help-39

[fast heart]

t = 1/(viSinThetai + 1/2(-g)t)

[plush bramble]

where does the 1 come from?

[fast heart]

I mean t = (viSinThetai + 1/2(-g)t)

right?

[plush bramble]

what equation do you have before this one

[fast heart]

is it not this one?

[plush bramble]

yes

follow this

before moving on

[fast heart]

so I followed at+bt^2 into a factored version

and it got me this?
t(viSinThetai + 1/2(-g)t) or no?

[plush bramble]

that's half the equation. what is that expression equal to

[fast heart]

oh 0 = t(viSinThetai + 1/2(-g)t)

right?

[plush bramble]

yes

[fast heart]

then divide by t? meaning 0 = t(viSinThetai + 1/2(-g)t)/(t) right?

[plush bramble]

yes?

[fast heart]

and then? I'm sorry but can you walk through this I'm so rusty

[plush bramble]

do you know how to divide t/t ?

[fast heart]

cancels out?

[plush bramble]

$\frac{at}{t} = a$

yes

[jolly parrot]

riemann

[fast heart]

and then it would turn out like this 0 = (viSinThetai + 1/2(-g)t)

and then I isolate t again?

[plush bramble]

yes

[fast heart]

would I have to isolate by multiplying 1/t to cancel out the t and go to the otherside?

[pearl pond]

@fast heart Has your question been resolved?

[fast heart]

?

[plush bramble]

you're just solving for $t$? $at +b = 0$

[jolly parrot]

riemann

[plush bramble]

$t =$?

[jolly parrot]

riemann

[pearl pond]

@fast heart Has your question been resolved?

[fast heart]

How would I isolate t in this scenario? I think this is what I'm bad at. I can isolate very simple equations but not like this where it is a mess

[pearl pond]

@fast heart Has your question been resolved?

[pearl pond]

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[midnight haven]

I tried checking if its a geometric sequence

[midnight haven]

Can someone perhaps help me out?

Im new to the topic

Or series?

[forest dew]

what about it

[smoky widget]

$\frac{a_{n+1}}{a_n}$

[jolly parrot]

ngX

[smoky widget]

if this is a constant then it is a geometric sequence

[forest dew]

i dont even understand the question

[smoky widget]

you could use the 2 values you calculated in your work

its easy to see you will get 3 which is constant

[granite sundial]

then y u replying bruh

[forest dew]

I'm asking what they need help with

[midnight haven]

I just dont really know what to do

[forest dew]

what is that picture you sent

[midnight haven]

The question asks if its geometric

[forest dew]

is what geometic

[midnight haven]

I believe its called sequence in english

[forest dew]

an?

oh I just read your caption

gotcha

so give me an example of a basic geometric sequence

[midnight haven]

This is the sequence i think and i have to say if its geometric appearently

Im not sure if what i did was correct, i dont even know what i was doing really :/

[forest dew]

wait you basically solved it

so you get 11*3^n

which is a geometic sequence

[midnight haven]

But how do i know that? What makes it a geometric sequence?

[forest dew]

look up the defintion of a geometic sequence

this is something that your teacher should have mentioned

[midnight haven]

May i ask how this is related to this? I keep seeing this but dont know what it means really

[forest dew]

this means that the ratio of preceding terms is a constant

so like 3^n+1 / 3^n = 3

meaning it is a geometic series

[midnight haven]

But we have a series or sequence ?

Thats whats confusing me

We dont have this fraction thing here do we ?

[forest dew]

uh well it doesnt matter here

you can have either

[forest dew]

thats only for a defintion of a geometic series/sequence

you could use it in your explanation i guess

but it is pretty clear that 3^n * some constant is geometic

[midnight haven]

Is there some type of guide on how to approach these questions ? Like what do i have to manipulate the equation to look like?

[forest dew]

for geometic series

you want to get to something like constant + constant*something^n

you dont want to have n anywhere else

you want the sequence to grow by only something^n

no 3n or 1/n etc

[midnight haven]

What about this for example

[forest dew]

so for that you have a sum of two geometic sequences

what is it asking you

you cant make that into one sequence

if it was 3^n times 2^n then you could

[midnight haven]

It asks if it defines a geometric sequence or not

[forest dew]

ah okay

so you can just compare terms with eachother

a geometic series has a common ratio

to get from any term n to the next term n+1

multiply the term a(n) by the ratio

and this ratio is whatever is under ^n

this means that for any n, a(n+1)/a(n) should be the same

in that photo they are showing that is not the case

therefore not geometic

does that make sense

[midnight haven]

There is also this

[midnight haven]

I thought in the example at the very beginning the 11 was the ratio term thing that you multiply with ?

