help-17

[elfin moon]

I rewrite it

[viral copper]

Put z = 1 or i or something

[elfin moon]

Is it necessary?

Can I say thita is argz and it is related to tan so tan is negative only in second and fourth quadrent?

I tried this this way too please check@viral copper @soft walrus @empty frigate

[viral copper]

Arctan 0 is not pi

[elfin moon]

Ahh so then?

[viral copper]

arg(-1) = π but arctan(0) = 0

[elfin moon]

Can I not put -1 as -1+0.i as arc(y/x)

[soft walrus]

I don't think so because arctan is limited in range

$\tan(\pi)=0$ but $\arctan(0)\neq\pi$ however $\tan(0)=0$ and $\arctan(0)=0$ because of arctan's range

[twin meteor]

XxMrFancyu2xX

[elfin moon]

What is value of Arg 1 = 0, pi?

Or both

Is it correct?

Sin (log i^i) how to solve this

[vocal sleet]

@elfin moon Has your question been resolved?

[viral copper]

$$\sin \ln i^i$$
$$\sin (i\ln i)$$
$$\sin(i\frac{\pi}{2} i)$$
$$\sin (-\frac{\pi}{2})$$
$$-1$$

[twin meteor]

NEONPerseus

[viral copper]

(note that the logarithm isn't well defined for complex numbers though)

[elfin moon]

U put log = pi/2 why?

3rd step

[vocal sleet]

@elfin moon Has your question been resolved?

[viral copper]

I put pi*i/2

$i = e^{i\frac{\pi}{2}}$
$\ln i = i\frac{\pi}{2}$

[twin meteor]

NEONPerseus

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[north venture]

I need help :’)

[north venture]

I don’t understand how this gets split off from the absolute value

And determining those equations from the absolute value equation

Like why can’t 3t-5 go with the t<5/3 equation

[left crest]

Ok, what happens to the function 3x - 5 after x>5/3

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[undone pier]

when you take an integral from X = A to X = B in a scenario like this

will the outputted area under the curve be the area of X minus the area of Y?

[elfin wedge]

yes

[river minnow]

Assuming X and Y represent the areas of those geometric shapes, yes

[undone pier]

the highlighted ones

X being green and Y being orange

thats what they represent, so we agree here right?

[elfin wedge]

x-y = total area

[river minnow]

Yes

[river minnow]

x - y = total integral*

[undone pier]

okay

thanks guys

.close

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[sturdy bough]

Hello

[sturdy bough]

I want to ask a doubt and I am new here??

[still tendon]

That's the purpose of the server

[sturdy bough]

if f is defined from S to S, where S is the set: {1,2,3,4,5,6,7}. Find the number of functions such that the following condition is satisfied:
f(m*n)=f(m)f(n), where mn, m and n lies in set S

Here is the question I am stuck in

[still tendon]

We just started this topic

Idk anything in this

[sturdy bough]

hmm where are you from?

[paper depot]

any progress?

[sturdy bough]

maybe but f(1)=1??

[paper depot]

it feels like f(mn) = f(m) f(n) is only relevant for a handful of different pairs (m, n)

yes, f(1) is forced to be 1

[sturdy bough]

my teacher explained this that f(1)=1 but why

[paper depot]

f(1 * 1) = f(1) * f(1) => f(1) = f(1)^2

[sturdy bough]

hmmm

can anything be said about f(4)=f(2)^2??

[paper depot]

f(4) must be a perfect square

[sturdy bough]

i can't wrap my head around this, but my teacher said its to be done by permutation and combination

any idea??

[paper depot]

figure out what constraints we have first.

other than the case where either m or n is 1, what pairs (m,n) do we have where m, n and mn all belong to S?

[sturdy bough]

what does f(m) and f(n) exactly mean here so if i can put m=2 here which is f(2), but what can that be equal to?

[paper depot]

what does f(m) and f(n) exactly mean here
f is a function from S to S

f(m) is the value of f at the input m

[sturdy bough]

yes so for a function every value in the domain should have an image?

[paper depot]

wording...

but yes.

[sturdy bough]

any starting points you have??

[paper depot]

for what

answering this leading question that i asked you?

[sturdy bough]

uhhh didn't understand what you meant sorry

[paper depot]

other than the case where either m or n is 1, what pairs (m,n) do we have where m, n and mn all belong to S?

i asked you this question

it looks to me like you cannot answer it

[sturdy bough]

yes

i cannot

[paper depot]

just check all possible pairs one by one

there's only 36 of them

it will not be harder than making a multiplication table

[sturdy bough]

my teacher said there are close to 600 such functions

something there

[paper depot]

we have not yet gotten there

[sturdy bough]

oh

[paper depot]

okay let me just say it since i couldnt get you to do it

the only products we need to worry about are 2 * 2 = 4 and 2 * 3 = 6

what this means in practice is this: when we construct our function, once f(2) and f(3) are chosen, f(4) and f(6) will become forced.

f(5) and f(7) are free to be whatever they want.

