help-49

[wet vector]

I got everything else on my own but when I try to find the ange it says its wrong

I tried many different answers

[midnight plank]

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[wet vector]

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[muted iris]

oh what the fuck

[cobalt silo]

What's the least common multiple of 5, 7 and 3?

[muted iris]

105?

or is there smth smaller ??

[midnight plank]

@lucid kraken Has your question been resolved?

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[quick salmon]

How can i say if i can derivate this function in X0 using this formula?

[terse lodge]

check whether the limit exists

[quick salmon]

yes but what is DeltaX

[terse lodge]

a dummy variable

[quick salmon]

how to calculate Δx

[terse lodge]

?

delta x is going to 0

[quick salmon]

idk how to do the exercise

[terse lodge]

check whether either of those equivalent limits exist

[quick salmon]

I don't know how to use the formula

so i can't check if the limit exist

[terse lodge]

delta x is a limiting variable

you can’t know it

but you know everything else

so substitute the values for x_0 and use the definition of f

[quick salmon]

so basically

f(1) = ( f(1+ Δx)-f(1) ) / Δx

and then, what should i do with absolute values?

[terse lodge]

should be f’(1), and the right-hand side should be a limit

[terse lodge]

simplify where possible

what expression do you get?

[quick salmon]

but my book solutions is "not derivable in X0"

[terse lodge]

that’s correct

it’s because the limit on the right does not exist, but you should see that after simplifying the expression

what is f(1)?

[quick salmon]

Δx + Δx / Δx

[terse lodge]

how did you get that?

there should be an absolute value

[quick salmon]

that s the problem

i m doing the exercise wrong

[terse lodge]

you’re given f

[quick salmon]

f(1) is not 1?

[terse lodge]

yes

[quick salmon]

so 1 + Δx

• f(x)

[terse lodge]

then what is f(1 + delta x)

[quick salmon]

1 + Δx

[terse lodge]

no

you’re given f

just substitute

[quick salmon]

1 + Δx + Δx

[terse lodge]

where is the absolute value?

[quick salmon]

disappear

[terse lodge]

why?

[quick salmon]

idk what should i do with it

[terse lodge]

why would it disappear?

keep it

delta x is not necessarily positive

[quick salmon]

so is 1 + Δx + | Δx|

[terse lodge]

yes

and f(1) = 1

[terse lodge]

so what is this expression

[quick salmon]

so the final is | Δx | / Δx

[terse lodge]

no

you have a delta x in the numerator

[quick salmon]

1 + Δx + | Δx | -1

so Δx + | Δx |

[terse lodge]

that is just the numerator

[quick salmon]

uesd

yes

Δx + | Δx | / Δx

[terse lodge]

yes

now split the fraction

[quick salmon]

1 + | Δx |/ Δx

[terse lodge]

yes

[quick salmon]

why is not derivable

[terse lodge]

so, f is differentiable at 1 only if the limit as delta x approaches 0 of 1 + |delta x| / delta x exists

[terse lodge]

check the left and right limits of your last expression

[quick salmon]

it s different because it s abs

wait

[terse lodge]

approaching 0 from the left, |delta x| = - delta x so |delta x| / delta x = -1.

[quick salmon]

is like 1 + | 0- | / 0+

?

-1 and +1

[terse lodge]

yes

[terse lodge]

don’t know what this means

the left limit is 0 and the right limit is 2

when Δx approaches 0 from the left, | Δx | = -Δx

when Δx approaches 0 from the right, | Δx | = Δx

[quick salmon]

0- is the value of x approaching from left

abs of 0- is 0+ so 0+ / 0- is -1

and the right same but positive

[quick salmon]

WHAT

How

[terse lodge]

because you’re adding 1

[quick salmon]

omgg I m so dumb

O

[terse lodge]

this is the expression

1 + | Δx |/ Δx

[quick salmon]

wait i m missing something

i m sorry

[terse lodge]

as long as you can see that the left and right limits are different at 0, then you’ve solved the question

[quick salmon]

i have lim x-> 0 of 1 + | Δx |/ Δx

right?

[terse lodge]

lim delta x -> 0

look at your screenshot

[terse lodge]

here

[quick salmon]

yep

so i assume the Δx is negative

1 + (-1)

[terse lodge]

yes

[quick salmon]

OMGGG

FINALLY

[terse lodge]

from the left of 0

[quick salmon]

And 2 from right

[terse lodge]

and 1 + 1 from the right

yes

[quick salmon]

TYSM

[terse lodge]

so derivative can’t be defined

[quick salmon]

yes because different values

❤️

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[median oxide]

what is 8 x 209

[warm magnet]

Use a calculator

[median oxide]

i cant!

my teacher wont let me

[steel night]

8 x 209 = 8 x 200 + 8 x 9

[median oxide]

now i try to solve that?

[steel night]

thats easier right

are you still stuck

[median oxide]

yeah i got it i got 1672

[thorn crown]

Can ask Discord but not use a calculator. 🧐

[median oxide]

yes

.close

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[lyric ridge]

I’m so stuck on this probability question

[lyric ridge]

Would I start like this?

[midnight plank]

@lyric ridge Has your question been resolved?

