive infinity

[grizzled sonnet]

correct, can you see why if you think about values close to 0 on either side?

[deep grail]

But in our question we excluded negative numbers

[grizzled sonnet]

yes!

[deep grail]

So it should be infity??

[grizzled sonnet]

that circles back to this

[grizzled sonnet]

no.

[grizzled sonnet]

if we cant go into the negatives

what is the closest we can get?

[grizzled sonnet]

well, maybe depending on what you mean

[deep grail]

Y or x?

[grizzled sonnet]

1/u cant be negative

so u cant be negative

[deep grail]

So 0

[grizzled sonnet]

as u tends towards 0, 1/u becomes large

[deep grail]

Ok so the range is infinite?

[grizzled sonnet]

i mean, yes, but that doesnt mean anything

(-inf, inf) is just as infinite as (0, inf)

you still dont know the range, lol

[grizzled sonnet]

you were close here

you recognize that we cant go to negative infinity

if we cannot go into the negatives, what is the next smallest "target" number we should have

[deep grail]

This is the graph🫠

[grizzled sonnet]

and then how do we get there

omg

i mixed up my log rules 😭

ln(-1) exists
ln(x) = -1 doesnt

or wait

other way around

fuck

i did it twice 😭

[deep grail]

I give up if this comes in the exam i will solve the domain and leave the range

[grizzled sonnet]

its not that bad i just made a stupid mistake

[deep grail]

I know how to solve the range for any other function

[grizzled sonnet]

i promise you dont

those are elementary functions

this is all youll see in higher levels

they wont give you nice pretty graphs

[deep grail]

Either way I don’t have enough time 😂

My exam is in 15 minutes

[grizzled sonnet]

you'll get something like $f(x) = e^{-\frac{sin(x^2)}{x}}$

[elfin berry]

Karma

[grizzled sonnet]

good luck drawing that

its easy to solve tho

[deep grail]

Thanks for your time

[grizzled sonnet]

ye just try to find the min and max of the overall function and check for which x is undefined

log rules, limits, beware negative sqrts, etc.

gl

[marsh citrus]

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[marsh citrus]

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[serene cloud]

In a rectangular parallelepiped, the lengths of the sides of the base are 7 cm and 17 cm, and the diagonals of the parallelepiped form angles of 45° and 30° with the plane of the base. Find the length of the height of the parallelepiped.

[serene cloud]

I think I have tried almost every method

please enlight me

[marsh citrus]

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[winged quartz]

Help me understand the following points:

• what is b-spline in simple terms? And how to use it in a simple function.

• what is the difference between p-spline and b-spline?

• what is the difference between bizier and b-spline?

[winged quartz]

What are knots and control points (p)?

[marsh citrus]

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[marsh citrus]

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[marsh citrus]

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[timber hamlet]

In this task, we prove some fundamental properties of divisibility. We assume that
𝑎
a,
𝑏
b, and
𝑛
n are integers and that
𝑐
c is a positive integer. Prove the following statements and, in each case, provide a numerical example.

a) If
𝑐
∣
𝑎
c∣a, then
𝑐
∣
𝑛
𝑎
c∣na.

What the heck does the vertical line mean here

[timber hamlet]

More clear

In this task, we prove some fundamental properties of divisibility. We assume that a, b, and n are integers and that c is a positive integer. Prove the following statements and, in each case, provide a numerical example.

a) If c∣a, then c∣na.

[stray hound]

the vertical line means "divides", or I like to think of it as "is a factor of"

so for example, 2|4 since 2 is a factor of 4

[timber hamlet]

So its not doing the operation, but it means the number in front is a factor?

[stray hound]

yes exactly

[timber hamlet]

Ok thx

[stray hound]

yeah, usually if you say a|b in general, it means b = ka for some integer k

that's the general way of doing it

[timber hamlet]

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[marsh citrus]

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[urban grove]

Hello.
Im looking to find a solution to this problem. Basically how strong should a pinned circular beam be if a 52 cm 200kg concrete ball is dropped on it from 30 cm by free fall. I have done multiple tests and so far a S235 50x5 rolled beam did bend by 5mm after one drop. Or if there is any online free calculator where I can put the point load and beam types in ? 🙂

[marsh citrus]

@urban grove Has your question been resolved?