[sturdy bough]

ok

hey can i continue this tommorpw

its getting late i am sorry

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[vocal sleet]

Please don't occupy multiple help channels.

[timber orchid]

Close the old one if you want

[gritty zenith]

Where’s it

Never mind

So how do I solve for C?

[timber orchid]

See if you can identify how far the incoming mass pushes the 1.3 kg mass into the spring, by considering the speed + acceleration of the 1.3 kg mass as it compresses the spring

[full arch]

that would be the maximum displacement of the spring from the equilibrium

essentially at the point of maximum potential

[gritty zenith]

I know what it meant but I don’t know how to solve for it, I solved all the other questions including d and I tried using various formulas that referenced each other but it didn’t work

[gritty zenith]

Huh?

[gritty zenith]

So how do I go about solving it…

[full arch]

conservation of energy

think about where all of the kinetic energy of the combined block is 'going' and then calculate x from that

[gritty zenith]

K1+U1 = K2+U2

?

[full arch]

that would be in general sure

[gritty zenith]

I don’t really understand

[full arch]

all of the kinetic energy is being used to press the spring into the wall, away from its equilibrium spot, that displacement is 'x' , you know how much energy will be in the spring at the maximum displacement. It would be the amount of kinetic energy injected into it.

[gritty zenith]

So should I use 1/2k*x^2?

[full arch]

yes

and you're solving for the maximum displacement hence the energy it would equal would be ?

[gritty zenith]

kinetic energy of both objects?

0.12J

[full arch]

yes

[full arch]

not sure haven't worked through the problem

I would choose to describe it as one object of a collective mass of 1.5kg after the collision tho

[gritty zenith]

yes I did that

To get 0.12J

[full arch]

cool cool

[gritty zenith]

How did you know to use conservation of energy?

[full arch]

ehhh

you have a system that takes a moving object and its smashing it into something that is responsible for 'storing' energy

I guess

for part d provided the spring obeys hooke's law and your derivative of the wave equation is correct you can obtain an expression for T

[gritty zenith]

I used 2pi * sqrt(k/m1+m2)

[gritty zenith]

I see

[full arch]

👍

[gritty zenith]

Well thank you I’ve been hear in help channels for ages no assistance

I appreciate it

[full arch]

wait

arent you supposed to have m/k ?

[gritty zenith]

Oops

Sorry I forgot to mention I used frequency

Then I did t=1/f

I don’t know why

[full arch]

kk

in that case remember its the reciprocal of 2pi you multiply by

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.close

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[burnt turret]

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[burnt turret]

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[timber orchid]

Try graphing them on a plane

[burnt turret]

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[timber orchid]

You can plot as is

[burnt turret]

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[cobalt gale]

This has to be integration by parts right?

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<@&286206848099549185>

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[wicked pawn]

i need help with a power series solution for a differential equation

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[regal shuttle]

hello

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[vast shale]

How to start, last time channel closed and they didn’t see the -1

[floral pike]

isn't this just geometric series?

[vast shale]

How would you start solving for convergence or div pls

[elfin wedge]

i don't think this thing converges

[hushed pewter]

Is the -1 inside or outside the sum?

[vast shale]

Inside

[paper depot]

no

$2^{1/n} - 1 = e^{\ln(2)/n} - 1 \sim \frac{\ln(2)}{n}$

[twin meteor]

Ann

[vast shale]

Pretty tricky compared to a few the other problems in text lol

[flat whale]

Ann gave you a hint to use limit comparison test

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[vast shale]

how would i find epsilon here

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[wraith venture]

the function is nice and simple. Just solve for delta

[sly sierra]

hint: $x^2 = (x^2 - 9) + 9$

[twin meteor]

Bungo

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[vast shale]

tysm

.close

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[burnt galleon]

Noting that $sin (t\pi) = t\pi \prod_{n \geq 1} (1 - \frac{t^2}{n^2})$ why does $f(t) = \prod_{n \geq 2} (1 - \frac{t^2}{n^2}) = \frac{sin(t\pi)}{t\pi(1-t^2)}$

[twin meteor]

LeftySam

[burnt galleon]

.close

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[pliant plume]

Need help with question 5

[vast shale]

i need help with my own math equation

[pliant plume]

ask another secxtion cuh

[thin vale]

this channel is occupied, read #❓how-to-get-help and open your own

[thin vale]

post your question

[pliant plume]

5 e

so what i did was that i got all the possibilites for even numbers using 4!*2

which gave me 48

then i took away all the possibilites when it began with 4 and 5

which was 2^2*3!