Not the 3 below the ^n

[forest dew]

not quite

i think watching a video on what geometic series are would be helpful

what are you learning in the class

[midnight haven]

I have exam in a couple hours

[forest dew]

use the same test with the fraction

[midnight haven]

But how do i determine if for example from the picture i just sent if it geometric or not ? I didnt quite understand that part yet.

Like, whats the first step?

Create a fraction?

[forest dew]

yes

find a1, a2, and a3

compare a2/a1 and a3/a2

[midnight haven]

Do i have to turn the 1 inside the brackets into n/n first for same numerator ?

[forest dew]

not sure what you mean

[midnight haven]

This is ok?

I tried to do what you said but now im a little lost, should i input numbers already ?

[forest dew]

yes

i mean look

if this is how they want you to explain it every time theres no way around it

you might be able to just use words if you are allowed to

for it to be a geometic series, the value under ^n needs to be constant

but (1+ 1/n) is not constant

therefore not geometic

[midnight haven]

So basically we just put the equation we get on top of each other and for the upper one we input n+1 and compare to the lower one?

[forest dew]

yes

remember you are trying to find if the sequence has a common ratio

where a(n+1) = ratio * a(n)

if that ratio exists and is constant for all n then it is geometic

[midnight haven]

Thanks a lot ! I will try to read about it online a bit more

Thanks for the help

👍🏻🙏🏻

[forest dew]

happy to help

[midnight haven]

I was wondering if there is a name for what im doing here ?

Because honestly when i look up online i only see videos that describe it different, like they have just numbers and look at how they change

Nothing with these equations like i have:/

[forest dew]

yeah idk why they are doing it that way

my guess is "finding common ratio of a geometric sequence"

[midnight haven]

Is there a better way ?

Like to solve these questions

[forest dew]

i cant think of one without just using words and logic

its not too bad to write it out though using fractions

[midnight haven]

But could we even have done the fracture thing here ?

Because i just manipulated the equation thing but didnt bring it into the fracture form where you divide it

[forest dew]

you could

but thats so much more work

your way to simplify the expression is better

but you cant always do that

[midnight haven]

Oh okay i see

Thanks a lot again

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[vast dune]

partial fraction decomposition

[hasty galleon]

Do you know what form the answer should be in?

[vast dune]

A/x+1 + B/a-x

[hasty galleon]

Yep good so far just should add brackets

[hasty galleon]

So then A(a-x) + B(x+1) should equal 1

[vast dune]

ya

[hasty galleon]

So expand those brackets

[vast dune]

(i put C as A to not get confused)

this was my system of equations i got

[hasty galleon]

If we go one step at a time

[vast dune]

i did on my notebook

C=B

[hasty galleon]

Okay yeah that looks good

[vast dune]

this is the part where i felt like my answer is wrong

and also on all the calculators online they arent giving me the same answer

[hasty galleon]

Personally I'd have left it in the parenthesis form here, since the (1+a) will likely be a constant in anything you do with this later

Is this a problem from a textbook or homework or?

[vast dune]

no clue im pretty sure its from the textbook

[hasty galleon]

I'm just wondering if there's a better defined endpoint to the question, like are you just meant to decompose it or integrate or smthn else?

[vast dune]

im in precalc

its just decomposing

[vast dune]

ye its from the textbook i found it

cant get the solution bc its an even problem :(

[hasty galleon]

Well I just checked it with wolframalpha too and it looks correct there too

[vast dune]

ok thanmks

.close

[pearl pond]

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[sage patrol]

can someone explain how i can calculate sin(45deg) = 1/square root 2

[west sapphire]

pythagorean theorem?

[autumn narwhal]

draw the triangle

[sage patrol]

here is the question

i am having a problem with c

[karmic fern]

have you heard of sohcahtoa

[sage patrol]

yes

[autumn fossil]

Using pythagoras theorem

[sage patrol]

yeah thats what i reached, hyp is square root 2

[autumn fossil]

Now sin(45) is opposite/hypothenuse

therefore it's 1/sqrt(2)

Which can be also $\frac{1}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$

[jolly parrot]

MathIsAlwaysRight

[sage patrol]

so whats the answer?

