help-23

[safe radish]

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[fleet plaza]

help

[fleet plaza]

<@&286206848099549185>

[ancient escarp]

wait 15 minutes to ping helpers

what have you tried so far

[fleet plaza]

im stuck

do i derive this?

like idk how to start

@ancient escarp how long does help usually take

im ina lil rush

[pulsar condor]

easy to note that $f(x)=\dv{x}\frac{-1}{3+x}$

[flat frigate]

Mosh

[fleet plaza]

ok but now what

[pulsar condor]

use the hint and try the problem

[fleet plaza]

if i didnt do that i wouldnt be here XD

ik that $1/(1-x) = \sum{^{\infnty}_{n = 0} x^n}$

[flat frigate]

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

[pulsar condor]

yep

how do you use that fact here?

[thin bridge]

\sum_{n=0}^{\infty}

[fleet plaza]

factor 1/3?

[pulsar condor]

Yep

[fleet plaza]

so 1/1+x/3

so 1/1-(-x/3)

but what about the negative?

[pulsar condor]

brackets but yes

$f(x)=\frac{-1}{3}\dv{x}\frac{1}{1-(\frac{-x}{3})}$

[fleet plaza]

ok now what

[pulsar condor]

apply the formula you posted.

[pulsar condor]

.

[fleet plaza]

dont we need the negative

[pulsar condor]

what negative?

[pulsar condor]

oh yeah

[flat frigate]

Mosh

[fleet plaza]

sooooo

[pulsar condor]

what's the power series of 1/(1-(-x/3))?

[fleet plaza]

x^n

[pulsar condor]

no

[fleet plaza]

(-x/3)^n

[pulsar condor]

yep

[fleet plaza]

but we need to find the derivative

[merry zenith]

it might help if you use another variable for this $\frac{1}{1-a} = \sum_{n=0}^{\infty}{a^n}$

[flat frigate]

vrang

[pulsar condor]

$f(x)=\frac{-1}{3}\dv{x}\sum_{n=0}^\infty (\frac{-x}{3})^n$

[merry zenith]

oops nvm you alr got it

[flat frigate]

Mosh

[pulsar condor]

but you can easily differentiate a summation.

[fleet plaza]

so i derive (-x/3)^n?

[pulsar condor]

yes

[fleet plaza]

so n(-x/3)^n-1 * (-1)?

[pulsar condor]

$\dv{x}\sum_{n=0}^\infty (\frac{-1}{3})^n x^n$

[flat frigate]

Mosh

[fleet plaza]

so we kick (1/3)^n out

[pulsar condor]

you leave it, yes

and d/dx x^n = nx^(n-1)

[fleet plaza]

(1/3)^n n(x)^n-1?

[pulsar condor]

-1/3, but yes

[fleet plaza]

ya negative

[pulsar condor]

so $f(x)=\frac{-1}{3}\sum_{n=0}^\infty (\frac{-1}{3})^nnx^{n-1}$

[flat frigate]

Mosh

[pulsar condor]

which can be simplified slightly by combining the factors of -1/3

[fleet plaza]

(-1/3)^n+1

[pulsar condor]

yep

[fleet plaza]

and then (-1)^n+1(1/3)^n+1

[pulsar condor]

yes if you want to seperate the alternater

[fleet plaza]

and do i do ratio test to get radius

[pulsar condor]

Yeah then you'd do the normal tricks for finding radius which I forget but I think ratio is correct

[fleet plaza]

man calc 2 is work

😭

[pulsar condor]

Calc 2 is strangely the hard one yeah

,w power series of 1/(3+x)^2

[flat frigate]

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Requested by Omegabet_#9771

[fleet plaza]

so this would be the same

[pulsar condor]

yeah apply a similar trick

[fleet plaza]

and then this i kickout the x^2 right

[pulsar condor]

define kick out

[fleet plaza]

actually idk wat to do here

do i still derive?