[steel radish]

yeah it starts with either 1 2 3

[pliant plume]

then took that awway from 48 which left me with 24

but thats wrong and i wanna know where my understanding and working out is wrong

[steel radish]

why this

oh you said even

[pliant plume]

all the numbers which end in even

so either 2 or 4

[steel radish]

since you say it's even, you might not have 4 anymore

[pliant plume]

yes but all the possibilites so it can end in both

[steel radish]

48 cases, 24 end with 2 and 24 end with 4

[pliant plume]

4! for arrranging the rest 4 nunbers in different ways then 2 possibilites for final answer

yep

so in total 48 end in even

then i need to take away all possibilites it is a number greater than 40,000

[steel radish]

now, in case it ends with 2, you have to remove "4" from the start which could've been 1 3 4 or 5

[pliant plume]

whihc is any number beginin g with 4 and 5

yes

[steel radish]

so you remove 6 possibilities here

you also remove the 5 so another 6 which is in total 12 removed ones if it ends with 2

[pliant plume]

yep

[steel radish]

if it ends with 4, you only remove the 5 out of 1 2 3 5 which is just 6 so you remove 18 in total for all even numbers

[pliant plume]

ah yes

i see

makes sense

i would need to find 2 cases to take away from 48

then i would end in 30 which is correct

[steel radish]

yes

the other way would be if you started with the first number and said it's 1 2 or 3 then looked at the last number which is either 4 or possibly 2 and you'd still have different cases to consider

[pliant plume]

emmhmm thx for helping makes sense now ahem

[steel radish]

np

[pliant plume]

.close

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[kind harness]

"In the plane the locus of points with the same distance from two given distinct points is:A) two perpendicular lines B) an ellipse C)an oval D) one or two lines,depending on the position of the two points E) a line" need some help with this question

[kind harness]

i think it could be option D but im not sure

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[main spade]

Hint. Let (x_1, y_1) and (x_2, y_2) be two points on some curve and examine (x - x_0)^2 + (y - y_0)^2 = (x - x_1)^2 + (y - y_2)^2.

[kind harness]

would i get two perpendicular lines?

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[hearty storm]

Can someone tell me where I’ve gone wrong finding the eigenvalue?

[hearty storm]

Answer should be 4 4 4

But I got 4 4 5

Have I multiples it all by (5-lambda) when it shouldn’t all be

I think that’s why

[vast shale]

ur handwriting so bad

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[vast shale]

how can i find out the equation of this polynomial graph

[vast shale]

how can i find out the equation of this polynomial graph

anyone?

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[twin meteor]