.close

[pearl pond]

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[faint onyx]

hi can someone help me with this? im not sure how to continue

[bold estuary]

whats the problem

[faint onyx]

i can convert x - 1 to delta

[bold estuary]

just substitute x = 1 into the limit

[faint onyx]

oh right i should send the question

[bold estuary]

yeah lol

[faint onyx]

'Prove the following limits using the epsilon delta definition'

[midnight haven]

no they are trying to do an epsipon-delta solution

You can't just plug in 1 with that

[faint onyx]

[bold estuary]

oh I dont know this stuff then

sry

[faint onyx]

[midnight haven]

Anyways notice how you have $0 < \abs{x-1} < \delta$ and $\abs{(x-1) (x^2 + x +1)} < \epsilon$ so you can get delta to be in terms of epsilon

[faint onyx]

yes

[midnight haven]

Right

This statement holds if [
\abs{x-1} < \f{\epsilon}{\abs{x^2 +x +1}}]
But we want it to be only comprising of constants on the right side. So can you say anything about $\abs{x^2 + x +1}$

[faint onyx]

hmm wait i can just do that?

[midnight haven]

yes

[faint onyx]

woah

wait

[midnight haven]

Like

The idea is that

Consider some arbitrary number $r$, you want to show that for
[
\abs{x-1} \le r \textss{and} \abs{x-1} > r
]
$\delta$ takes into account both possibilities

For now, you say r = 1

But any number would've been fine too

[faint onyx]

hmmm okay i see it

so like presentation wise

would this be enough?

[faint onyx]

oh wait

[midnight haven]

Yeah but again, you have to consider delta for both possibilities

Like I said consider r to be 1

Like

Let's consider the first Possibility

We have [
\abs{x-1} \le 1
]
Which holds when
[
-1 \le x-1 \le 1
]
Which is
[
0 \le x \le 2
]

[faint onyx]

[faint onyx]

right

ah ok so ill have to write out both possibilities

to show that the statement holds for both

[midnight haven]

Yes

[faint onyx]

wait how exactly lol

[faint onyx]

like ill continue from the last sentence here

[midnight haven]

For example by considering the range you can say [
\abs{2^2 + 2 +1} = 7] which means $\delta = \f{\epsilon}{7}$

[faint onyx]

ah ok i see it now

[midnight haven]

This basically verifies the first possibility

[faint onyx]

so were using the boundary values

[midnight haven]

You actually don't have to verify the second possibility too actually

[faint onyx]

why tho

oh wait by definition

delta > 0?

[midnight haven]

Like the idea is, can we make $\delta$ small enough where $\abs{x-1}$ is never greater than 1. That way we wouldn't even have to worry about the other case

[faint onyx]

hmm

[midnight haven]

Basically

Notice that
[
\abs{x-1} < \delta
]
To ensure that
[
\abs{x-1} \le 1
]
We just need to ensure that $\delta < 1$

[faint onyx]

right

[faint onyx]

unsure

lmao

[midnight haven]

[faint onyx]

but yeah i think i get it

tysm hah

[midnight haven]

That's goood

[faint onyx]

[midnight haven]

[faint onyx]

.clos

.close

[pearl pond]

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[pearl pond]

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[brave pulsar]

Do these numbers look right. trying to figure out how to graph this thing

[tacit mulch]

There are also points of inflection at x=2 and 3

since the concavity changes there

Everything else looks good

[pearl pond]

@brave pulsar Has your question been resolved?

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[midnight haven]

Hey

[midnight haven]

#help-30 message

I posted this in the channel below by accident

So here is my channel

Perhaps you can help me out ?

Here again pictures

I dont get why its not L=[1,5] at the very bottom like with the first example

[open mist]

can you translate that sentence near the bottom of the 2nd pic

[midnight haven]

It says that the lL = of the inequality is:

The solution

[open mist]

seems it provides a different inequality

|x-3| > 2 instead of |x-3| <= 2

[midnight haven]

I dont know why

[open mist]

without context i don't know why either

[midnight haven]

This is the question

To solve this

[open mist]

then the answer is to the original question

just a different method to solving it

[midnight haven]

Can you please explain

Like why they use => instead of >

[pearl pond]

@midnight haven Has your question been resolved?

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[west lintel]

I have (i+1) up to the power of 6 to see if it would make the pattern more obvious but I still cant seem to find it, either I calculated them wrong or I'm idot haha

[west lintel]

i+1, 2i, 2i-2, -4, -4i-4, -8i

I can see a pattern but I cant figure out what the pattern is

[midnight haven]

Look at the signs of the imaginary part and the real part

The imaginary part will go positive, positive, positive, 0, negative, negative, negative, 0

Then the real part will go positive, 0, negative, negative, negative, 0, positive, positive

Which is no coincidence

It has to do with how imaginary numbers are visually multiplied

@west lintel Do you get what I'm saying?