[agile iron]

def calculate_beam_strength(mass, height, length, width, height_beam):
g = 9.81
delta_t = 0.001

potential_energy = mass * g * height
velocity = math.sqrt(2 * g * height)
momentum = mass * velocity
impulse = momentum
average_force = impulse / delta_t
bending_moment = average_force * length / 4
section_modulus = (width * height_beam**2) / 6
bending_stress = bending_moment / section_modulus

return bending_stress

mass = float(input("Enter the mass of the sphere (kg): "))
height = float(input("Enter the height of the drop (m): "))
length = float(input("Enter the length of the beam (m): "))
width = float(input("Enter the width of the beam cross-section (m): "))
height_beam = float(input("Enter the height of the beam cross-section (m): "))

required_stress = calculate_beam_strength(mass, height, length, width, height_beam)
print(f"The minimum bending stress required for the beam is: {required_stress:.2f} Pa")

[marsh citrus]

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[still temple]

Can anyone help me solve this?

[valid cape]

well what have you tried?

[still temple]

Let me grab it really quickly.

[still temple]

Wait, nvm. I see where I went wrong. Thanks anyways.

.close

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[marsh citrus]

Please don't occupy multiple help channels.

@inner nimbus Has your question been resolved?

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[wind nacelle]

hey i am supossed to differentiate 4x/(x^2+1). the solution I come to is 4(-x^2+1)/(x^2+1)^2. thats also the solution my computer comes to, but the book says its -(4x/(x^2+1)^2). what is right?

[cloud iron]

,w D[4x/(x^2+1),x]

[elfin berry]

Results provided by WolframAlpha

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

Requested by lexitorius

[cloud iron]

Book's might be a different rearrangement of it, try doing some algebraic manipulation to get the book's answer if you'd like

But your solution is right

[whole thorn]

the computer is almost always right

[wind nacelle]

thanks! .close

.close

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[lyric bay]

Hello

[lyric bay]

Where is the √3cos(ø) coming from in the numerator?

[merry pewter]

$du = \sqrt{3}\cos(\theta)d\theta$

[elfin berry]

caspar

[marsh citrus]

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[lyric bay]

Ohhh ic

Tysm!

.close

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[zinc tiger]

Imagine creating a program that analyzes the current price of stocks and calculates various indicators. These indicators are then used for further calculations, referred to as "triggers." If these triggers are met for a stock, it suggests that the stock has a higher probability of increasing in value. The more triggers that are met, the greater the likelihood of growth.

Each trigger has been tested on historical data and has its own individual success rate. This success rate can be considered the probability of the stock increasing in value if the specific trigger is met.

How can one calculate the overall probability of a stock's success, based on the number of triggers met? There are 13 triggers in total.

[sleek lake]

you can't

you should use the data that determined individual trigger rates, to learn what they do when combined

[zinc tiger]

how would i do this? i have 20 differens kinds of data available

[sleek lake]

jus the same thing you already did

you learned that trigger #4 has 32% rate or something

learn what rate do 4 and 7 and 10 together have

there's ~8000 conbinations

[zinc tiger]

But i cant really backtest data tho, as they dont say if a stock is likely to fall or grow. Only the triggers do

Data is like RSI and SMA
Triggers are calculations based on multiple data, that determines the likelihood of growth

[mental garnet]

If you only have the individual success rates you can't as the triggers may not, and are likely not, independent to one another.

[sleek lake]

someone showed a problem like this, about restaurants

[zinc tiger]

I feel like there should be a way idk

[sleek lake]

the obvious way is that you calculate failure rate

by subtracting from 100%

and multiply the fail rates

and subtract from 1 again

i don't remember if this problem did literally that or there was some small difference

but it's just wishful thinking anyway

[zinc tiger]

with failure rate, you mean 1 minus successrate?

[sleek lake]

yes

this problem has at least some intersection data, compared to yours

[zinc tiger]

hmm, how else could i then calculate the probability of growth by using data?

[marsh citrus]

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[marsh citrus]

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[strong ivy]

need help

[strong ivy]

with greens theorem

<@&286206848099549185> who got me wit help

[strong ivy]

i just dont know

how to start

[marsh citrus]

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[split vigil]

im slow what did they do here

[unborn condor]

they just substracted the top fractions

[dry prawn]

Common denominator'd the numerator terms

[sharp sonnet]

hope this explains

[marsh citrus]

@split vigil Has your question been resolved?

[split vigil]

thank you!

[marsh citrus]

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[wind imp]

yoyo thats a fairly exercise on sequences

the exercise is not difficult in itself

im a just having trouble finding the right way to prove all points

for the a) i wanted to do a proof by using the absurd

but my demonstration is pretty empty

it goes like if U doesnt have a maximum then Un converges to + infinite

and so contradiction bcuz it is supposed to be - infinite

but it feels wrong

[wind imp]

or that it converges to a real

[marsh citrus]

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[marsh citrus]

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[vernal herald]

How did we simplify this?

[quiet anvil]

That seems to be the simplification of this expression

[full flume]

divided top and bottom by x^(1/6) i think

[quiet anvil]

Did you have a question about a specific step?

[full flume]

the 2 into 11/6 was the big hint

[marsh citrus]

@vernal herald Has your question been resolved?