ExperiencedPilot

$\displaystyle\sum\limits_{r=2}^{n} \dfrac{4r+2}{r\left(r+2\right)(r+1\right)}$
```Compilation error:```! Missing } inserted.
<inserted text> 
                }
l.57 ...\dfrac{4r+2}{r\left(r+2\right)(r+1\right)}
                                                  $
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```

ExperiencedPilot
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[left crest]

Is the given question correct

[vocal sleet]

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[cloud quiver]

not sure what value they're looking for here. I tried pulling out the constant 9/20 but that wasn't it

[finite wraith]

it looks like you should be making the substitution with w and substituting the values for the integration

[karmic imp]

If you know the concept of u sub, that's what it's applying. The question is using w instead because it used u already

[finite wraith]

then in the second line you are flipping the values of integration. this can be done by pulling out a negative sign

[cloud quiver]

i remember the second line

flipping the limits

but the first line is where i'm confused

[karmic imp]

Do you know the concept of u sub?

[cloud quiver]

yes

1/11-9u

so 1/w?

[karmic imp]

Almost there, you have to do du

Because you need to change that du to dw

So if you have w = 11-9u, you need to take the derivative, right?

[cloud quiver]

ok

-9

[karmic imp]

What's the proper equation when you take the derivative?

[cloud quiver]

0 - 9(1)

[karmic imp]

No

You have this, but magically wrote -9 with zero variables

[cloud quiver]

-9du

[karmic imp]

What happened to the w?

[cloud quiver]

dw = -9du

[karmic imp]

If you have y = 3x, the derivative would be dy/dx = 3

[karmic imp]

Yes

[cloud quiver]

i need to practice more u sub

[karmic imp]

Now you want to replace that du in terms of dw

[cloud quiver]

i forget the steps here often

du = dw/-9

[karmic imp]

Now plug that in

[cloud quiver]

[-1,1]?

[karmic imp]

Also do you see how it's du = -1/9 dw?

[karmic imp]

No

You need to look back at u sub

[cloud quiver]

yes

they're equivalent

[karmic imp]

You are replacing du, with an expression in terms of dw

You have that. If w = 11 - 9u and dw = -9 du => -1/9 dw = du, you can replace du with that expression

[cloud quiver]

so i would place -1/9 dw there?

shouldn't it be a constant there?

[karmic imp]

Well, that question is skipping all the in between steps but yes, the constant goes in that blank

[cloud quiver]

ok

let's review the steps here again

regarding u sub

so first find the derivative of 11-9u

or 1/11-9u?

[karmic imp]

Let's use different variables, like this $\int_{-1}^{1} \left(11 - 9x\right)^{-1} dx$

[twin meteor]

dldh06

[cloud quiver]

ok

[karmic imp]

If you had that expression instead, could you do u sub?

[cloud quiver]

yes

u = 11-9x

[karmic imp]

Continue on

[cloud quiver]

ok

[karmic imp]

And try that yourself

[cloud quiver]

take the derivative (0-9)^-1 dx

-1/9 dx

i've forgotten the next step

is it du = -1/9dx

[karmic imp]

Yes

What should you do to write $\int_{-1}^{1} \left(11 - 9x\right)^{-1} dx$ in terms of u?

[cloud quiver]

dx = -9du

[twin meteor]

dldh06

[karmic imp]

Wait, what?

If u = 11-9x, how did you get du = -1/9dx?

[cloud quiver]

let me check again

dx = 1/9du

would i just flip that value here?

-9

+9 rather

[karmic imp]

If you flip the bounds, you just flip the sign

[cloud quiver]

to flip the limits

[karmic imp]

Why would you flip the fraction?

[cloud quiver]

ok

just the sign

in our example above is dx = 1/9du?

[karmic imp]

No

u = 11-9x

What's the derivative?

[cloud quiver]

-9dx

forgot i'm not considering the exponent in u sub

[karmic imp]

Should be du = -9 dx

[cloud quiver]

ok

du = -9 dx

[karmic imp]

Then you set that equal to dx so you can replace the dx in terms of u

[cloud quiver]

dx = du/-9

ok

does it want me to set up the subtraction first?

as in 1/20 - 1/2

[karmic imp]

It wants you to integrate

[cloud quiver]

do i sub in 20 and 2 before integrating?

after

[karmic imp]

When it has [ ], that means you write the integrated function

[cloud quiver]

so basically i take the anti-derivative of 1/20 and 1/2?

[karmic imp]

No

You are overcomplicating it

This is what you have

Integrate that expression

Plug it into the [ ]

[cloud quiver]

1/20 - 1/2

[karmic imp]

No

Why are you plugging in 20 and 2?

That's not integrating

[cloud quiver]

take the antiderivative of 1/w?

[karmic imp]

Yes

[finite wraith]

yeah then you plug in

[cloud quiver]

1/2w?

[karmic imp]

No

You need to look back at your integral/derivatives

[cloud quiver]

add 1 to the exponent and bring that number down into the denominator?

[karmic imp]

No

Not for that one

[cloud quiver]

how does this one differ?

[karmic imp]

As mentioned

need to look back at your integral/derivatives

[cloud quiver]

i don't remember a special case

[cloud quiver]

natural log

[karmic imp]

Yes

[cloud quiver]

1/x

yes

because the variable was different it didn't trigger my memory

not good

so i end up with ln20 - ln2

[karmic imp]

That's for the final answer

But you need the blank before it, the stuff in between [ ]

[cloud quiver]

ok

i can't see the intermediate step

[karmic imp]

Just integrate 1/w and plug that in