[west lintel]

well I can see this but I dont know how I would generalise it

[midnight haven]

Yeah and honestly I'm not sure if it helps with question (ii)

[west lintel]

ohh I think I understand what they want now

[midnight haven]

Oh, you do?

[west lintel]

yeah its to do mostly with simple power rules pretty much lol

[midnight haven]

Simple power rule, hmmm?

[west lintel]

((i+1)^4)^900 = (i+1)^3600

is it not?

and then (i-1)^4 would be -4 again

so its 0

thanks anyways

.close

[pearl pond]

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[pulsar lark]

Bestäm = Determine, där = where

[pulsar lark]

I messed up last time so i is not the same as x_i

[plush bramble]

what's $x_i$ ?

[jolly parrot]

riemann

[glass salmon]

Do you know the formula for sum of first n natural numbers and first n perfect squares?

[midnight haven]

That's what I thought too at first, but check the message right above yours

[pulsar lark]

x_i = a + i (b-a) / n right?

[glass salmon]

oh

[midnight haven]

How are we supposed to know? Send us what's right above the question

[pulsar lark]

but the question have no intervals

yeah this the full question

I don't know how am I supposed to know a and b if [a,b] is not given

[pulsar lark]

you mean the formula? I got it from here https://www.youtube.com/watch?v=YTKQswb60Pw&ab_channel=TheOrganicChemistryTutor

[midnight haven]

No, I mean that we can't possibly know what x_i is without it being defined somewhere

[midnight haven]

Really? If you go even further up, is there really nothing?

[pulsar lark]

no that is the full question

maybe my proff forgot to write the intervals?

[midnight haven]

Your prof forgot more than the intervals

[midnight haven]

We can't just assume that, for example

x_i doesn't have an agreed upon mathematical meaning

So if it isn't defined anywhere we just can't solve the question

[pulsar lark]

😭

this is from the book if it helps anything

[leaden wadi]

It depends on if it is a left-, right-, or mid-point Riemann sum.

[pulsar lark]

These Riemann sums and limits really bother me

normal differentiation and integration is so much easier

[midnight haven]

From the book, it seems this is a right-point Riemann sum

[pearl pond]

@pulsar lark Has your question been resolved?

[pearl pond]

@pulsar lark Has your question been resolved?

[pearl pond]

@pulsar lark Has your question been resolved?

[pearl pond]

@pulsar lark Has your question been resolved?

[pearl pond]

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[paper gust]

So for number 5a. Would the answer be the same as 5b?

[near echo]

how did you come to that conclusion

[paper gust]

I kinda forgot how limits work, but wouldn’t be the same lim t-> a f(x) == f(a) ?

[near echo]

yes, and that's because the function is continuous

[paper gust]

So the answer sheet is giving two different answers

For that problem

[near echo]

what are those values

[near echo]

b is correct, a should be the same as b

they say so in part c as well

[paper gust]

Ok so just ignore what they put for a then

.close

[pearl pond]

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[fossil lodge]

Every convergent sequence is a Cauchy sequence

[fossil lodge]

How can I show this?

Suppose $(a_n) \rightarrow L$. Let $\epsilon >0$. Then we show that $|a_n - a_m| < \epsilon$

[jolly parrot]

KN

[forest dew]

look up epislon delta proof of converging sequence

[fossil lodge]

think i got it

.close

[pearl pond]

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[neat silo]

3w+3x+9y-6z = 33
2w+5x+4y-2z = 20
-w+2x-3y+z = -1
w-3x+2y+3z = -17

can someone walk me through this

[pearl pond]

@neat silo Has your question been resolved?

[neat silo]

.close

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[primal spindle]

When do I have the +- in front of the radical?

[plush bramble]

when solving $x^2 = a$ for some $a > 0$ and solving for $x$

[jolly parrot]

riemann

[primal spindle]

Oh DAMN ITS when solving for x specifically

Thank you so much

.close

[pearl pond]

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[primal spindle]

.reopen

[pearl pond]

✅

[primal spindle]

Does that still abide?

Does that still abide? Am I looking at the final answer to be positive or the initial number

when solving $x^2 = a$ for some $a > 0$ and solving for $x$

[jolly parrot]

stacheg0d

[primal spindle]

In this

[pearl pond]

@primal spindle Has your question been resolved?