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[craggy notch]

tan^(2)(x)-sec(x)=2sec^(2)(x)-3

[warm magnet]

What are you tryna do

[sudden topaz]

Solve for x I presume?

[craggy notch]

find all possible solutions

[deep vine]

Start with the identity sin² + cos² = 1

Divide through by cos²

What does that give you?

[craggy notch]

I know that's tan^2+1=sec^2

[deep vine]

Yes

So then you can substitute

Replace the tan² with sec²-1

[craggy notch]

ok

I got to -sec^2(x)-sec(x)+2=0

[latent bolt]

what does that form remind you of

[craggy notch]

trinomial

[deep vine]

Let s = sec(x)

[latent bolt]

yup

[craggy notch]

(secx-1)(secx+2)

=0

[latent bolt]

yep

[craggy notch]

cosx=1 and cosx=-1/2

[latent bolt]

yes

[craggy notch]

cos is the x

0/2pi

[latent bolt]

what

you mean 0 and 2pi?

[craggy notch]

yes

ok

[latent bolt]

,w cosx=1

[grand pond]

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[latent bolt]

this is correct

,w cosx = -1/2

[grand pond]

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[latent bolt]

other is not quite correct

[craggy notch]

x=(2pi/3)+2pi and x=(4pi/3)+2pi

[latent bolt]

there are infinitely many

and those are wrong I think

[craggy notch]

I forgot the n's

x=(2pi/3)+2pin and x=(4pi/3)+2pin

there

[latent bolt]

second one is incorrect

(I think)

might be true for some choice of n

[craggy notch]

,w cos(4pi/3)

[grand pond]

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[latent bolt]

oh

I guess it is

[craggy notch]

,w cos(0pi/3)

[grand pond]

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[craggy notch]

,w cos(0/3)

[grand pond]

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[craggy notch]

???

[latent bolt]

I don't know what you are trying to do but I think you are done with your question

[craggy notch]

,w cos((2pi)/3)

[grand pond]

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[craggy notch]

k

.close

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[normal citrus]

,w series expansion e^x

[grand pond]

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[normal citrus]

if f(x) = exp(x)
does it means that f(0) = 1
f'(0) = 1/2
f''(0) = 1/6
f'''(0) = 1/24 etc...
?

[steep hinge]

NO

$\sum f^k(0)x^k/k!$

[grand pond]

everg

[steep hinge]

this is the taylor expation with centre x=0

[normal citrus]

ye

[steep hinge]

the fraction that you see are the contribuition of 1/k!

[normal citrus]

ye

[steep hinge]

ideed $f^k(0)=1$ for f=exp

[grand pond]

everg

[normal citrus]

because 1! = 1

i think i got what's wrong

i have to devide it by k!

[steep hinge]

yes

0!=1

[normal citrus]

hum no multiply it

[steep hinge]

gg

[normal citrus]

thx

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[knotty veldt]

how do i do this?

[still rose]

subtract sin^2x from both sides, add (cos^2x-cos^2x) to the left side, merge the -sin^2x and -cos^2x (into -1, via the pythagorean identity)

you want to get all cosx terms

then you can solve it quadratically @knotty veldt

[knotty veldt]

ok ill try that now

.close

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[still rose]

hope you got it! good luck.

[knotty veldt]

yh i did thanks bro

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[warm pulsar]

Someone know how to do B?

[latent bolt]

by any chance, is this an online test?

that you will be graded on

[warm pulsar]

No

Just homework

[latent bolt]

can I request the link to be sure

[warm pulsar]

Wym

[latent bolt]

the url to the exercise

[warm pulsar]

I mean you would have to log in through my account then

But yeah on the bottom it says unlimited attempts

[latent bolt]

I guess it does

so I assume some school/government site

[warm pulsar]

Yes

[latent bolt]

I guess that's acceptable

moving onto the question

so

[warm pulsar]

Yes

[latent bolt]

you start the population at 13

and after one year it'd grow by 13 × 7%

[terse spear]

I mean just post a screenshot of the entire page, crossing out any personal info so you don't doxx yourself, if you wanted sufficient evidence

[latent bolt]

so 13 + 13 × 7%

one year further and it grows by (13 + 13 × 7%) × 7%

[latent bolt]

in other form it's 13 × 7% + 13 × (7%)²

at year 2

I think you can see the pattern

[warm pulsar]

Thank yiuuu

[latent bolt]

so can you write the function for it

[warm pulsar]

Wait I’m confused

[latent bolt]

let me help a little by writing it all together

wait a min

[warm pulsar]

?