It's literally doing step by step process

[cloud quiver]

that would be ln20 - ln2

[karmic imp]

No

[cloud quiver]

o wait

it just wants ln

[karmic imp]

Not quite

[cloud quiver]

given the notation

[karmic imp]

You need the variable

[cloud quiver]

lnw

[karmic imp]

Almost

Look back at the table I sent

What's the integral of 1/x?

[cloud quiver]

ln

• C?

[karmic imp]

First off, stop leaving off the variable

Second, look at the table

Do you not see the absolute value signs?

[cloud quiver]

yes now i see it

ln abs(u) + C

[karmic imp]

So then what do you need to input into your question?

[cloud quiver]

ln abs(w) + C

not sure what my constant is there

as i already have 1/9 on the outside

[karmic imp]

You don't need the + C because it's a definite integral

[cloud quiver]

right

that's only for indefinite

forgot

just ln abs(w)

in that case

[karmic imp]

Yes

[cloud quiver]

for the final answer i should simplify

ln20 - ln2

[karmic imp]

Yes

[cloud quiver]

i've forgotten my rules of logs... need to go look that up

[karmic imp]

And you need to look into u sub and integrating as that was not a difficult question

[cloud quiver]

true

[karmic imp]

It was asking for a step by step process

[cloud quiver]

i learned u sub a few sections back but i didn't retain the information

more problem sets?

[karmic imp]

That's a good way to practice

[cloud quiver]

honestly my biggest issue is lacking the intuition to see the logic behind the steps

i can remember rules but when applying them often times i don't follow the logic

how can i improve that skill set besides doing problems?

[karmic imp]

More practice

[cloud quiver]

ok

thanks for you help. i appreciate it.

.close

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[kind harness]

" In april of a certain year there were 5 sundays and april 1st was not a sunday. On which day of the week was April 5th?" I think april 5th would be Wednesday but im not sure

[vocal sleet]

Please don't occupy multiple help channels.

[sturdy bough]

Thanks for this

[sturdy bough]

Correct

April 2nd has to be Sunday for 5 Sundays in April

[kind harness]

thank you!

.close

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[real raptor]

do the variables have to line up? or is f(8+h) what i fill in for f(x)

[fickle crypt]

8+h

[real raptor]

so f(8+h) = (8+h)^2 + 4(8+h) - 25?

[fickle crypt]

yeah

[real raptor]

okay thanks

the answer should be h+20?

-(c+h)^3 = -c^3+(-h^3) ?

[fluid obsidian]

Of what?

[fluid obsidian]

Nope

[real raptor]

above

[fluid obsidian]

Don't think so

[real raptor]

uhhh

of the whole equation

it should be .. .

[real raptor]

^

[fluid obsidian]

Having trouble

[real raptor]

huh

[fluid obsidian]

Sorry but I'm still checking

[real raptor]

im not worried abt first problem anymore

[fluid obsidian]

Okay that's great

[real raptor]

having brain fart w this one tho lmfao

[fluid obsidian]

The expansion will be -(c³+3hc²+3h²c+h³)

[twin meteor]

fäf

[real raptor]

no

[fluid obsidian]

Well you can use the formula for binomial expansion for such problems

[real raptor]

= 3c^2 + 3hc + h^2 ?

[fluid obsidian]

I doubt

Where is the h

Okay nvm

Cool

[real raptor]

?

huh?

h cancels

one h cancels

[fluid obsidian]

Yes

[real raptor]

ok

[fluid obsidian]

Don't mind my breakdowns

[real raptor]

lol ur fine

[vocal sleet]

@real raptor Has your question been resolved?

[vocal sleet]

@real raptor Has your question been resolved?

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[prisma stag]

Help me I don’t know how to do the limit

[wicked edge]

idk what you mean by "do the limit" but as x heads towards 2, the expression becomes undefined
other than that, idk anything else

[prisma stag]

Can I not do L’Hopital?

[flat whale]

l'hopital requires indeterminate form

[prisma stag]

What is indeterminate form?

[flat whale]

very nice table

[robust oracle]

thank you

but

when you take a limit and you get any of the forms of the left side of the table

those are indeterminate forms

this means you would have to alter the limit or do something else to try to get a valid form

think of indeterminate forms as like an inconclusive answer

[prisma stag]

Thanks that make more sense

[robust oracle]

Since with this limit you get 9/0, it is not an indeterminate form meaning this limit does not exist

[vocal sleet]

@prisma stag Has your question been resolved?

[vocal sleet]

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[ivory anvil]

I got:
length = 32/cosx + 42/sinx

f(x) = 32secx +42cscx

f'(x)= 32tanxsecx-42cotxcscx

f'(x) = 32 (sinx/cosx)(1/cosx)-42(cosx/sinx)(1/sinx)

not sure how to find critical points

[opaque shard]

set f'(x) = 0 to find the minumum?

lol .... mimumum

[ivory anvil]

lol

I'm having trouble solving for f'(x)=0

32/cosx(sinx/cosx)=42/sinx(cosx/sinx)

[opaque shard]

try timesing by cos and sin and i think it wil lresolve to a tan^3 = k

[ivory anvil]

multiply everything by cosxsinx?

[opaque shard]

yes... i think so

[ivory anvil]

32sinx/cosx^2(sinxcosx) = 42cosx/sinx^2(sinxcosx)

32sinx^2/cosx = 42cos^2x/sinx

[opaque shard]

So your equation is, $0 = 32\frac{sin(x)}{cos^2(x)} - 42\frac{cos(x)}{sin^2(x)}$

Then multiplying by $cos^2(x)$, $ 0 = 32sin(x)- 42\frac{cos^3(x)}{sin^2(x)}$

[twin meteor]

totalminer

totalminer

[opaque shard]