[vernal herald]

both steps actually

but yeah I got it

thank you

.close

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[quiet anvil]

As citrus munch said first step in dividing by x^(1/6) from both the top and bottom.

The second is pulling out a x^(1/3) from the denominator

[marsh citrus]

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[gusty wasp]

can someone explain part b to me, I dont understant where they got -2.8 from

[night mica]

$1.2=4+(-2.8)$

[elfin berry]

everg

[night mica]

$\sqrt{1.2}=\sqrt{4+(-2.8)}=f(-2.8)$

[elfin berry]

everg

[gusty wasp]

ohh so to solve this problem you first have to solve to the x value of y = root 12?

[night mica]

you want to use your studied function f, but in doing so you have to find the right x to plug in

[marsh citrus]

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[limber hearth]

!original

[marsh citrus]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[open seal]

Still here

[marsh citrus]

@open seal Has your question been resolved?

[open seal]

Still here

No

[open seal]

Still here

Got it!!

.close

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[mint sonnet]

help?

[marsh citrus]

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[marsh citrus]

@mint sonnet Has your question been resolved?

[marsh citrus]

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[tiny bear]

what do I have to prove exactly for the first implication

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[echo scaffold]

I’m not sure if I did this correct and I don’t know how to evulate e

[echo scaffold]

Because I thought you would decide the expoinets but it’s negative so idk

[north wadi]

exponent devided by exponent

is what property

[echo scaffold]

I have no idea I’m very confused

[north wadi]

recall that

[smoky spire]

minus

[echo scaffold]

Is it the square root symbol

[north wadi]

$$ \frac{a^b}{a^c} = a^{b-c} $$

[elfin berry]

ziming

[echo scaffold]

Oh

[proud arch]

Hello @echo scaffold

[smoky spire]

this is when something is ^1/2

[proud arch]

We meet again

[echo scaffold]

I must of put it in my notes wrong

Yes

New unit

Help

I hate it so much

[proud arch]

I think we should invite the other guys too

[echo scaffold]

I still got to study for English 😭

I tried to start studying math earlier then 11 pm but then I dowloaded block blast and got addicted

[proud arch]

Lol

Anyways

a isn't it

We got that right

?

[echo scaffold]

Wdym sorry

I got the math problem

[proud arch]

Like a isn't the answer

We want 4^10

That's just 2^7

[echo scaffold]

I got confused with my notes I looked how to do it with differnt bases but it had the same bases

[echo scaffold]

Is (4/4)^10 equivalent to 4^10. Or would it turn into 1^10

[north wadi]

the latter

[echo scaffold]

Whoops that’s seven

Silly mistake

[proud arch]

It's alright

[echo scaffold]

1^10?

[north wadi]

yea

[proud arch]

Let's try 2^20

2^(2*10)

Correct?

[echo scaffold]

I just put it into my calucltor and it was the same as 4^10

[proud arch]

Your calculator is a moron

Anyways

[echo scaffold]

The main issues I’m having so far in this unit is how to tell the difference between all these things

[proud arch]

This make sense

[north wadi]

$$ 2^{20} = 2^{2*10} = 4^{10} $$

[proud arch]

We can do without that you know

[elfin berry]

ziming

[proud arch]

Exponent rule

[echo scaffold]

Ohh

[proud arch]

The first thing on the list

[echo scaffold]

I was supposed to learn this in 8th grade but you know Covid

And crazy teachers

[proud arch]

Biology one 💀

Still haven't forgotten about that

[echo scaffold]

No this is my math one she used to shake us and call us chickens

Tho the next year I think she either said the n word to a kid or a slur to a Jewish kid

And got suspended for a while for that

[proud arch]

I still can't imagine what shaking us means

[echo scaffold]

Like you know our shoulders

And she would call us chickens a lot

It was weird

[proud arch]

Anyways

Before we go too oftrack

c

[echo scaffold]

She also put all the iep kids at the same table in the corner which is breaking like so many rules

You add the exponents right

[proud arch]

Yup

We did that right

Good job

[echo scaffold]

Yay

[proud arch]

d on the other hand

[echo scaffold]

Oh no

[proud arch]

Add them

What's 7 + (-3)

4 or -4

???

[echo scaffold]

Oh

4

[proud arch]

Yes

Correct that

Onto e

[echo scaffold]

I prob made the 7 an negative by accident

[proud arch]

It's ok

When exponents to the same base are in division we ........the exponents keeping the base same.

Fill in the blank

[echo scaffold]

Ooo I just found some extra pratice on the back of the summary page and I’m going to see if I can kinda do it

[proud arch]

?