[latent bolt]

oh nvm

just confused my self

[latent bolt]

it grows by this from year 1 to 2

so it's 13 + 2(13×7%) + 13×(7%)²

one year further and it becomes 13 + 3(13×7%) + 2(13×(7%)²) + 13 × (7%)³

I think the pattern is now a bit more seeable

at year 0 we have, 13
at year 1 we have, 13 + (13×7%)¹
at year 2 we have, 13 + 2(13×7%) + 13×(7%)²
at year 3 we have, 13 + 3(13×7%) + 2(13×(7%)²) + 13×(7%)³

I guess it is a bit tideous without expanding

can you see how can this be written for general t

[warm pulsar]

Im sorry im really confused 😭

I see the patterns in the different years im just confused

Im like trying to process what you’re saying im sorry😭

[latent bolt]

yeah that's sensible

[warm pulsar]

SORRY IM LIKE REALLT BAD AT MATH

😭

[latent bolt]

hmm

you can try with factoring out the 13's

maybe that's easier

[warm pulsar]

Umm…

[latent bolt]

I can help a little

[warm pulsar]

Bro I’m so sorry

[latent bolt]

at year 0 we have, 13
at year 1 we have, 13 + 13×7% => 13( 1 + (7%) )
at year 2 we have, 13 + 2(13×7%) + 13×(7%)² => 13(1 + ( 2×7% + (7%)² ) )
at year 3 we have, 13 + 3(13×7%) + 2(13×(7%)²) + 13×(7%)³ => 13(1 + ( 3×7% + 2(7%)² + (7%)³ )

[warm pulsar]

No yeah I see it but I’m like confused as to how to generalize it idk if that makes sense

[latent bolt]

hmm

like

at year 0 it's 13(1 + 0×(7%) )

at year 1 it's 13( 1 + 1×(7%) )

at year 2 it's 13( 1 + 2×(7%) + (2-1) (7%)² )

[warm pulsar]

OHHHHHHH

[latent bolt]

at year 3 it's 13(1 + (3-0) (7%) + (3-1) (7%)² + (3-2) (7%)³)

a bit confusing over text

[warm pulsar]

Wait I thought I had it 😦

I thought it was 13(1+1(0.07)^t

[latent bolt]

sadly not so simple

[warm pulsar]

😭😭😭😭

I don’t get it then fr

[latent bolt]

hmm

[warm pulsar]

You probably like damn.. this girl dumb as hell😭 IM SORRY FR I DONT MEAN TO BE DIFFICULT

Should I just leave this chat😓

I’m on my 20th attempt 😂😂😂😂

[latent bolt]

nah not really

it's kinda hard to get a grasp on

[warm pulsar]

CAN U GIVE ME A HINT

where does the T go..

[latent bolt]

I mean t is the years

do you know the summation notation

[warm pulsar]

No

[latent bolt]

it's easier to write it that way

hm

[warm pulsar]

At least I think

I Never heard of that

The last time I took a math was sophomore year of hs😿

[latent bolt]

so basically

as i increments one by one until it reaches n

we sum the terms like x_1, x_2, x_3, ..., x_n

you can think of it as just a short hand for writing large sums

[latent bolt]

you can see that

we have 13(1 + (t-0) (7%)^(0+1) + (t-1) (7%)^(1+1) + ... )

[warm pulsar]

You left me speechless

[latent bolt]

so something like $13(1 + \sum_{i=0}^{t-1} {(t-i)× (\frac{7}{100})^{i+1} })$

[grand pond]

biggboy

[latent bolt]

yeah, sorry....

well

I think you can just google compound growth and how it works

and come up with a nicer closed form

mine is a bit forced and a lil stupid too :P

[warm pulsar]

Bro

LXNDNCJDNCN

THE ANSWER

IS 13 x 1.07 ^t

😭😭😭😭😭😭😭😭

[latent bolt]

wut

[warm pulsar]

YEA

[latent bolt]

I thought "grows by 7%" meant Current + (Current×%7)

not just Current×7% 😔

[warm pulsar]

Omg It’s okay

Wait I have another problem I need help with

[latent bolt]

go on

[latent bolt]

hmm

there are 3 roots so one has a multiplicity of 2

does f(0) = 3

I kinda can deduce that from the graph but unsure since they didn't label the horizontal values

[warm pulsar]

Yes I am pretty sure

Yeah sorry this website is ass

[latent bolt]

lol

then since we know the other 3 roots

we can write our polynomial as f(x) = (x+2)(x-1)(x-3)(x-a)

so f(0) = (2)(-1)(-3)(-a) = -6a = 3

huh

"a" should be one of our other roots though...

[warm pulsar]

Uhhh

[latent bolt]

graphing f(x)=(x+2)(x-1)(x-3)(x+2) gives the general shape but then the y-intercepts don't match

and I assume they don't allow you to use another site to just graph things

weird

[warm pulsar]

Yeah I don’t think we do that

[latent bolt]

either the ungiven y-intercept is 12 and the question is unsolvable by what's given or the y-intercept is 3 and the graph is false

might wanna ask your teachers

[warm pulsar]

Yeah 3 or 12 didn’t work 😦

Idk why it makes that face I typed a sad face

[latent bolt]

it's just a default discord setting

can be changed at "text and ..." I think

[latent bolt]

if the ungiven y-intercept is 12 the last factor is (x+2)

for 3 it just doesn't work regarding the graph

[warm pulsar]

Um…

Well this is sussy

wait okay that assignment is due Wednesday

I HAVE THIS LAST ONE DUE TODAY

LAST ONE I PROMISE

I put it in the graph and I’m confused

[latent bolt]

which are you stuck on

a, b, c?

[warm pulsar]

All of them ..

Here wait I’ll pull it up

I’m like confused

Idk why my graph looks so small and thin

Like I zoom in my then it’s like confusing

Like u can’t see everytbing

[latent bolt]

you can drag the horizontal axis to enlarge it

[warm pulsar]

?