Then multiplying by $sin^2(x)$, $ 0 = 32sin^3(x)- 42cos^3(x)$

[twin meteor]

totalminer

[opaque shard]

Then,
$$ 32sin^3(x) = 42cos^3(x) $$
$$ \frac{42}{32} = tan^3(x) $$
Is this helpful/correct...?

[ivory anvil]

hmmm

[twin meteor]

totalminer

[ivory anvil]

wouldn't that work out to 42/32 = tan^3(x)?

[opaque shard]

Yes, I changed it now. I am not sure if its right answer, it is what I would do. Hope this helps

[ivory anvil]

so then x = 42/32^(1/3)

sorry

tan x = 42/32^(1/3)

[opaque shard]

I hope so...

[ivory anvil]

trig identities kill me

[opaque shard]

If you think our derivation is also correct, then I doubt the solution is not.

[ivory anvil]

thank you for your help!

[opaque shard]

trig derivatives kill me...

np, happy to

[ivory anvil]

the basic of the trig derivative is okayyyy for me, just memorize the 6 core ones

but applying it?

nty

[opaque shard]

yeah, I need to memorize them. Once you're happy just do .close, but I think you know that already... Have a good day

[ivory anvil]

likewise!

.close

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[hearty storm]

How do I test for convergence? I don’t even know where to start

[vocal sleet]

@hearty storm Has your question been resolved?

[maiden iron]

the integrand isnt defined on 0

[vast shale]

so?

[robust oracle]

I think it turns into an improper integral then

[vast shale]

ah ok

[vocal sleet]

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[vast shale]

How can I prove this statement?

[wraith venture]

Look at the dimension of V

[vast shale]

We didn't learn dimensions yet. I thought maybe its something with the zero space

that if I know that V is also a linear subspace then there is v in V such that v != 0

I'm not sure if it's true tho...

[wraith venture]

Honestly I can't not do a proof that's not basically dimension based

Simply done by not mentioning the word dimension

Based on whether there is a v such that V = span(v) basically

[vast shale]

since span({v}) is a subspace of V

span({v}) = {0} or V

if v!=0 then span({v}) = V

[wraith venture]

Yeah I like this more. More detached from dimension

[vast shale]

Can you explain more why there is v != 0 tho? I can't wrap my mind about it :/

[vast shale]

v could be 0

but there is a v that is not 0

[wraith venture]

you can handle that case separately. It is possible that v must be 0

[vast shale]

Oh I see. so I just need to prove that v != 0 exists

[wraith venture]

You don't have to. Because you can't

[vast shale]

yeah and if it doesnt, it means V = {0} and in that case span({0}) = {0} = V

[wraith venture]

Either V = {0} = span{0}
Or there is a nonzero v in V

[vast shale]

Hmmm. V can be {0} right? unless I assume that V != {0}

[wraith venture]

Yes

[vast shale]

So if V=0 it's straight forward and if not I have v != 0 in V and therefore span(v)=V or span(v)=0

[hearty storm]

Yes I know. I’m not finding the integrand but rather just showing convergence

Sorry for using your channel bro

[vast shale]

Hahah it's ok. The more the merrier

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

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[hearty storm]

.reopen

[hearty storm]

.

[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[vast shale]

express the area in terms of the areas of the square and the circle

[devout flower]

Mate I'm just fucking confused

I don't know how to do this

Or what to do

[devout flower]

If the length is 10 and it's a square ig the area is 100

@vast shale

[vast shale]

ok

what is the area of the circle

[devout flower]

No clue

[vast shale]

what is the formula for a circle

[devout flower]

Circumference wise πr²

But in this case I'm looking for the shaded region which is what I'm confused on

[vast shale]

so what is the shaded area equal to in terms of the areas of the circle and the square?

add/subtract the areaas

[devout flower]

Ibut how do I find the area for the circle

Ohh nvm I think I get wym

[vast shale]

what is the radius?

[devout flower]

Is the answer 215.2 (rounded to 1 s.f)

[devout flower]

314.2

[vast shale]

the radius is 5

[devout flower]

Huhhhhhh

[vast shale]

diameter is 10

[devout flower]

This is why I'm bottom set for math

[vast shale]

so radius is 5

[devout flower]

I just realised

I'm fucking stupid

Wait

I did that

Ohhh

No

[devout flower]

I meant the circumference is 314.2

[vast shale]

and shaded area = square - circle

[devout flower]

Ik and I got 214.2

Was it correct?

[vast shale]

i got 21.46, u shouldnt get more than 100 tho

[vocal sleet]

@devout flower Has your question been resolved?

[vocal sleet]

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[wet cloak]

Trying to get a grasp of log_2 for cs purposes but I dont really see how it has anything to do with doubling a number.
Am I stupid or something

[wet cloak]

"How often you need to double 1 to get N"

What has that to do with 2^lgN = N

[vast shale]

by definition log2 is "how many times you need to double 1 to get N"

[wet cloak]

Please give me an example

[vast shale]

lg8 = 3

[wet cloak]

Yes

[vast shale]

means that if you double 3 times its 8

2^3 = 8

[wet cloak]

but thats exponential

something doesnt click in my brain.
lg_2(8) = 3 yeah sure but what has to do with 2^3 = 8

[vast shale]

2^3 means doubling 3 times