[echo scaffold]

Add …

No shbtaxt

Subtract

[proud arch]

That in multiplication no

Yeah

Good

Try that for

e

4^4 / 4 ^(-6)

[echo scaffold]

It’s 10

[proud arch]

= 4^ (4 - (-6))

[echo scaffold]

The two - cancel eachother out

[proud arch]

Nice

So b,c and e will be our answers

[echo scaffold]

How would I do this one

[proud arch]

What is 78

Can you write is a multiplication of things

[echo scaffold]

Huh

Nothing multiplied by itself equals 78

[proud arch]

Like 18 = 3 * 3 *2

In terms of prime numbers

[echo scaffold]

It would be between the numbers 4 and 5 but it is a decimal

[proud arch]

.-.

Prime factorize

[echo scaffold]

No idea

[proud arch]

78 = 13 * 3 * 2

See it now

[echo scaffold]

Not really because we cannot make that into an expoinet

[proud arch]

So is it just (78)^1/3

That's it

[echo scaffold]

How did we get that?

[proud arch]

It's cube root

[echo scaffold]

So anhtbing that looks like that would be 1/3

[proud arch]

Yes

That symol

With a 3 next to it

[echo scaffold]

Kk

[echo scaffold]

What about this

[proud arch]

It's correct

[echo scaffold]

Even if it isn’t raised the third power for number 3?

[proud arch]

Wait

Oh

I didn't read the question

[echo scaffold]

I don’t know how I would raise it to the third power if the bottom is three

If the top was three I could

[echo scaffold]

Huhhh

That cannot be equivalent

[proud arch]

This make more sense

??

[echo scaffold]

Not really I don’t see how those are equivalent

Do they have to be?!

[proud arch]

We are supposed to take the thing in red

To the 3rd power

[echo scaffold]

Ohh

I was making the question mroe complicated then needed

[proud arch]

Lol

[echo scaffold]

How would I solve that?

[proud arch]

This make sense now right

Use exponent law

[echo scaffold]

For whole numbers I would multiply the expoinets but idk with fractions

[proud arch]

Yes

You do

Same for fractions

No difference

[proud arch]

What I did here

[echo scaffold]

So it would equal 2^5

[proud arch]

Perfect!

[echo scaffold]

Ok done with math now english 😭

After some blcok blast tho

[proud arch]

Lol

some block blast

Sureeeee

Is that all for today

@echo scaffold

If yes then please .close the channel

If no then ping me

I will come back

[wraith cairn]

Shart I missed this

[proud arch]

.close (I waited 10 minutes)

[marsh citrus]

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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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[amber raft]

i am so very confused i dont even know where to start

[grizzled sonnet]

are you just simplifying?

[amber raft]

me when exam is tomorrow and i dont understand

[amber raft]

i think?

yes

i was dislexic for a sec

[grizzled sonnet]

Remember:

$x^n \cdot x^m = x^{n + m}$

$(x^n)^m = x^{nm}$

$(x^ay^b)^c = x^{ac}y^{bc}$

also know that square roots and cube roots are just powers of 1/2 and 1/3
in general, the 2nd root is a power of 1/2, the third root is a power of 1/3, and the nth root is 1/n.

[elfin berry]

Karma

[grizzled sonnet]

given this, let's go through one problem

first, let's turn all of those roots into exponents, its much easier to look at these properties that way

$\sqrt[3]{-27a^{11}b^7} = (-27a^{11}b^7)^{\frac{1}{3}}$

[elfin berry]

Karma

[grizzled sonnet]

@amber raft does this make sense?

[amber raft]

it does :)

[grizzled sonnet]

so, looking at this, what can we do here?

[amber raft]

multiply everything in the parthenesis (sorry for spelling these things () ) by 1/3?

[grizzled sonnet]

we multiply the exponents

so this becomes:

$(-27a^{11}b^7)^{\frac{1}{3}} = (-27^{\frac{1}{3}}a^{11\cdot \frac{1}{3}}b^{7\cdot \frac{1}{3}})$

[elfin berry]

Karma

[amber raft]

ah okieee

[grizzled sonnet]

do you know what the cube root of -27 is? thats sort of just the type of information you have to have on hand

[amber raft]

i have desmos up hol on

-3

[grizzled sonnet]

will you have a calculator for the exam?

[amber raft]

yep! im using the same calc in test mode to study :)

[grizzled sonnet]

okay, no problem then

[grizzled sonnet]

so you see how we've used the rules i laid out to get from where we started to here, yes?

[amber raft]

yep! :)

[grizzled sonnet]

try to simplify the rest yourself

you'll know its simplified when every constant has no exponent attached, and all the variables are raised to a number, with no other noise going on (like roots or parenthesis)

[amber raft]

-3 a^(34/3) b^(22/3) is as far as i can get without getting stumped

idk how to use the fancy bot to get the pic

[grizzled sonnet]

where are you getting 34 and 22?