Wait

[latent bolt]

like click and drag

[warm pulsar]

Is that even how u do a

[latent bolt]

it just how you visiualise the graph

desmos handles the values on the axis so the function doesn't change

[warm pulsar]

Ohh okay

[latent bolt]

and I think you can describe the restrictions for t in a new line

(≤ is equivalent to <=)

and ≥ is to >=

[warm pulsar]

I just press the add button and type 0 ≤ t ≤ 3

?

[latent bolt]

yeah

[warm pulsar]

But it didn’t allow

Me

[latent bolt]

hm

[latent bolt]

I see

then I think it's {0 ≤ t ≤ 3: your function}

[latent bolt]

what does the error say

[latent bolt]

try something like this

[latent bolt]

should be s(t) = 64 - 16(t-1)² there

[latent bolt]

it's still s(x) there...

my s(x) was just an example

[warm pulsar]

It won’t let me use t

I don’t know why

[latent bolt]

huh

try writing your function in x instead

and delete that parameter for t

[warm pulsar]

Uh

Like this

It won’t let me delete the t slide thing

[latent bolt]

what

[warm pulsar]

Oh wait I forgot to change that other t

[latent bolt]

now just stop rendering your fourth line by clicking on that colored-wave thing

[warm pulsar]

The red one?

[latent bolt]

grey/black one

[warm pulsar]

Wym

Press the play button?

OH

?

[latent bolt]

yes

you can now see the trajectory of the ball

by adjusting the graph visual to your liking I think you can answer the questions now

[warm pulsar]

How do you save points to the graph?

[latent bolt]

just add lines like (x,y) where x and y are the coordinates of the point

[warm pulsar]

Thank you

Wait

What’s the behavior of the ball???

SORRY

[latent bolt]

either gaining altitude or falling

or stable at a single particular point

[warm pulsar]

For B?

[latent bolt]

yesh

[warm pulsar]

Thank you

Sm

Frr🙏🏼🙏🏼🙏🏼

[latent bolt]

🦦

[warm pulsar]

In another life… I would be the one teaching u 👩🏻‍⚕️👩🏻‍⚕️👩🏻‍⚕️

LMAO

Sayonara >_<

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[latent bolt]

bai

[midnight plank]

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[void kiln]

you pick two marbles (without replacement) from jar A which contains 3 red marbles and 5 green marbles, then you roll a dice, if the dice roll is strictly less than 4, you pick another marble (without replacement) from jar A, else pick a marble from jar B which contains 6 red marble and 2 green marble. Given a marble is red, is it more likely that it has been picked from jar A or jar B?

[void kiln]

I'm confused on the given condition there, like do you randomly stops the process in the middle and whatever marble was the latest picked is red or you do all the picks and then you randomly choose from the three you already picked and it is red?

[midnight plank]

@void kiln Has your question been resolved?

[void kiln]

<@&286206848099549185>

[midnight plank]

@void kiln Has your question been resolved?

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[gleaming atlas]

Question 16, the book says the answer is E, which is equal to 3/8

But I don’t understand where they got that numbers from, there are 2*4=8 possible outcomes, and its equally likely to get heads or tails, so why wouldn’t the probability be 4/8 or 1/2?

[violet pasture]

No, there are 2^4 possible outcomes

You can also get 1 tail, 3 tails, 4 tails so getting exactly 2 tails isn’t 1/2

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[ocean parcel]

Can someone help me understand this problem?

[ocean parcel]

, rotate

[ocean parcel]

I am confused on the diagram and what it is meant to mean.

[midnight plank]

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[fiery snow]

can someone help me with this cylindrical shells problem? i really dont know where im going wrong, pretty sure its in calculating the radius and height though

[midnight plank]

@fiery snow Has your question been resolved?

[fiery snow]

<@&286206848099549185>

[stray steppe]

just think of it like you're taking the area and then carving a portion out

[fiery snow]

right, i get that part

at least at a theoretical level

[stray steppe]

i mean that you revolve the integral around, not that that is the revolution

[fiery snow]

ohhh

thank you for the whole sketch, that is really useful

[stray steppe]

you take the area of the blue and red for one integral and subtract the red out to get just the area of the blue

the integral of 1dx contains both the blue and red parts, since you want the blue, you just subtract the parts underneath that curve which is just that integral

[fiery snow]

do i just solve for the integral with bounds 0 to 1, for (1-x^6)dx ? is there no 2pi or anything like that? is that the volume?

[stray steppe]

No, that gives the area of that region, you need to revolve it around to get the volume of the shape

To revolve it, multiply the solution to that definite integral by 2 pi

So the volume is just 2pi* (that definite integral)

2pi is just a constant

It wont affect calculating the area of the region you are revolving itself since you can just move it outside the integral

[stray steppe]

actually i dont think this is right

[fiery snow]

oh? thats ok -- any idea what i should do instead?

[midnight plank]

@fiery snow Has your question been resolved?

[fiery snow]

figured it out.
v= integral from 0 to 1 (1-x^6)^2 dx
v = 72/91
still tysm for your help @stray steppe :)

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[twin ridge]

This is the question I am stuck on.