[primal spindle]

<@&286206848099549185>

.close

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[pearl pond]

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[frozen forge]

log_2(cuberoot1/4)

[frozen forge]

so what i did was

i converted cuberoot1/4 to (1/4)^1/3

which is 1/12

so i ended up with log_2(1/12)

but dont know what to do next

[mossy canopy]

2^x=1/12=2^(-1/3)
2^(x+1/3)=1
x+1/3=0
that is what i would do

dunno if correct

[frozen forge]

tf

[mossy canopy]

xD

[frozen forge]

that wrong fs lol

[mossy canopy]

really?

lemme check

[frozen forge]

ye

bro dipped

[mossy canopy]

oh yeah i read it wrong

[timid spindle]

How did you decide this

[frozen forge]

nvm

because

u multiply

is it 1/64?

[timid spindle]

But its $\left(\frac14\right)^\frac13$

[jolly parrot]

ΣAC

[frozen forge]

yea

1/64?

[timid spindle]

You don't just multiply the numbers by the powers

2^5 isn't 10

[frozen forge]

true

so is it 1/64

[timid spindle]

no

[frozen forge]

bruh

what is it

[timid spindle]

You want to write it as 2^(something)

[frozen forge]

sooo

(2^-1/2?)

[timid spindle]

Okay here's a tip: $\left(\frac{1}{a}\right)^\frac{1}{b} \neq \frac{1}{a^b}$

[frozen forge]

?

[jolly parrot]

ΣAC

[frozen forge]

ok there

hmm ok

then what is it

[timid spindle]

Go and look up a table of exponent laws

[frozen forge]

didnt find it

?

@timid spindle

.close

[pearl pond]

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[frozen forge]

uh

[pearl pond]

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[minor dune]

how am I supposed to know how to graph functions like xe^x

[minor dune]

Curve sketching would just take way too long

[tacit mulch]

For certain functions like f(x) = xe^x, you can probably use your intuition to get a basic idea of the shape

But it's not like there's a general process for all functions

other than just plugging in values

(or using desmos)

[minor dune]

😢 well guess Ill just have to obtain the intuition. Can't even have calculatorz smh

.close

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[bitter path]

i got this but not sure

can anyone lemme know if 625.5 is correct?

.got it right

.close

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[merry patio]

Uhh how do I answer this

[west sapphire]

simplify the original expression as much as possible

[merry patio]

ik but i need help answering the question

[west sapphire]

6(3c-4) = what

carry out the multiplication

[merry patio]

18c-24??

[west sapphire]

yep

now how about the other term

2(5c-1) = ?

[merry patio]

10c-2

[west sapphire]

right

so now you want to subtract the second one from the first

18c - 24 - (10c - 2)

[merry patio]

10c-2=8c? so 10c-24?
this is pretty confusing for me and I want to understand it

[west sapphire]

18c - 24 - (10c - 2) = 18c - 24 - 10c + 2

do you agree with that?

i just distributed the - across (10c - 2)

[merry patio]

ok

is it 8c-22? @west sapphire

[west sapphire]

yes!

[merry patio]

😄

[west sapphire]

👍

[merry patio]

thx for the help

[west sapphire]

cheers

[pearl pond]

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[tacit merlin]

Can anyone help me find n

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[glass token]

I have 4 dimensional space. I have 3 vectors.
y1=1 -2 1 3
y2=1 0 -1 -2
y3=5 -6 1 5

How to get orthogonal complement?

[glass token]

.close

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[ashen jay]

Hi

[viscid oxide]

https://nohello.net

[ashen jay]

Is B and C correct?

Did I do the right approach?

<@&286206848099549185>

[pearl pond]

@ashen jay Has your question been resolved?

[ashen jay]

@vast sluice

[forest dew]

check the advanced channels

also this server is not meant to help with checking answers

if you get something wrong we can help

[ashen jay]

where?

Ok mb but do you have a idea of how to do this?

[forest dew]

get the advanced roles

no

[ashen jay]

ok np

[forest dew]

this is what, lin alg?

[ashen jay]

ye

[pearl pond]

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[ashen jay]

.close

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[unborn galleon]

How to check if the function odd or even in this situation?

[plush bramble]

find f(-x)

and compare it to f(x) or -f(x)

[unborn galleon]

See

What about the case of 0

[plush bramble]

the definition of odd/even has to be true for all x where f(x) is defined

[plush bramble]

you should be more careful about what x sign x is here

if -1 <= x <= 0, then f(x) = 2x+2

but if 0 < x <= 1, then (x) = 0

so if -1 <= x<= 0, then f(-x) equals 0

[unborn galleon]

So in case 0 output its not odd or even then

f(x) =0 = -f(x)
-f(x) =0 = f(-x)

[plush bramble]

x=0 is not a case that's important

the other values in [-1, 1] are important

[unborn galleon]

So every time i only need to check the function thats it ouput is not the 0?