[tulip nebula]

Any log can be converted to exponential

[wet cloak]

Sure but this part

"How often you need to double 1 to get N"

Thats just exponentials

Right?

2^lg(N) = N

I cant connect this part to that definition

is it cause 2^lg_2 cancel out?

[vast shale]

yes it is just exponentials, but in oposite direction

[wet cloak]

when you say opposite direction

wdym?

on a graph?

[vast shale]

2 ^ lg(N) = N

exp(ln(x)) = x

as a function

[wet cloak]

Im just gonna ponder over this for abit. Something doesnt click

But appreciate the help

.close

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[weak oasis]

can someone help me with this question, where did the 1/3 come from??

[weak oasis]

im stuck after the evalue the integral part

[maiden iron]

reverse power rule

[weak oasis]

so anti derivative?

[maiden iron]

yes

[weak oasis]

when i did it, i got 11/3

[maiden iron]

let u = 11x-7

[soft walrus]

$u=11x-7$ hence $\frac{u^3}{3}=\frac{(11x-7)^3}{3}$ because to substitute everything

[twin meteor]

XxMrFancyu2xX

[maiden iron]

$\int 11 u² \frac{du}{11}$

[twin meteor]

Herels

[maiden iron]

since du = 11 dx

[weak oasis]

what is this supposed to be?

[soft walrus]

u-substitution

[maiden iron]

your integral after u substitution

[weak oasis]

i have a question then, so im able to understand how i get to this

but i dont understand where htey get this

<@&286206848099549185>

[timber orchid]

Same u-sub

u = 11x - 7

The derivative of the RHS = integrand

[weak oasis]

thank you

.close

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[edgy token]

hey i don’t know what to do here. i’m not sure how to get the value of any of the variables and i don’t really know where to start. can someone help me?

[ornate ember]

I would set up the similar triangle ratios and see if there's anything provided that can isolate the values for you.

For example, I'll do one side for you.

$\frac{DB}{DE} = \frac{AB}{AC}$

[twin meteor]

MellowDramaLlama

[ornate ember]

$\frac{5y}{3x-6} = \frac{5y + 10z}{xz}$

[twin meteor]

MellowDramaLlama

[edgy token]

so i would find a ratio that still has the unknown y and z?

[ornate ember]

so that similar triangle ratio is no good/messy

so I would try the other sides and see if it's any easier to solve

[edgy token]

so i should do something like the ratio of be to de and the ratio of bc to ac?

[ornate ember]

seems like a good idea!

[edgy token]

ok thanks

wait but how does this give me the values of the variables

[ornate ember]

so the idea is that we can isolate/eliminate variables

also, this was the first approach that I thought of given the information provided

also, I think you'll get the same issue with those sides

[edgy token]

the last problems i just used how the midsection is half of the bottom line and got the values there

[ornate ember]

maybe try DB/AB = BE/BC

[ornate ember]

oh maybe try that and see where it takes you

[edgy token]

i end up with z= 5x-12

and i end up not getting the values of either variable

when i do 5y / (10z+5z)= (2y+2) / (2y+3z+7)
it simplifies down to
10z=2/3z+7
should i multiply the 3z+7 out to 30z^2 + 70z = 2 or did I do something wrong?

<@&286206848099549185>

[cursive kelp]

yes.

[edgy token]

the worksheet was midsection problems and finding the value of variables

but this problem i can’t find a way to get the values of any variables

usually xz is something that only has the same variable as the midsection

[floral seal]

any more info?

like parallel

or something

[edgy token]

that’s the entire problem

i’m probably going to ask my teacher tomorrow because i don’t see any way to get anywhere

.close

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[quartz arch]

how was this simplification done?

[quartz arch]

more specifically the random 0

[sly sierra]

which part are you unsure about?

[quartz arch]

the -0-(e^3-1)

[sly sierra]

$\left. xe^x\right|_0^3 = 3e^3 - 0e^0 = 3e^3 - 0 = 3e^3$

[twin meteor]

Bungo

[sly sierra]

they're just being explicit that the first term evaluated at 0 is 0

[quartz arch]

ok i see how 3e^3-0 was done

what about the (e^3-1)

is e^0 = 1

[sly sierra]

$\left. e^x \right|_0^3 = e^3 - e^0$, which is...?

[twin meteor]

Bungo

[sly sierra]

yep, e^0 = 1

[quartz arch]

oh i see

didnt know e^0 is 1

makes sense now thanks

[sly sierra]

anything (nonzero) to the 0'th power is 1

[quartz arch]

just came to my head

havnt studied in a while

rusty

[sly sierra]

nw

[quartz arch]

cheers

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[rancid mist]

Hello I need to show R\Rad(0) or R\sqrt(0) is a reduced Ring

[rancid mist]

any ideas how I can start with this, I know this is equivalent to R\Rad(0) containing no elements besides 0

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[limber rock]

I am having trouble with this question: consider f(x) = ax^3 + x + 1, where a is real. I need to find all possible values for a such that on the interval [-1,1], f(x) has a global maximum of 4/3 and a global minimum of 2/3

[limber rock]

i can only figure out 1 value for a

could you explain why

so why does the question ask for all the possible values?

is that common?

for questions to aks for all when there's only 1

ok

[ornate ember]

I would guess that these kind of problems there might be more than one correct answer