[twin ridge]

This is what I've tried.

How does one even integrate a term that large?

[midnight plank]

@twin ridge Has your question been resolved?

[tribal temple]

Okay, so first off, this term can be simplified

[twin ridge]

Dang you right

[tribal temple]

And I see you're trying to do the integrating factor
$$
e^{-\int \frac{x}{1 + x} dx}
$$

[grand pond]

chartbit

[tribal temple]

• may I ask what you get that as please? It's just a little bit unclear reading through?

[twin ridge]

I got -xln(x+1)+x-ln(x+1)

[tribal temple]

As in you get that
$$
e^{-\int \frac{x}{1 + x} dx} = -x\ln(x+ 1) + x - \ln(x+1)
$$
or?

[grand pond]

chartbit

[twin ridge]

Precisely.

Err

[tribal temple]

Hmmmm

[twin ridge]

Not including the e

Just the integral

[tribal temple]

Oh fair alright, but still, hmmm

,w int -x/(x+1)

[grand pond]

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[twin ridge]

It's a log instead of an ln?

[tribal temple]

The log here is natural log, ln

[twin ridge]

Gotcha

[tribal temple]

Wolfram writes log for ln

[twin ridge]

Understandable.

[tribal temple]

But how did you get that integral though? For me I get the above and can't see that they're equivalent

[twin ridge]

The last guy I got a chat with told me to use a Frobenius thingy, so I used the method he showed me and got that

Oh wait

I forgot a term

Ok yeah, I get the same thing as the wolfram now

ln(x+1)-x

[tribal temple]

Cool cool, perfect, then you can simplify
$$
e^{\ln(x+1) - x}
$$

[grand pond]

chartbit

[twin ridge]

Can I simplify that into 2 terms?

[tribal temple]

Yep, rules of indices and all

Then you'll see something somewhat nice happen

[twin ridge]

If it's a subtraction, that means it's a division or a subtractioN?

[tribal temple]

It would be a division, but it's better to treat it as "addition of a negative", by which, I mean

[grand pond]

chartbit

[tribal temple]

Then do that as multiplication

[twin ridge]

Gothca

And then I have to integrate again to get y?

[tribal temple]

When you split them, what do you end up getting, for reference?

[twin ridge]

(y(x+1)e^(-x))d/dx = int(x^2+x)(e^-x)

[tribal temple]

Yep [but write it as
$$
\left(y (x + 1) e^{-x} \right) = \int (x^2 + x) e^{-x} dx
$$
]

[grand pond]

chartbit

[twin ridge]

I got the integral as -(x^2+x)(e^(-x))-(2x+1)(e^(-x))-2e^(-x)

[tribal temple]

,w int (x^2 + x)e^(-x)

[grand pond]

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[tribal temple]

Too lazy to do it out lol

[tribal temple]

But looks right

[twin ridge]

Looks like they equate to the same thing

Just factored the -e^-x out

[tribal temple]

Yea and simplified

[twin ridge]

Doesn't look like I can factor x^2+3x+3 though 😦

[tribal temple]

Don't think you can? At least not nicely, but anyways that doesn't matter I wouldn't think

[twin ridge]

Would be super nice if it was x^2+4x+3, then I could do (x+1)(x+3) then cancel the x+1 with the one on the other side

[tribal temple]

Yea it would be haha, but anyways, I guess they didn't want your life too easy here lol

[twin ridge]

Some of the most satifisfying math problems are the ones that take 2 pages of writing then simplify to like 2 terms

[tribal temple]

That is pretty true, you do so much work and it turns out that the answer in the end is simple, you're like "damn that's nice!"

[twin ridge]

Should the answer be -(x^2+3x+3)/(x+1)?

Oh shoot, I forgot the + c

[tribal temple]

Yea was about to say, the c

[twin ridge]

Nice.

When I'm looking for the interval of definition, do I only look at P(x) and Q(x)?

Or do I look at every single piece?

The way I'm seeing it, x can't = -1

[tribal temple]

Hmmm to be fair I would think that for one we obviously can't have x = -1 (division by zero otherwise in multiple places), but other than that I'm actually not too sure, it's a slow moment for me today haha

[twin ridge]

Ok cool. For some reason, the question is the "largest" interval" over which it's defined, but -infinity to -1, and -1 to infinity are relatively similar.

Infinity is always somewhat relative

[tribal temple]

Yea "largest" is throwing me a bit here - not sure what the intention they meant by that is. Think that in any case it should be valid for numbers that are less than -1 too, right?

,w (1+x)y' -xy = x + x^2

[grand pond]

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[twin ridge]

It took (-inf, -1) and (-1, inf)

As in I submitted each one as a separate answer and it accept both,.

That's weird

Intrinsically, you would think -1,inf is bigger, but it's so relative that I guess it doesn't actually matter.

[tribal temple]

Ah, well it makes sense in a way, but strange what they would mean

[twin ridge]

Yeah

Thanks for the help though!