Like here i should check only the middle func

[plush bramble]

plotting is probably best

you're not quite understanding what "checking f(-x) = f(x) or f(-x) = -f(x) for all x" means

[unborn galleon]

Okay wait

This is true here ?

-1<=x<=0

[plush bramble]

no

[plush bramble]

read this

[unborn galleon]

Oh

So in the second row we get 2=2

And in the first row 2= -2

[pearl pond]

@unborn galleon Has your question been resolved?

[plush bramble]

nahhhh

go through this unit on khan
https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:symmetry/a/intro-to-symmetry-of-functions

[pearl pond]

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[hushed pelican]

hello, the derivative of -sqrt(x^3) = -3/2x^1/2

[hushed pelican]

am i correct?

[cedar sphinx]

Yup should be

[pearl pond]

@hushed pelican Has your question been resolved?

[hushed pelican]

thanks

[pearl pond]

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[opaque zealot]

can somoene help me with this prolblem

[opaque zealot]

i identifed delta x as 2^k-1/n

and f(xk) is too long i wont write it out but

i dont know where to go from herer

[pearl pond]

@opaque zealot Has your question been resolved?

[opaque zealot]

<@&286206848099549185>

[pearl pond]

@opaque zealot Has your question been resolved?

[opaque zealot]

i got excited that someone pinged me, it was just the bot

[topaz terrace]

bro this question is extremely easy the answer is ln2

ur bad

[opaque zealot]

i cant write this on the test tho

[topaz terrace]

what

what made u think i ask lol

[opaque zealot]

i have to write it in summation notation

[topaz terrace]

LOL

who

asked

LLL

bro got muted

for saying the n word

@opaque zealot

[pseudo gulch]

a

[topaz terrace]

b

@merry carbon bro come back

i saw you type

where did you go

wait at least verify if its right lol

pls

negativerizz needs you

im conveying this message for him because hes muted

[pseudo gulch]

actual metalbubble activities

[pearl pond]

@opaque zealot Has your question been resolved?

[honest lagoon]

[pearl pond]

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[fresh wren]

why is the example formula for my exam

top*

different from the khan academy formula

bottom*

for maginification

[somber needle]

but the image u shared shows different formulas

one for magnification and other is lens formula

[fresh wren]

yea sorry its cut off a bit one sec

@somber needle

see when khan talks about it

the v isnt negative

which refers to image distance

is anyone around

please im stuck

<@&286206848099549185>

[pearl pond]

@fresh wren Has your question been resolved?

[fresh wren]

nah i got ghosted

<@&286206848099549185>

@somber needle yo

[fresh wren]

<@&286206848099549185>

[fresh wren]

<@&286206848099549185>

[pearl pond]

@fresh wren Has your question been resolved?

[pearl pond]

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[fresh wren]

.reopen

[pearl pond]

✅

[fresh wren]

bruh i just need someone to help with this basic formula

[midnight haven]

there's a physics server in #old-network

[fresh wren]

oh?

[fast zealot]

it may be due to the sign notation

but better to ask in the physics server

[fresh wren]

ill do that thanks

.close

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[uneven pewter]

Ignore the ask professor note

This is a diff eq im trying to solve using an integrating factor to make it exact

I know i messed up i just cant find where

Because im close to getting the answer and it looks nothing like this. Answers in the back of the book but i wanna know how to get there

Found 1 mistake. Updated.

[pearl pond]

@uneven pewter Has your question been resolved?

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[twilit harbor]

lets say you have

[twilit harbor]

$\frac{1}{2g} / g$

[jolly parrot]

geoxcaliber

[twilit harbor]

how do you turn that into a multiplication

Multiply by the inverse?

lets say you had

gh = 1/2 (v0 + v1)

and you want to find h

you divide by g

why does the g divide with the 1/2 and not the parenthesis

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[merry stirrup]

.reopen

[pearl pond]

✅

[merry stirrup]

It divides with the parenthesis too

You have to expand the parenthesis

To understand it

[jolly parrot]

Arnab

[timid spindle]

This is literally just a suvat equation written in an awkward way

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[small plover]

Help with this question: given that the graph of y=(2k+5)x²+kx+1 does not meet the x axis, fing the possible values of k

[empty pollen]

so if it doesnt meet the x axis, it doesnt have any zeroes

ie the roots of y=0 dont exist

[small plover]

Does it mean D<0

[empty pollen]

exactly

[small plover]

Here's what I did but I got 1 mark off

I don't know where I got wrong

[empty pollen]

u solved for D=0

[small plover]

Ohh

[empty pollen]

gotta find the set of values where D<0

[small plover]

but I don't know how

Wait so like when k is negative?