[grizzled sonnet]

if that were right, youd be done

the -3 is correct though

[amber raft]

i did 11/1 +1/3 -> 33/3 +1/3=34/3 and 7/1+ 1/3-> 21/3+1/3=22/3

[grizzled sonnet]

its not 11 + 1/3 its 11 * 1/3

same with 7 * 1/3

[amber raft]

ah i was trying to follow this first rule

[grizzled sonnet]

Remember:

$(x^n)^m = x^{nm}$

And so,

$(a^{11})^{\frac{1}{3}} = a^{11\cdot \frac{1}{3}} = a^{\frac{11}{3}}$

[elfin berry]

Karma

[amber raft]

-3 a^11/3 b^7/3 ?

[grizzled sonnet]

yup

[grizzled sonnet]

here's an example of the first rule:

$a^3b^6a^{12}b^{-2} \rightarrow a^{15}b^4$

[elfin berry]

Karma

[amber raft]

ah ty

[grizzled sonnet]

thats how youd simplify it all the way, but looking back at the original question, they dont seem to be simplified, lol

funny enough, D is the only option that can be right, at a glance. this work isnt even required, apparently

its the only one with a -3

[amber raft]

it is d i have the answers provided lol but im confused how they got the squ root

[grizzled sonnet]

i think what they want you to do is keep the "remainder" of 11/3 and 7/3 in the radical

[amber raft]

ahh ty

[grizzled sonnet]

$\sqrt[3]{a^{11}} = a^{\frac{11}{3}}$

$\frac{11}{3} = 3 + \frac{2}{3}$

The whole comes out of the radical, the remainder of 2 stays in the radical.

$a^3\sqrt[3]{a^2}$

We know that this is the same because:

$a^3\sqrt[3]{a^2} = a^3(a^2)^{\frac{1}{3}} = a^3a^{\frac{2}{3}}$

By the rule $x^nx^m = x^{n+m}$, we get

$a^{3 + \frac{2}{3}} = a^{\frac{11}{3}} = \sqrt[3]{a^{11}}$

[elfin berry]

Karma

[grizzled sonnet]

there we go

this is sort of how they got what they got

[amber raft]

makes sense :)

[grizzled sonnet]

if i had to give a recommendation for you, just simplify the answers the same way we simplified this

[amber raft]

another question, what if the number isnt an easy cubed root like -27 where you get 3, and its something more like the cubed root of 98 =4.61 (rounded)

[grizzled sonnet]

usually you just leave it like that. there are ways to approximate roots in your head but they are hard to remember and ive never run into a school that requires learning them

[amber raft]

alright :) ty

[grizzled sonnet]

especially since such things are often irrational there's literally no other way to write them than under a radical

e.g.

$\sqrt[3]{2^{\frac{3}{2}}}$

[elfin berry]

Karma

[amber raft]

ty!

i think i am good, thank you very much!

[grizzled sonnet]

np

[amber raft]

.close

[marsh citrus]

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[marsh citrus]

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[cosmic raptor]

How to approach this question?

[static quarry]

tell mitchell to solve his own damn problem

[rancid geode]

this is what im thinking

[still pumice]

Should be -20)

Open interval

[cosmic raptor]

hmmm, apparently the answer is [-20,infinity)

[rancid geode]

what 😭

[cosmic raptor]

idk how though since if it is infinity, then function goes to infinity as well

yeah, ikrr

[rancid geode]

there is absolutely that converges

[proud arch]

.-.

[static quarry]

-20 itself seems dubious, for large x the integrand will look like 1/x

[still pumice]

Wtf

[proud arch]

How

[static quarry]

and 1/x ain't integrable

[still pumice]

Yeah

[crystal lintel]

that is the laziest attempt at making a word problem i've ever seen

[still pumice]

-20 is diverage

[static quarry]

fr

[rancid geode]

holy damn

the more power

the closer it gets a square

[cosmic raptor]

yeah i'm confused as well

[proud arch]

I don't think the answer is correct

Idk what the question maker thinking

[still pumice]

For sure its not…

[merry pivot]

Isn’t it ln(x)

Wait

Nvm

[merry pivot]

Im stupid

[static quarry]

not integrable to +infty i meant

[rancid geode]

it doesnt even converge here

[merry pivot]

I read thay wrong

[still pumice]

a -> +infinity the whole thing blows up

[merry pivot]

mb 💀

I didn’t read it

[static quarry]

also [-20,infty) is laughable, if mitchell thinks this is gonna converge with a=100 then he needs to go study poetry

[rancid geode]

i think it should be (-infty, -18)

[chilly spoke]

it says

such that the integral ... diverge

[rancid geode]

real

[static quarry]

why -18?

anything less than -20 will work

[cosmic raptor]

oh wait, i didn't realise the question lol

[static quarry]

(strictly less)

[cosmic raptor]

my bad, it's supposed to diverge not converge

[static quarry]

ohhh

[rancid geode]

x^1 diverges

[static quarry]

oh right it does say "diverges"

[rancid geode]

that

makes sense

[static quarry]

even more stupidly written than initially thought

[cosmic raptor]

hahaha

[proud arch]

They want to be unsolvable .-.