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[toxic flower]

Hiya, no clue where to even start with this one (I am unsure if it’s even in my specification anymore, it’s quite old) if anyone could give me a nudge in the correct direction that would be great, thanks

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[wanton oar]

i dont understand why its -infinity

[fallow scarab]

what do you think the answer is

[wanton oar]

the answer is -infinity but idk why

i just input problem into calculator because i didnt know what to do

[fallow scarab]

find the "dominating" term. when x gets more and more negative, which one of the two terms is larger in absolute value?

that one will be the dominant term

[wanton oar]

idk what you mean by absolute value here

2x^9 has the highest power so i think that makes it the dominant term

divide by x^9 both terms gives me 1/7x and 2

[fallow scarab]

correct

so the limit will be determined by the dominant term

what does 2x^9 go towards as x goes to -infinity

[wanton oar]

idk how we find that

[midnight plank]

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@wanton oar Has your question been resolved?

[wanton oar]

brother

[winter swift]

factorize by x²

then calculate the limit

[wanton oar]

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[wet vector]

How do u find rn

[gritty violet]

Whats the relationship between ATP and ARN

[wet vector]

similar triangles

is it 9?

because i did 6/10 = x/15

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[wraith flame]

If anyone can help me, pls do so, I gotta turn this by tomorrow, any help is appreciated.

[vapid echo]

Do you know what an acute and obtuse angle is

[wraith flame]

yes but I would just usually forget bc I barely learn it.

[wraith flame]

so can u help me?

[vapid echo]

acute is less than 90 degrees

obtuse is greater than 90 degrees

[vapid echo]

so use that to answer those questions

[wraith flame]

ik

[wraith flame]

ik

[vapid echo]

ok so for the first triangle is that angle greater than or less than 90 degrees

[wraith flame]

Acute angle?

[vapid echo]

yes and why

[wraith flame]

Idk how to explain but

The angles is exactly just like a acute angle.

[vapid echo]

ok well you know the definition of an acute angle is any angles less than 90 degrees

so for you explanation you could put that the angle is clearly less than 90 degrees

[wraith flame]

yep

[midnight plank]

@wraith flame Has your question been resolved?

[wraith flame]

@vapid echo sorry for pinging you, can you help me with the next one?

[vapid echo]

yeah what do you think it is

[wraith flame]

lemme see

Obtuse?

[vapid echo]

yes why?

[wraith flame]

because it’s more than 90 degrees if yk wha I mean

so like it would also be less then 180 degrees

[vapid echo]

yes

[wraith flame]

Mk lemme get it done rq

[wraith flame]

can you help me with the other one?

[vapid echo]

yeah what do you think it is

[wraith flame]

hm..

Right angle?

[wraith flame]

?

no wait not right angle

Acute angle

[vapid echo]

$\perp$

[grand pond]

clip

[vapid echo]

So that would be a right angle

[wraith flame]

o

[vapid echo]

one second let me draw this for you

[wraith flame]

No, it’s not necessary, I said acute angle because you didn’t answer so I thought it would be wrong.

[vapid echo]

See so if you have a right angle and push it further away its obtuse but if you push it closer its acute

[wraith flame]

so

a right angle is 90 degrees?

right?

[vapid echo]

yes

[wraith flame]

@vapid echo sorry again but you help me better, can you help me?

[vapid echo]

I think D is pretty obvious?

That symbol on the angle means it’s a right angle

[wraith flame]

yeah I just need you just in case I get sum wrong

[vapid echo]

Ok fs just ping me, I’m on my phone now though so no promises I see it

[wraith flame]

@vapid echo next one

@vapid echo

<@&286206848099549185>

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[floral bronze]

Here, I got 75° as my answer, but apparently it’s wrong

Could someone plz help?

Here’s my work

,rotate

[floral bronze]

@terse spear do u have time to help by any chance?

[midnight plank]

@floral bronze Has your question been resolved?

[floral bronze]

Actually, I fixed my answer and got 69

Does that seem right?

Nvm

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[empty lantern]

a curve C is defined by the equation x^2+xy^2-y^3=1. use implicit differentiation to compute the slope of the line tangent to the curve at the point (1,0)

[empty lantern]

I don't know if I'm solving it right

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[empty lantern]

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[rocky stream]

Fix an orthonormal base B and be [u] and [v] vectors of V³ such that:

---Image---

Then ---Image--- is an orthogonal set

[rocky stream]

How do I know if this is true?

[last slate]

take the dot product of the two vectors in the set

[rocky stream]

so [u] * thisv

[last slate]

yes

[rocky stream]

ah ty

the statement will only be true if the result is = 0, then?

[last slate]

yeah

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[gusty glen]

can someone explain to me why this diverges

[runic hamlet]

tan(x) is very close to x near 0

so this is very close to the series sum 1/n

which diverges

(this isnt a proof yet, just some intuition)

[gusty glen]

but

hm

[nova yoke]

or if you didn't know that fact offhand, when in doubt write tan = sin/cos.. and observe that cos(x) is very close to 1 near 0, and sin(x) is very close to x near 0

[midnight plank]

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[fallow scarab]

if you need a further hint beyond dena's hint, ||limit comparison test||

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[dusty girder]

how do I solve this?

[visual tiger]

Partitions have the following properties :

• Cover
• Disjoint
• Non-empty

Let's start by wondering if the first example of A1,A2,A3 is a cover of R²

Do you think this first example is at least a cover ? @dusty girder

[dusty girder]

ye

yes*

[visual tiger]

Have you tried looking at multiple example points?