[pulsar condor]

x^2(thing from part b)

so you'll just multiply through by x^2

[fleet plaza]

so its the same sum from part b

but x^2 multiplied before it

[pulsar condor]

yes

[fleet plaza]

so y is it we dont derive the top x^2 but we derive 1/(3+x)^3

[pulsar condor]

so if you had for part b $\sum_{n=0}^\infty x^n$, c is $\sum_{n=0}^\infty x^{n+2}$

[flat frigate]

Mosh

[pulsar condor]

(which obviously you don't, but you get the idea)

[pulsar condor]

cause your sum is a "sum of n"

x^2 is independent of n

so it's a constant in regards to the sum

[fleet plaza]

i seee

ok ok

u said u forgot how to do radius right

[pulsar condor]

Yes, but it involves ratio test

[fleet plaza]

can i get help on this

[pulsar condor]

differentiate, find the power series, then integrate

[fleet plaza]

so 1/9-x

[pulsar condor]

-1/(9-x)

chain rule

[fleet plaza]

oh right

[pulsar condor]

and you can find the power series of -1/(9-x) from tricks we did at the start

[fleet plaza]

factor -1/9?

[pulsar condor]

I leave it to you, cause Im going to bed.

[fleet plaza]

aight

.close

[safe radish]

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[narrow kraken]

Hi

[narrow kraken]

for restricting the domain of a sin function

it's [-pi/2, pi/2]

so is 7pi/4 not in this domain

but -pi/4 is

which gives you the same sin value?

[safe radish]

@narrow kraken Has your question been resolved?

[pastel verge]

Yes

[pastel verge]

For sin inverse to exist

[winter pivot]

1/x^n = (1/x)^n

holy shit!

[fleet plaza]

steps?

[fleet plaza]

this doesnt tell me anyhting

[winter pivot]

ok

there is a certain type of series

that we call a "geometric series"

and basically it looks like this

1 + x + x^2 + x^3 + ...

and so on and so forth

now the thing is, this series will converge! if |x|<1

[fleet plaza]

u can stop

[safe radish]

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[safe radish]

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[grave flame]

Questions about the semantics of fractional division

2/3 divided by 4 = 1/6, this value describes one piece of the newly divided whole

4 divided by 2/3 = 6, this value describes how many "groups of 2/3" are in the newly divided whole

Can someone break down conceptually the reason why the solution of each represents something different?

[stoic dune]

You're hiding some of the difficulty with the phrase "newly divided whole"

[grave flame]

Not intentionally! I suppose I just don't understand it

[stoic dune]

First one is when you take two pizzas, divide them between 3 people. AND THEN take one person's cut, and split that between 4 people.

Those 4 people get 1/6 of a pizza

.
Second one is a bit tougher to get across though. Take 4 pizzas and split it between "2/3rds of a person".

That is, this person expected more than 4 pizzas, haha

So they are getting only 2/3rds of what they wanted, or they wanted 6

.
Ultimately there's no real difference between these two processes, this is the same division after all.

[grave flame]

So it other words you're trying to see what 4 is 2/3rds of?

[stoic dune]

Yes, because if 4 ÷ 2/3 = 6
Then 4 = (2/3)×6

That's one way to think of it, of course

Naturally if a ÷ b = c
Then a = b×c

.
Note that we can find the answer by flipping and multiplying instead:
4 ÷ 2/3
= 4 × 3/2
= 6

Which is normally how you compute these

[grave flame]

I think I understand ty!

.close

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[sharp fern]

Discrete Mathematics for Computer Science - Can someone help me? I need to prove that it's a tautology but I can't get past this point

nevermind I figured it out

.close

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[sharp fern]

to be clear, the issue was that I forgot to negate (p ^ ~q) once more

[sharp fern]

.close

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[cerulean sparrow]

https://i.imgur.com/RhO1jgL.png

[cerulean sparrow]

How do I calculate sample size here?

I was using the 80% chance as a symmetric 80% confidence level

and taking the intervals of norminv (0.1) and norminv (0.9) to equal -4.95 and -4.85 respectively but I think thats the wrong approach

[safe radish]

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[safe radish]

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[novel gust]

Hi, I'm trying to find a tangent on P1.
I calculated grad(f)(P)=(-3,2) and I know this is the norm but I don't understand why dot product (-3,2)(x,y)=0 doesn't work.

[safe radish]

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[novel gust]

<@&286206848099549185>

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@novel gust Has your question been resolved?

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@novel gust Has your question been resolved?

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[polar lynx]

My calc sucks but can't you just do implicit differentiation here?

That'll give you an expression for y' in terms of x,y. So you can compute the slope of the tangent at (1,1). Then you have a slope and a point on a line, so you should be able to use basic algebra to come up with a line of the form y=mx+b.

Just a guess.

Actually I guess that doesn't really answer your question now that I think about it.