[rancid geode]

we are dumb ourselves

[static quarry]

reading is hard

[rancid geode]

damn

[still pumice]

D:

[static quarry]

mitchell should teach us

[rancid geode]

real

[still pumice]

Fr

[proud arch]

What the hell kinda question is this

'Make my life harder' ~ mitchell

[cosmic raptor]

final exam questions 😦

this was another question that i got stuck on, any points would be appreciated

[merry pivot]

Alldis math to work a 9-5 job

[static quarry]

you'll never miss an important tax deduction thanks to mitchell and his wild integrals

[merry pivot]

Whos mitchless

Mitchell

He sounds wise

[static quarry]

ugh

[proud arch]

Put 2 = 2((sinx)^2 + (cosx)^2)

And then put x = pi/ 2 -x

Should do the trick I think

[static quarry]

or try plugging in x=0 and x=pi/2

(probably)

[cosmic raptor]

someone from an upper course said expand and compare, but not sure how

[static quarry]

too much work

[merry pivot]

Don’t do thay

Actually maybe if pluggin in value done work

[static quarry]

plug in two values of x that make it simple, then you have two linear equations with two unknowns

[merry pivot]

Dont

💀💀🗣️

But expanding that would cost an arm and leg

[static quarry]

my arm and leg both hurt just thinking about it

[proud arch]

The nice thing is that

-(16x)^2 - (64-x^2)^2 = -(64-x^2)^2

[merry pivot]

I mean if you put enough thought into it you can do anything 🗣️🗣️

[proud arch]

So it's easier to think of c and b

[cosmic raptor]

hmmm, if i plug it in some x values though, how will i get c and b

[proud arch]

Why your leg hurting

What are you doing with your leg bruh 💀

[merry pivot]

Cuz they thinking too mich

[static quarry]

the cost of having it removed in order to finance the cost of expanding

tbf it won't be my leg, it will be dlsyl's

[proud arch]

And the incredible ability that leg carries as the epicenter of all though processes

Makes it hurt

Gotcha

[static quarry]

yes that

[merry pivot]

Yall r good at english too??

Cuz tf r u saying

Put this in math terms pls

[cosmic raptor]

mitchell got more questions lol

then his friend ali came in

[static quarry]

oh no, ali is piling on

time to find a better class of friends

[marsh citrus]

@cosmic raptor Has your question been resolved?

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[marsh citrus]

@small stream Has your question been resolved?

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[winter anchor]

Any ideas?

[winter anchor]

Sorry it's B^3 + C^3

[marsh citrus]

@winter anchor Has your question been resolved?

[marsh citrus]

@winter anchor Has your question been resolved?

[marsh citrus]

@winter anchor Has your question been resolved?

[modern sedge]

I just tried to write A as B + C such that B = B^3 and C = C^3 and it worked

[twin cape]

this is a good approach. You know that, given B, C must be integer matrices, you will probably want some 1s and -1s, since A has small entries. So, given that -1^3=-1 and 1^3=1, you can probably figure out matrices to fit together such that you get A.

[winter anchor]

What were your B and C?

[marsh citrus]

@winter anchor Has your question been resolved?

[marsh citrus]

@winter anchor Has your question been resolved?

[marsh citrus]

@winter anchor Has your question been resolved?

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[still temple]

Hi, i was trying to solve this question but i havent been very good at it
Can someone help me? I dont know what to calculate its very vague

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[still temple]

Hello

[smoky spire]

derive it

and let it = 0

then solve for

x

[still temple]

so first i differentiated this function and got 3x^2 - 10x + 3
and i used the quadratic formula to find x = 3, and a 1/3

[smoky spire]

yes

[still temple]

for the critical point analysis

How do i determine whether they are min max or neither?

plug in x = 3 and a 1/3 into the original function?

[smoky spire]

u can plug x values back to the original function

[high robin]

then you do the quadratic formula

[still temple]

okay

nothing to do with the second derivative?

[glass silo]

Considering part b), you could also e.g. second derivative test

[still temple]

I see

Ok

so

find the 2nd derivative and plug in the x values

see if they're increasing or decreasing by looking at the sign?

[glass silo]

Basically, if it's strictly positive it's a min, if it's strictly negative, it's a max

[still temple]

hmm

these are from my notes

Is this relevant for this problem?