[dusty girder]

oh, so no.

[visual tiger]

Yeah

[visual tiger]

Try to find an example point that doesn't fit in any of those 3 subsets

[dusty girder]

So it Option B.

[visual tiger]

Yeah but we're trying to understand why

[dusty girder]

In option A, the Cover condition is not met, the sets {A1,A2,A3}{A1,A2,A3} in Option A do not form a valid partition...

[visual tiger]

Yep

(For example point (1,3))

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[rose kayak]

so first off, what is sin(x + y)?

[wraith flower]

I don't understand this exercise, I tried something but I didn't get anywhere

[rose kayak]

ok that's a good start

[wraith flower]

it's equal to cos(x) sen(y) + cos(y) sen(x)

[rose kayak]

ok so we know that sin(x) = 1/3, and we know that sin(x) = opp/hyp

so we can find cos(x) with this info

you just have to use pyth theorem

[wraith flower]

hmmm

how ?

I dont understand how to use the triangle formulas here

[rose kayak]

ok good. Now use this fact with a^2 + b^2 = c^2. We know the hypotenuse is c. So now we just gotta set the opp to either a or b and then solve for our missing value.

So for our triangle for sin(x) is (3)^2 = (1)^2 + b^2, so b^2 = 8 so b = sqrt(8) = 2sqrt(2)

we we know that our adj side is 2sqrt(2)

does that make sense?

[wraith flower]

no sorry

I don't get it

what triangle do we have ?

[rose kayak]

hold on

we have to solve for the adj side

[wraith flower]

why is the hypotenuse 3 and the opposite 1 ?

[rose kayak]

becuase that's the definition of sin

sin(x) = opp/hyp

[wraith flower]

ohh 🤦‍♂️

I understand your explanation now

so

this would be cos(x)

[rose kayak]

bingo!

well done

so we know our cos(x) and sin(x)

now we have to contend to sec(y) = 5/4

[wraith flower]

yes

[rose kayak]

so what is sec(y)?

[wraith flower]

hyp/adj

[rose kayak]

yep exactly!

but it's the recipricol of a trig function. Which one? Which one is adj/hyp?

[wraith flower]

cos

[rose kayak]

yep!

now follow the same logic about

to find sin(y)

then you have everything you need

[wraith flower]

I did

I got the answer in the book so it works

👍👍👍👍👍👍

[rose kayak]

nice work!

[wraith flower]

thanks a lot I was so stuck here

💟

[rose kayak]

yep no problem. Practice makes perfect 🙂

[wraith flower]

🏆

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[desert patio]

Hey guys, I have a matrix $M=\left[\begin{array}{ll}1 & 3 \ 4 & 2\end{array}\right]$.

I want to know what kind of matrix it is (i have a lot of matrices), so what online tool can I use to do this?
Wolfram won't understand latex for some reasons

[grand pond]

Schrodinger

[desert patio]

sorry, it does understand the matrix, but it won't tell me what kind of matrix it is. I want to know if it's a hermitian matrix, symmetric matrix etc etc

any clever keywords which can get the desired result? I will bookmark it

[blissful pier]

wolfram does matrices far different than LaTeX

wolfram actually has it's own language

,w det({{a,b},{c,d}})

[grand pond]

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Requested by XxMrFancyu2xX#6050

[blissful pier]

WolframAlpha is just a free version, (but is optionally payable) of it's much more powerful cousin (Wolfram) and that is how it understands matrices,

this is the docs for matrices in Wolfram, most of these will not work on WolframAlpha https://reference.wolfram.com/language/howto/CreateAMatrix.html but for WolframAlpha https://www.wolframalpha.com/examples/mathematics/algebra/matrices those are the examples it gives

[blissful pier]

for example in this problem, i would type "eigenvalues {{2,2,1},{1,3,1},{1,2,2}}" into W|A

,w eigenvalues {{2,2,1},{1,3,1},{1,2,2}}

[grand pond]

Results provided by WolframAlpha

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

Requested by XxMrFancyu2xX#6050

[blissful pier]

that is how matrices work in W|A :)

[midnight plank]

@desert patio Has your question been resolved?

[midnight plank]

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[tidal mortar]

hi

[tidal mortar]

I wanna see if I did this right

for the first one I put r= 2-4/3t

for the second one I PLUGGED IN f(-3)= 2-4/3 x -3/1

for the third one I solved if r were equal to 26 is that correct?

[brazen palm]

you need a number for 2nd and yea, you solve that for 3rd

[tidal mortar]

what do u mean number for second

[brazen palm]

like you need a number like 1 or 2 or 3 something like that, but not 2-3-4 or 5-3-2

[tidal mortar]

no I plugged in -3 in place of t for that function and solved it right

[brazen palm]

yes, you'll have to solve it

[tidal mortar]

oh yes

thanks

[tidal mortar]

and the third one I have to make 26=2 - 4/3t ?

[brazen palm]

yep, and solve it

[tidal mortar]

thanks my brother

[brazen palm]

cheers!