[novel gust]

look, I just got the grad

[polar lynx]

What is your thinking for why that dot product equation should work?

Oh shoot okay, that dot product equation is supposed to be a formula of a line.

I feel dumb lmao.

[novel gust]

wait, why it is (-3,2)(x-1,y-1) and not (-3,2)(x,y)?

[polar lynx]

Probably because the correct line is translated by some value.

(-3,2)(x,y)=0 is thru the origin

Is (-3,2)(x-1,y-1)=0 supposed to be the correct answer here?

[novel gust]

so actually (-3,2)(x,y) is just the slope through the origin and because I need the line across the point I take (x-1,y-1) instead?

[novel gust]

I guess so haha

[polar lynx]

I think that's what happened but in general (x-1,y-1) might not always be correct for other curves.

[novel gust]

what do you mean?

[polar lynx]

Since the amount the line is translated by might be some other value.

[novel gust]

it is correct for this specific P

[polar lynx]

Yah probably, I'm just pointing it out because they're probably using a specific form of a line in R^2 that you might need in other q's

Lemme try and look it up.

[novel gust]

they just say "find the tangent formula at this point"

[polar lynx]

Yes I know

Well the general equation of a line in R^2 or R^3 is what you'd expect, it's just r(t)=r_0+tv where r_0,v are vectors, v is the direction of the line (like the slope) and r_0 is just a pt on the line. t is just a scalar parameter.

I think there's a dot product version too but I do not remember it.

I'd probably just use the other version since it's basically a generalization of y=mx+b.

So for these kinds of problems you can just use r(t)=r_0+tv: find v=the gradient at the given pt and let r_0 be the given point on ur curve.

[novel gust]

yeah that's makes sense

[tame raft]

if r(t) = r_0 + tv, then (r(t) - r_0) dot v = mag(r(t) - r(0)) * mag(v)

[safe radish]

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[candid ibex]

did i get this question right?

[sleek latch]

idk

from the square u get the diameter

divide the diameter by 2 then square it then multiply by pi

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[rapid radish]

Which of the following sets has the least number of members...

a. The set of multiples of 3 less than 15
b. The set of factors of 25
c. The set of tens numbers (10,20,30...) which can be divided by 27
d. The set of prime numbers between 30 and 40

[rapid radish]

i need to submit in 10mins

homework

c is 0, d is 2, so do i piick c?

yeah

ok thx

.close

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[lean otter]

An airplane is flying on a bearing of 80deg at 540 mph. A wind is blowing with the bearing 100deg at a constant 55 mph. FInd the component form of the veolocity of the plane aka the air speed, and the actual spped, aka the ground speed, and the direction as a bearing of the airplane

[lean otter]

help me to understand this

it looks like this is some sort of a law of cosine problem?

the theta being 20 i think

540 and 55 being side lengths?

or is this a r cos theta, r sin theta problem

does it matter if i have the wind in component form

help

<@&286206848099549185>

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[lean otter]

luckily somebody made a quizlet for my exact problem

lol

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[dire spoke]

$\textrm{If} \ S \ \textrm{is a symmetric matrix and } O \ \textrm{satisfies} \ O^TO=I_n. \ \textrm{Find \textit{H} in terms of \textit{O} and \textit{S} such that} \ OH+H^TO = S $

.reopen

.close

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[river niche]

Can anyone help with this?

[safe radish]

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[river niche]

<@&286206848099549185>

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[pastel verge]

,rotate

[pastel verge]

Did you find value of x first

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[pseudo geode]

is there a quick way to compute this?

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[lean otter]

i need help

[lean otter]

with prealgebra

[raw shoal]

send the question you need help with

[lean otter]

it’s not a specific one

[inland ivy]

That's fine just ask

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[humble sail]

hello

[humble sail]

how should i solve this

is a 2x2 equation system

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@humble sail Has your question been resolved?

[lost patrol]

Is there any other part of the question

[safe radish]

@humble sail Has your question been resolved?

[humble sail]

Oh i forgot

Find the value of A and B following the exersice, knowing that S={(3;-2)}

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[humble sail]

<@&286206848099549185>

[river niche]

i got it

.close

I'm not sure how to close my question or whatever it says to do!

[humble sail]

it closed by itself so you dont need to do anyhting

[pastel verge]

It's already closed

[safe radish]

@humble sail Has your question been resolved?