[empty pollen]

nope, when D is negative

imagine the graph for this

y=D and x=k

[small plover]

I don't quite understand

[empty pollen]

D=(k+2)(k-10)

imagine plottin the graph for y=(x+2)(x-10)

[small plover]

so (k+2)(k-10)<0

[empty pollen]

yeah

[small plover]

then k=-2 and k=10

[empty pollen]

y=0 at -2 and 10

[small plover]

So it's because I put the wrong sign

[empty pollen]

so if y is positve before x=-2, itll become negative after that

and if y is negative before x=-2 (for x<-2), itll b positive after that

[small plover]

ohh ok thank you

[empty pollen]

since k^2 has a positive coefficient, its the 2nd graph

so y=d is negative for k belonging to (-2,10)

[small plover]

how do you know it'll be the second graph

so when coefficient is positive?

[empty pollen]

have you learnt differentiation?

[small plover]

A bit

[empty pollen]

yeah if its quadratic and x^2 coeff is +ve, its the 2nd one

[empty pollen]

know how to find maximas and minimas?

[small plover]

I kind of forgot

We did it a while ago

But they were like badic questions

[empty pollen]

okay if u try the 2nd derivative test with a quadratic eqn

having +ve coeff

ull realise it has a minima

[small plover]

Ohh

[empty pollen]

which is in the 2nd graph

[small plover]

Ok I understand now

Thank you

[empty pollen]

cool

[small plover]

.close

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[copper kestrel]

so like I understand this answer

but could I use nth term test here?

like if a_n = 1

then lim to inf of 1, is 1

so that means it diverges?

so with that, could I say it's just n?

[pearl pond]

@copper kestrel Has your question been resolved?

[timid spindle]

the nth term test is not gonna tell you what the nth partial sum is

it just gives you a criteria under which your series does not converge

[copper kestrel]

oh

could you explain what an nth partial sum is?

[timid spindle]

its the result of adding the first n terms of your series

[copper kestrel]

okay

and n is just like

a random number?

[timid spindle]

sure, like a general number

so if you're just adding ones all the time in your series

the nth term is adding the first n 1's i.e. n

[copper kestrel]

okok

that makes sense

[timid spindle]

another example: $\sum_1^\infty n^2$
the nth partial sum is just the sum of the first n square numbers

[jolly parrot]

ΣAC

[timid spindle]

(its confusing because you use the letter n for the dummy variable in the sum and the n in "nth partial sum")

even tho they're doing completely different things

[copper kestrel]

oh

i see

wait so

[copper kestrel]

for this one what is the nth partial sum

like how would you write it

is it just infinity?

[timid spindle]

$1 + 4 + \dots + n^2$

[jolly parrot]

ΣAC

[timid spindle]

thats the nth partial sum

[copper kestrel]

i see

but if it's a constant

it's basically just

the constant times n?

[timid spindle]

$\underbrace{1+\dots+1}_{n \text{times}}$

[jolly parrot]

ΣAC

[copper kestrel]

gotcha

[timid spindle]

uh huh yeah

[copper kestrel]

thanks

[timid spindle]

no worries:)

[copper kestrel]

.close

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[normal stag]

I got 0 but i can't find the answers online

can someone tell me if it's correct

[pearl pond]

@normal stag Has your question been resolved?

[plush bramble]

Show your work

[pearl pond]

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[outer hare]

how would i solve this

[leaden wadi]

I would first start by sketching a graph.

[outer hare]

Yup did that

[leaden wadi]

The problem wants you to use the washer method.

[outer hare]

so the bottom is the disc to find the area from -1 to 2 y

then i use washer to find 2 to 5 pi

so i got these two formulas

that one is for the bottom disc part

this one is for the washer part from 3 to 5

problem is the answer according to the book is

9pi

but this doesnt get me 9 pi

it gets me 18pi

/5

[leaden wadi]

What is the inner radius on the interval y = [-1,2]?

[outer hare]

symbalab could just be tweeking to be honest im gonna try and do it by hand

its just y+1/2

(y+1)/2

[leaden wadi]

Are you sure about that?

[outer hare]

yeah

x=y-2

sorry

y=2x-1

so x=(y+1)/2

I did it by hand and got 9pi

so

idk where symbalab is messing up but

i think i figured it out

kinda lost as to how symbalab got 18pi/5 lol

.close

[pearl pond]

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[hybrid flume]

need some help finding a error

[hybrid flume]

in my synthetic division problem to find real 0s

When I did it it didn’t equal 0 and I’m not sure where I messed up

would this mean that the remainder is 0

[coarse dawn]

Well you used 2 when you did your synthetic division

Aren't you supposed to use a root of that function, like -3?