[glass silo]

Well, you could do it by checking the signs of the first derivative too as well, esp if they haven't introduced you to the second derivative test

[still temple]

i got increasing for f''(3)

[glass silo]

(the idea behind the second derivative test is that e.g. for the local min, your derivative goes from negative to zero to positive, so "must be increasing", and the implications for the derivative of the first derivative that brings )

[still temple]

and decreasing for f''(1/3)

so is that correct?

[glass silo]

how do you mean "increasing" for those

[still temple]

ic

[still temple]

you said this

my answer is positive for f''(3)

so im saying its increasing

[glass silo]

Be very careful - what's increasing, and where?

[glass silo]

Notice my statement tells you that f has a local min at x = 3

[still temple]

Oh

Hm

[glass silo]

Damn it

[still temple]

so

i see

im confused

[glass silo]

Have you covered the second derivative test before this?

[still temple]

not really

i just googled how to do everything

i was sick for the past few days

and i have a test on it tmmr

so i think i understand now

i should pick two values

near x = 3 and near x = 1/3

from the left and the right of those

and see the sign change from the negative to the positive

to determine whether it's a local min, local max, increase or decrease

[glass silo]

(of the first derivative, sure)

And yep, have you heard that "your function is decreasing when its first derivative is negative, and increasing when its first derivative is positive"?

[still temple]

perhaps, not 100% sure

[still temple]

okay

so thats first derivative test

now for the second derivative test

i plug in 3 and 1/3

see the sign of the answer

and at that point

its a local max or min?

and if its 0 its inconclusive?

so

x is a local minimum at 3 (the value was 8, 8 >0)
x is a local maximum at 1/3 (the value was -8, -8 <0)

[glass silo]

(yep, strictly negative for max, strictly positive for min)

[still temple]

lovely

so

the answer for part a

is

the critical points are x = 3, and a 1/3

where x is a local minimum at x = 0 and
x is a local max at x = 1/3

[glass silo]

Yep seems good to me

[still temple]

alright

[still temple]

i have no idea how to do b

[glass silo]

Do you know what an inflection point is?

[still temple]

the point where the second derivative changes sign

[glass silo]

First derivative* but yep

[still temple]

wait what??

[glass silo]

An inflection point is where the first derivative changes sign, that’s how they’re defined

[still temple]

you sure?

[glass silo]

Ah wait yea you’re right, got myself mixed up

They don’t change signs got myself mixed up with two things at the same time, just my luck

[mossy parrot]

inflection point is when 2nd derivative changes sign

[glass silo]

Where the first derivative goes from increasing to decreasing, which you can check by seeing the second derivative changes sign

[still temple]

okay i think i understand inflection points so

find the second derivative

set it equal to zero

find that number

that x value is then plugged into the third derivative

[mossy parrot]

yep

wait

[still temple]

if its equal to a non zero value

[mossy parrot]

why 3rd derivative

[still temple]

then it is an inflection point

then you plug in the x back into the original equation to find y

[still temple]

Idk

[glass silo]

(Might be easier to just check that the signs of the second derivative differ on either side)

[still temple]

I think we have to do a specific method

for the exam tmmr

[mossy parrot]

just use a sign chart no?

[still temple]

so let me find the inflection point using that method

6x - 10 = 0
6x = 10
x = 10/6

f'''(x) = 6

so its already an inflection point

plug back in 6 into the original equation

(6)^3 -5(6)^2 + 5(6)

i got 66

[mossy parrot]

no

[still temple]

according to google calculator

[mossy parrot]

u plug in 10/6

[still temple]

Oh

Ok

Mb

[mossy parrot]

and that 3rd derivativemethod is wierd

just check

if values greater than 10/6 are positive or negative

and same for values below

[still temple]

cannot

[mossy parrot]

on the 2nd derivative equation

[still temple]

gimme 1 sec my calculator is giving some issues

[mossy parrot]

sign chart

u can see the change in concavity

[still temple]

i got

-4 (7/27)

so my inflection point would be

10/6 and that -4 (7/27) for
x and y

[mossy parrot]

is it right?

[still temple]

i dunno

[mossy parrot]

u have the answer key?

[still temple]

no

[mossy parrot]

bruh

did u plug in 10/6 correctly

then u should be fine

[mossy parrot]

also this method is good for finding inflection points

and plateaus

[still temple]

i think so yeah

[still temple]

i cant use it on my test tmmr

[mossy parrot]

damn

ab calculus?