[quasi bison]

@humble sail do you still need help with this

[safe radish]

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[real merlin]

Hiii, may I know how to do this question? Thanks?

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[real merlin]

.close

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[eager folio]

How do i go about solving this? I've tried plugging cos(2x) into the taylor series equation and tried comparing it to the cos(x) polynomial series (we have them written out on a handout) but the first polynomial i just labelled as 1.

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<@&286206848099549185> sorry for the ping!

.close

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[fleet folio]

can someone explain to me how its 20 pls

[fleet folio]

<@&286206848099549185>

[grizzled fossil]

What possible scores could team 1 have?

[fleet folio]

.close

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[modern lintel]

$\vec r_3$ is a unit vector. I'm stuck at finding angle between $\vec v$ and $\vec r_3$. I know plane passing through $\vec v $ and $\vec r_3$ makes angle 45 degree with y and z axis.

[flat frigate]

Bkas

[modern lintel]

<@&286206848099549185>.

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[topaz nest]

I am searching for equasion where if x=1 the answer is -1 and if x = 2 the anwer is 390

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[simple steppe]

wha

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[fluid iron]

hi

[fluid iron]

so if the chance of smth happening is 5%

i mean something happens over and over again, and every time the chance of smth else happening is 5%

the chance of that other thing not happening decreases overtime right?

no?

yeah but the chance of flipping 100 heads in a row would be 0.5^100 no?

yeah

[fluid iron]

and here the chance of "no" is 0.95 and if i do it 100 times, the chance will be 0.95^100

yeah and thats half a percent

im just trying to figure out why, with 5% chance, i havent got a rare drop after 131 attempts

whats a cf

oh

is my math correct though? shouldnt i almost surely have got it by now?

so i just try again and again?

true
i probably spent all my luck yesterday. got an item that has a 1 in a million drop chance

yup

ty for help

.close

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[lean otter]

How may I calculate term 100 of zn+1 = 1 - (1/zn) with z0 = 1 + i ?

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[lean otter]

Thanks, I answered my question already

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[cerulean dagger]

Hello, need some help with a question!
Victoria (age 65) is about to begin receiving a CPP retirement pension of S11,000 per year. The pension is indexed to the Consumer Price Index (CPI) Assume that the annual pension will be paid in a single year-end payment, the CPI is 3% per year and money worth 6% compounded annually. What is the current economic value of
a) 20 years of pension benefits
b) 25 years of pension benefits?

[cerulean dagger]

Cool

Here n = 1 right?

[outer vine]

yes

[cerulean dagger]

Great, thanks a lot!!

.close

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[cerulean dagger]

. reopen

@outer vine We are asked to find the current value of future pension payments right?

[outer vine]

yep

[cerulean dagger]

Then the formula would be PV = FV/(1+r/n)^nt

Right?

[outer vine]

I have never seen that formula ever

but if thats what youre learning in class, then yes

otherwise, idk where you got that

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[obsidian ice]

Hello! Ive posted the images with the question and how I went about solving it. Im just very confused about how I should illustrate these

We are currently working on double integrals

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[kind river]

q3 im stuck

<@&286206848099549185>

.close

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[wild folio]

stuck on q3 part b

[wild folio]

my part A answers

<@&286206848099549185>

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[ebon rock]

Is the first differential not (-3^-t-1 + 3.5e^-3.5t-1)

Do you not subtract 1 from the power when differentiating?

[tame raft]

no

not when differentiating exponents

that's only for polynomials

[tame raft]

i think the sign of the first term inside the bracket of the second derivative should be positive

otherwise fine

[wild folio]

currently stuck on b)

[tame raft]

you didn't specify that lol

[wild folio]

i did tho

[tame raft]

oh i'm a fool

ok use dA/dt to find when the concentration is constant

and then use d^2A/dt^2 to find whether it's increasing or decreasing at those points

and also consider the boundary points ig

[wild folio]

i did this
0=3.8(-e^-t - 12.25e^-3.5t)
i brought 3.8 over to 0

isit correct to bring the 3.8 over

[tame raft]

sure

you can divide both sides by 3.8

[wild folio]

but when i ln (-e^-t) to remove the e ,the other side also gets ln(0)
ln(0)=(-lne^-t - 12.25e^-3.5t)

im stuck on this part and got confused

[tame raft]

yeah so you can't do ln of both sides yet

i mean that wouldn't even work

you would have ln(-e^-t - 12.25e^-3.5t)

ln(A + B)

which doesn't go anywhere

so

0 = -e^-t - 12.25e^-3.5t

is there anything else you can do here

to try and make it look neater

[wild folio]

remove 12.25 over

[tame raft]

no

anything else?