[brazen palm]

you can type .close when you're done

[tidal mortar]

.close

[midnight plank]

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[quiet jackal]

i got 2sqrt2 =< |z| =< 6sqrt2

and pi/6 =< argz =< pi/3

is this correct

[midnight plank]

@quiet jackal Has your question been resolved?

[quiet jackal]

<@&286206848099549185>

[tender ocean]

hmm, |z| is probably triangle ineq if i had to guess

well what you could also do is actually break this down into the definition of |z - 4 - 4i|

and get like $\sqrt{(\mathfrak{Re}(z) - 4)^2 + (\mathfrak{Im}(z) - 4)^2}$ right

[grand pond]

most likely to honorable

[tender ocean]

i havent done much complex stuff so idk if thats how to go about it

[tame raven]

My answer is a bit different.for |z-4-4i|=2√2:

The range of |z| is [2√2, 6√2].
The range of arg(z) is [π/4, π/3] or [45°, 60°].

[tender ocean]

!nosols

[midnight plank]

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.

[midnight plank]

@quiet jackal Has your question been resolved?

[quiet jackal]

i have answers and i want them checked

so its ok

[quiet jackal]

how did you arrive at pi/4

[desert patio]

thank you very much

[midnight plank]

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[quiet jackal]

.reopen

[midnight plank]

✅

[midnight plank]

@quiet jackal Has your question been resolved?

[brazen palm]

i got the modulus part same as yours, but the argument part, I don't know how to find it 😔
but i drafted it on desmos and highly doubt its from pi/6 to pi/3

[olive matrix]

find a tangent line to the curve going through the origin

[brazen palm]

yea, but how? i forgot lol

[olive matrix]

implicit differentiation and uh

[brazen palm]

oh ok that

[olive matrix]

you'll get some system of eqns at some point

[brazen palm]

and use discriminant right?

[quiet jackal]

it’s not all that…

[brazen palm]

i was searching online to see if there's method using complex numbers

[quiet jackal]

it’s just pythag

the base of the circle

and the height from the origin to the circle

[brazen palm]

well, that line will pass through 2 points

[quiet jackal]

wair let me look at it again

[olive matrix]

the fact that the center is at 45º might give us a shortcut

[quiet jackal]

it’s just this no

[olive matrix]

yeah it's going to be a right angle between the radius and the ray from the origin

[olive matrix]

no

[quiet jackal]

why not

[olive matrix]

because that's a secant line

[quiet jackal]

that is the minimum argument though

[quiet jackal]

what about this

@olive matrix

[olive matrix]

that is, in fact, what i graphed

[quiet jackal]

so it is pi/4

isocoles triangle

yes my bad

[quiet jackal]

thanks for the help 🙏

[olive matrix]

what you need is for the line from the center of the circle to the exterior point to be perpendicular to the line to the origin

[quiet jackal]

why would you want that

isn’t my method fine

just simple trig

[olive matrix]

you don't want to hit the bottom of the circle

that won't work

[quiet jackal]

isn’t that the smallest possible argument that lies on the locus??

i don’t understand

[olive matrix]

no? look at the graph i posted

[quiet jackal]

you can’t get lower than the smallest point

every argument is bigger

[olive matrix]

what does "argument" mean to you?

[quiet jackal]

& the smallest point is below the radius

[quiet jackal]

angle from the real positive axis

[olive matrix]

right

[brazen palm]

they are different

[brazen palm]

opps, you've got it lol

[quiet jackal]

wait so

why is the bottom of the circle not the smallest argument

[olive matrix]

why should it be?

[quiet jackal]

it just looks like that is where the angle is smallest

[brazen palm]

looks like ≠ is

[olive matrix]

if you have a ball on a hill, the point that it connects with the slope is not its lowest point

or else part of it would be inside the hill

[quiet jackal]

right

[olive matrix]

at the bottom of the circle, the slope is flat

so you go up only a tiny bit by going across a lot

so, angle gets lower

[quiet jackal]

how is the angle lower

[olive matrix]

anyway yeah you want to find this point

[quiet jackal]

you are still going up aren’t you

ohhhh

that’s what you meant

by perpendicular

i was thinking of something different comepletley

by circle geo that is a right angled triangle

how do we find that point though

[olive matrix]

i think it's probably easiest to find the slopes directly

what's the equation of the blue line?

[quiet jackal]

y=ax

[olive matrix]

great

what about the green line

keep in mind it goes through (4, 4)

[quiet jackal]

y=-bx+c and substitute points

[olive matrix]

hmm you could

[quiet jackal]

or

perpendicular r

so it’s y=-x/a

?

plus domething

[olive matrix]

you need to translate that from the origin to (4,4)

point-slope form

i graphed y - 4 = b(x - 4)

[brazen palm]

or you can use this to find angles and thanks hayley for the graph

both works

[olive matrix]

oh hey that's a much better idea

[quiet jackal]

that’s what i was going to do but then i didn’t know how to find

the angle below theta

[brazen palm]

use the fact that it's symmetric along x=y

[quiet jackal]

this gets you pi/6

for theta

[brazen palm]

yep

[quiet jackal]

how to find small angle

hmm

[brazen palm]

.

[quiet jackal]

oh

[brazen palm]

you can draw the second tangent line

[quiet jackal]

what