[still temple]

No

not from america

[mossy parrot]

ah

its fine

we dont learn your third derivative method here

i am quite unfamiliar with it

[still temple]

i think i plugged it in wrong lemme try it again

[mossy parrot]

any other questions?

calc is kinda fun to do

[still temple]

nty

.close

[marsh citrus]

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[fierce fulcrum]

how would i do this

[fierce fulcrum]

,rotate

[vital dagger]

idk bro

[fierce fulcrum]

could you do the secotr of the line thing

[vital dagger]

I came here 4 help

[fierce fulcrum]

oh

ok

waht is you rproblom

[ebon solar]

no

@vital dagger you have to open your own channel

you can't ask it here

[fierce fulcrum]

my bad @ebon solar

[vital dagger]

oh

[ebon solar]

no

[vital dagger]

@fierce fulcrum look is this it?

[ebon solar]

@fierce fulcrum this is YOUR channel

@vital dagger get out of here

[vital dagger]

why

[fierce fulcrum]

yes leave @vital dagger

[vital dagger]

ok.

[ebon solar]

unless ur helping 🙂

which you seem to be? idk

[vital dagger]

I am

[fierce fulcrum]

ok

[rustic field]

well

How lost are you?

[fierce fulcrum]

well not that much i think

could you do the line fourmlua thing

for arc

[rustic field]

what have thought of doing

[fierce fulcrum]

like 60/360 x 8

right ?

[rustic field]

but u have to subtract something from it

what can it be ? to get the white area ?

[fierce fulcrum]

the traingle

area

[rustic field]

and that is ?

[fierce fulcrum]

um the furmla of equalaterial traingle

[rustic field]

slight correct it should be 60/360 * pi * 8*8

[fierce fulcrum]

o yes

[rustic field]

and that is ?

[fierce fulcrum]

root 3/4 x 8^2

[fierce fulcrum]

would you multiply by 3 to get all the arcs

[rustic field]

yes

Clear ?

[fierce fulcrum]

so it would by (60/360 * pi * 8*8) *3 - (root 3/4 x 8^2)

[rustic field]

no no

multiply the entire thing by 3

[fierce fulcrum]

oh

why

[rustic field]

cuz

60/360 * pi * 8^2 - root(3)/4 * 8^2

gives u the area

of 1 white portion

[fierce fulcrum]

of what

oh

yeah make sense

[rustic field]

since their are 3

[fierce fulcrum]

then times 3

[rustic field]

yes

[fierce fulcrum]

ok thanks

then

thank you disco

.close

[marsh citrus]

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[marsh citrus]

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[last bridge]

Where did they get the 2 in 2x(y+1)

[late geode]

coefficient of x^2

[last bridge]

Thanks

[marsh citrus]

@last bridge Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[ebon solar]

dawg what the fuck

is this hw

[runic swan]

no

its competition math

[ebon solar]

u-sub $u = \arccos(x)$

[elfin berry]

rain

[runic swan]

tried u sub

failed

[ebon solar]

it works

[mossy parrot]

u sub is not possible

idts

[ebon solar]

dawg what

[mossy parrot]

trust

when in doubt integral calculator

[runic swan]

no cuz

u sub arccos

is gonna be sqrt(1-x^2) du

theres gonna be u and x

u can't cancel out the x

[ebon solar]

$\int e^{\arccos(x)}, dx = - \int e^u \sin(u), du = -\frac{1}{2}e^u (\sin u - \cos u) + C$

[elfin berry]

rain

[runic swan]

how did u get sin u

[mossy parrot]

waat

derivative of arccos is not sin

integral calculator got that

[ebon solar]

yeah

$\sin(u) = \sqrt{1-x^2}, \cos(u) = x$

[elfin berry]

rain

[runic swan]

bro what

[ebon solar]

i got the same thing

[mossy parrot]

wtf

ohhhhhhhhhhh

i get it now

[ebon solar]

🙂

[mossy parrot]

x=cos u

then u plug into the derivative

1-cos^2u

is sin^2u

and rt is sinu

[runic swan]

oh wait i see

did u sin(arccos)

[ebon solar]

🙂

[mossy parrot]

😢

[runic swan]

damn

[ebon solar]

competition math is crazy

i dont really fuck w it

[mossy parrot]

hella stressful

[marsh citrus]

@runic swan Has your question been resolved?

[marsh citrus]

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[wicked hawk]

I need to solve this question using quadratic functions. Not sure what to do after this step.

[spare idol]

rearrange to make L the subject

and then sub L into the formula of a rectangle

then when you get an equation for A that only has the variable w unknown

[wicked hawk]

so 2L =-5W + 120?

[spare idol]

move the 2 to the other side to

[spare idol]

u differentiate it, so dA/dw

then you let it equal to 0

to find ur w value

[wicked hawk]

What is dA/dw

[spare idol]

derivative, have you learn differentiation yet?

[wicked hawk]

No?

Im in grade 11 pre calculus idk