it just so happens that this one only has one

[limber rock]

strange

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[full drift]

how to find the final velocity

[full drift]

what formula

[dim quail]

depends on the question

$v=v_0 +at$

[twin meteor]

bettim

[dim quail]

$v^2-v_0^2 = 2as$

[twin meteor]

bettim

[full drift]

so
V = 10 + (9.8) (0.5887)
?

[dim quail]

$v_x$ is contsnt

[twin meteor]

bettim

[dim quail]

what

how did you find t?

[full drift]

i did this

[full drift]

10 is V0
9.8 is acceleration and 0.5887 is the time i solved

[dim quail]

you have to find the vertical component alone

[full drift]

so the answer is 15.77?

[dim quail]

height is given

v_0 is 0

a is 9.8

calculate the time that way

[full drift]

how do i find time?

[dim quail]

$v=u+at$

[twin meteor]

bettim

[full drift]

what "u" again?

[dim quail]

$v_0$

[twin meteor]

bettim

[full drift]

wait I don't get it how do i solve it

[dim quail]

wait not that

[full drift]

lets look for time first 😭 i don't get it

time to reach the bottom

[dim quail]

$T = \sqrt{\frac{2h}{g}}$

[twin meteor]

bettim

[full drift]

so 1.42s?

[dim quail]

wait

,calc 3/9.8

[twin meteor]

Result:

0.30612244897959

[dim quail]

,calc sqrt(0.3061)

[twin meteor]

Result:

0.55326304774492

[dim quail]

im gettin this

what did you do

[full drift]

oh so it's right the first, next how do i find the final velocity😭

[full drift]

oh i thought height was 10 when 10 was the initial velocity lol

[dim quail]

lol np

[full drift]

now for final velocity i don't get itt

Vf = 10 + (9.8) (0.5533)?

[dim quail]

$v_x $ is constant

i think they are asking final vel of $v_y$

[twin meteor]

bettim

[dim quail]

in that case

$v_y = u_y + a_yt$

[twin meteor]

bettim

[dim quail]

$u_y =0, a_y = 9.8$

[twin meteor]

bettim

[dim quail]

t = .5533

$v_y = 9.8 \times 0.5533$

[twin meteor]

bettim

[dim quail]

,calc 9.8 * .5533

[twin meteor]

Result:

5.42234

[dim quail]

thats it ig

[full drift]

ohhh ok tnx

[dim quail]

and for range

$R = v_0 \times \sqrt{\frac{2h}{g}}$

[twin meteor]

bettim

[full drift]

is it negative?

cause it's going downwards

[full drift]

-5.42

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[hidden kelp]

Can someone help me through this problem?

[hidden kelp]

Idk how to go from here

[dim quail]

$\tan -\frac{4\pi}{3}$

[twin meteor]

bettim

[dim quail]

which is same as

$- \tan \pi - \frac{\pi}{3}$

which is

$-\tan \frac{\pi}{3}$

[twin meteor]

bettim

[hidden kelp]

How did you get rid of the 4?

[dim quail]

4pi/3 = pi + pi/3

[hidden kelp]

I am still a little confused]

[dim quail]

is this clear?

[hidden kelp]

Not really

[dim quail]

$\frac{4\pi}{3} = \frac{3\pi + \pi}{3}$

[twin meteor]

bettim

[dim quail]

$=\frac{3\pi}{3} + \frac{\pi}{3}$

[twin meteor]

bettim

[hidden kelp]

Oh ok

[dim quail]

$=\pi + \frac{\pi}{3}$

[twin meteor]

bettim

[dim quail]

now?

so

[hidden kelp]

So why would you do that?

[dim quail]

$\tan (\pi + \frac{\pi}{3})$

[twin meteor]

bettim

[dim quail]

bcz $\tan(\pi +\theta) = \tan \theta$

[twin meteor]

bettim

[hidden kelp]

Ok now I am super confused

[dim quail]

what is not clear?

[hidden kelp]

I do not get these steps

Like why are we doing them

[dim quail]

becuase we know this

this is a law or rule

[hidden kelp]

Oh

Can you teach me the way with the unit circle?

[dim quail]

i dont know to teach with it

well by angles

lets say theta is some angle and pi 180

so when we do tan pi + theta

it is just

tan 180 + theta

it will be in the third quadrant in which tan is +ve

so

tan pi + theta = tan theta

[hidden kelp]

I think I am going to look up a video

That might help more

I appreciate the help though

I just cant visualize it 😭

[dim quail]

sorry that i couldnt make you clear

just remeber that

$\tan \pi + \theta = \tan \theta$

[twin meteor]

bettim

[hidden kelp]

Okay thank you!

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[hidden kelp]

Can someone help me with this last problem I have?

[bold wharf]

use trig

[dim quail]

use tan

[bold wharf]

tan 30 = 72/x

1/sqrt3 = 72 /x

x = 72sqrt3

[hidden kelp]

I got 41 inches

Is tat correct?

[dim quail]

i dont think so

[bold wharf]

i thnk this

[dim quail]

,calc 72*1.73

[twin meteor]

Result:

124.56

[dim quail]

it should be 125

[bold wharf]

if you use sqrt3 value then you get final answer

can you help me bettin?

[hidden kelp]

Why do you multiply it by 1.73?

[dim quail]

$\sqrt{3} \approx 1.73$

[twin meteor]

bettim

[hidden kelp]

Where does the sqrt of 3 come from 😭

Is that from the 30 60 90

Triangle

[dim quail]

tan 30 =1/sqrt3

bruh basic trig

[hidden kelp]

I dont know basic trig

[dim quail]

tan 30

u know that right

[hidden kelp]

Yeah

[dim quail]

thats it

nothing much is there in the question

[hidden kelp]

Can you write all the steps out for me rq?

Just so I can study it

[dim quail]

$\tan \theta = \frac{\text{opposite}}{\text{adjacent}}\
\theta = 30^o\
\tan \theta = \tan 30\
\tan 30 = \frac{1}{\sqrt{3}}\
\frac{1}{\sqrt{3}} = \frac{\text{opposite}}{\text{adjacent}}\
\frac{1}{\sqrt{3}} = \frac{72}{x}\
x = 72 \sqrt{3}\
x = 72 \times 1.73\
x= 124.56 \
x \approx 125 in.$

[hidden kelp]

Thanks a lot man

[twin meteor]

bettim

[dim quail]

sorry for shitty formatting