[wild folio]

get -3.5 down?

[tame raft]

i don't think you can

anything else?

[wild folio]

common terms of e

[tame raft]

nice

yes, do that

factorise it

[wild folio]

ooooooo

i got 0 = -e^-t(1+12.25e^2.5t)

i think im wrong

[tame raft]

no, that's right

ok i gtg for a bit

but the key thing to note here is that e^-t never equals 0

[wild folio]

i got low confidence espeically when in math

[tame raft]

so you can divide both sides by it

[tame raft]

reasonable but in this case you're right

wait

ok wait

[wild folio]

one wrong step and the whole equation is wrong

[tame raft]

actually yeah

0 = -e^-t + 12.25e^-3.5t, sorry

and then divide both sides by e^-t

0 = -1 + 12.25e^-2.5t

gtg

[wild folio]

ight thanks

.close

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[twin grove]

Can anyone help me with this plz?

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[halcyon aurora]

<@&286206848099549185>

[halcyon aurora]

How to do this

Ping me too please

[inland ivy]

I'm not sure if this is the exact method you'd use in class but I use this a lot in programming

It's pretty much just the general linear interpolation formula

Which sounds fancy but it's fairly simple

(b-a)*proportion+a

You're basically just getting the vector from a to b and scaling the length by the proportion

Then returning it to a

@halcyon aurora

[halcyon aurora]

So this is the formula in general?

[inland ivy]

Ye

It'll work for a single number or a pair of points

And even in any dimension I think

Assuming all of the operations distribute over every point in the set

Or go to each respective value

Like x1+x2 and y1+y2

[halcyon aurora]

What does proportion a mean?

[inland ivy]

Proportion is the proportion from a to b you are

So for example halfway between would be 0.5

Or all the way to b would be 1

Or just starting at a would be 0

Etc

[halcyon aurora]

So how would that imply in this case

[inland ivy]

Well you want to be a third of the way from a to b

So proportion would just be 1/3

Same for any case where you want to be ____ of the way from a to b

[halcyon aurora]

So we multiply a by 1/3?

@inland ivy

This is very confusing

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[halcyon aurora]

@inland ivy

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[lean otter]

I need help how did he got the n+1/n+1 isn’t it 1/n+1 ?

[rustic summit]

@lean otter Well n is fixed right? So doing n+1/n+1 is possible because it's equivalent to multiplying by one, then the bounds of the multiplication were changed by one which affected the right-hand fraction by removing that extra + 1

[lean otter]

yea but like didnt he extract the highest elemnt which is n+1 in that case because the new highest one is n or is it just a different way of saying times 1

like did he insert n+1 to get n+1/n+1

[rustic summit]

Ah yeah I see what you're getting at

so he substituted n+1 into j to pull out that last highest term, and multiplied by it out front instead.

[lean otter]

but that would be 1/n+1 not n+1/n+1

[rustic summit]

hmm, yeah you're right

the denominator out front is cause by pulling out that highest index, but I'm trying to see how altering the formula to remove the +1 could cause that

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[graceful patrol]

Where exactly is the resultant force that I’m supposed to calculate?

Or will I have two resultants one for the horizontal and the other for the vertical axis?

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[rustic summit]

Did you figure it out?

you need to find the result of all forces added together

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[fading raft]

translate for me and i tell you

Oh. This is differentiation and trigonometry

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[lean otter]

hi could someone help me with this

[flint ledge]

isolate x

[little turtle]

Anyone knows what 150/100 is as a fraction

[peak solar]

Not your channel dude

[peak solar]

What did you start with?

[little turtle]

Oh wait i forgot i was in wrong channel sorry

[lean otter]

i don’t really understand sorry

[peak solar]

Start with factorization

What's 2(1+2x)?

[lean otter]

2 + 4x

[peak solar]

Ok now isolate the x like the other guy suggested

[lean otter]

x > or equal to 7/4

[peak solar]

No

How did you get to it?

[peak solar]

Is 4x-8x=4x ?

And what about the 2

And isn't it-7?