@hybrid flume

[hybrid flume]

umm

im not sure I thought you were supposed to use the first number

[coarse dawn]

Well you're supposed to use the first valid root of the function

Since 2 isn't a root, why would you use that?

[hybrid flume]

gotcha, I was just told to go off the first number and not the first root

but that would make sense

for what you explain

which would show my error

Thank you for clarifying

.close

[pearl pond]

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[viral trellis]

No idea how to find the test statistic and p-value.

[pearl pond]

@viral trellis Has your question been resolved?

[viral trellis]

<@&286206848099549185>

[pearl pond]

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[copper kestrel]

could you say that this diverges with the nth term test?

how does it work with the alternating series there?

because isn't it like alternating between +/- infinity?

[modern talon]

if its a monotonic sequence i believe

[copper kestrel]

uh I haven't learned that

@merry carbon I see you lurking

is that a yes?

[merry carbon]

Assuming by "nth term test" you mean that the sequence doesn't converge to zero, then it is

[the (3/2)^n grows faster than the n^2 of course ]

[copper kestrel]

oh okay

so is the alternating series irrelevant?

[merry carbon]

Well not really no [and to be fair, you can create the subsequences that diverge to ♾️ and -♾️, which is enough to deduce that the sequence it's made up of doesn't converge to zero]

[copper kestrel]

okay

ty

.close

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[fresh dune]

ke\

[fresh dune]

hello

[pearl pond]

@fresh dune Has your question been resolved?

[fresh dune]

no one helped me at all

[old geyser]

You didn't even post anything

Clearly you didn't read the directions

[pearl pond]

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[zenith rain]

can anyone help me? I dont know how to get 513

[midnight haven]

f(-3/2) means everywhere you see an x in f(x), you set x=-3/2

[cursive fulcrum]

Also, you have to tell whether you can get 513 or not?

Not how you can get there

[pearl pond]

@zenith rain Has your question been resolved?

[pearl pond]

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[balmy basin]

Hello

[balmy basin]

So I have a question

Idk if u will know

In gas with an absolute pressure of 1 atm, what is the greatest possible air pressure in atm due to a sound wave in gas

[pearl pond]

@balmy basin Has your question been resolved?

[balmy basin]

Uhhh I’m going to ping

<@&286206848099549185>

[midnight haven]

Idk sry

[balmy basin]

Can anyone else help

Or should I close

Hello

[balmy basin]

.close

[pearl pond]

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[pearl pond]

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[final gate]

@pearl pond

[final gate]

Sales of fair trade honey products in 2012 were 95% of what they were in 2011. In 2012 sales were 3.6 million. What were they in 2011?

im confused on how to find for 2011

but i know how to find original amount

[midnight haven]

isnt that the same thing

[final gate]

really?

but then

[midnight haven]

can u show ur work

[final gate]

ok

oh wait

i dont have a camera

but my q is

am i supposed to do 95% of 2011

for example: 95/100 x 2011

[midnight haven]

2011 is just the year

[final gate]

so the year is only showing the timeline

[midnight haven]

yes

you know in 2012 that 3.6 million was produced

and 3.6 = 95% of (2011 amount)

call that amount in 2011 x

do you know how to find x?

[final gate]

i should be able to

but when finding 3.6

should i round 3.6 to the nearest whole

[midnight haven]

wdym by finding 3.6?

[final gate]

95%

of 3.

[midnight haven]

if the question says round, then round to whatever sig figs

if not then leave it

[final gate]

oh alr

ty

🙂

[midnight haven]

what did you get?

[final gate]

im still calculating

is it 3.42?

[midnight haven]

well your amount in 2011 cant be lower

so no

[midnight haven]

can I see your working out here

[final gate]

i did 95/100 * 3.6000000

[midnight haven]

thats 95% of 3.6 million

3,600,000 = 95%

you want 100%

[final gate]

100%?

[midnight haven]

huh

[final gate]

no like

[midnight haven]

wdym?

[final gate]

i dont get it

[midnight haven]

okay so like in 2012 you produce 3.6 million right?

[final gate]

yes

[midnight haven]

that 3.6 million is 95% of whatever was produced in 2011

you still with me?

[final gate]

ohh

so it cant be less

[midnight haven]

yws

[final gate]

so is it 3.7 million?

[midnight haven]

can i see the working out?

[final gate]

unfortunately i dont have a camera