[lean otter]

sorry my bad

@peak solar

[peak solar]

Good job

[lean otter]

how would i do it out on a number line

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[haughty mason]

Hi can someone answer my question? I was wondering, for solving limits, could you always just sub in a value that is close to what x is approaching? Like if it is x -> 3, for whatever the function is, could I just find the limit by subbing in x = 2.99, and x =3.01 ?

[haughty mason]

Because I was wondering, why not just use this method every time? Because it seems like this would always work

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[jagged snow]

Well in some functions even a second decimal place makes a huge difference in value of y.
Like suppose you were getting, y=7.2 on substituting x=2.9, where x->3
And on putting 2.99, you r getting 8 now that's makes a huge difference

[haughty mason]

Oh ok I see that makes sense

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[haughty mason]

Also I have another quick question
Lets say I were to multiply the limit by the conjugate. Can I only do that if the numerator is a binomial?

[queen parcel]

You can do anything to a limit like this provided you're multiplying by one

It just may or may not be helpful

[haughty mason]

oh i see

ok thank you!

[wanton swift]

So I understand this question all the way up to this point but i'm not too sure how the answer is 176/9 pi. can you please help me?

[pulsar condor]

#❓how-to-get-help

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[warped imp]

how do i solve this question?

[azure pilot]

My only thinking is simultaneous equations using the variables x and y where:
x is the number of apples bought
y is the price of 1 apple

So something like:
xy = 20

(x+10)(y-10) = 20

But just looking at that is painful

[tidal imp]

I’d say, let the number of oranges John bought be x, and then find some equation for the prices of the oranges for each stall

you can do simul and it should be solvable, but solutions tend to be easier with one variable, even if the expression seems more complicated at first

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[tawny totem]

let’s say timmy is playing a video game. timmy makes sixteen dollars over nine hours, or y=1.7x. for every three hours played, he gets a permanent +0.02% boost in all money received. these boosts accumulate. this process continues until the boost has been achieved fifty times. after repeating for fifty times, boosts will still grant +0.02% bonuses BUT they will be granted after the three hour “waiting period” is multiplied by 2.5. this repeats fifty times again, and the 2.5(3x) “waiting period” turns into 5(3x), then 7.5(3x), and on to infinity

[tawny totem]

I have no idea how to format this in anything but a word problem.

so my question is, how would this be graphed

where would I even start

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[tawny totem]

I’m not leaving until someone wastes their time trying to understand the sh**y question just to give up after ten minutes

I don’t care if I have to sit here another three hours, I need closure

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[pastel verge]

Hi

[tawny totem]

hello

[pastel verge]

I don't understand some parts of your question

y=1.7x is not exact for 16$ in 9hrs btw

[tawny totem]

there’s a reason I dropped out of ap math :^)

I’d just ignore that though, it isn’t crucial

[pastel verge]

I understand the half part but the other half part is worded in a way its hard to interpret, I can help you if you can put in in stepwise words

[tawny totem]

Sure

[pastel verge]

Is this the question as the book says?

Or you can post image too

[tawny totem]

No to both

I thought of this problem* a few months ago while sitting in a class, couldn’t find an example of what I’m imagining the graph would look like, and now I’m here

pretty awful explanation, I know

[pastel verge]

So ok if you can put the question in good stepwise sentences then I can interpret what you on

[tawny totem]

I’ll try

Timmy makes 17$ over the course of 9 hours

for every three hours played, he gets a permanent +0.02% increase in all cash earned.

this +0.02% increase accumulates up until it has been “achieved” 50 times

after that, the cycle must take two and a half times longer to complete.

this loop is repeated, and when it reaches the next “goal”, the next “wave” of bonuses will take 2.5 times longer than what it had took before

so it takes 150 hours to complete the first cycle, 375 for the second, 973.5 the third, and so on

this is to get through all of them, not each of them individually

[pastel verge]

And what do you want to find by this?

[tawny totem]

I just want to see how this would be graphed.

or if there’s any equation to show what I’m asking

[pastel verge]

It will be a piecewise graph if you are plotting time vs money

You will get linear equations

An increasing graph whose slope decreases after some time

Tell me one thing about 2.5% increase

0.02%*

[tawny totem]

yes

[pastel verge]

Is it applicable for the cash you get in previous 3 hrs or the cash you get the while time

Like after 6 hrs whatever amount you have to from 3-6 hrs

[tawny totem]

it is only applicable to any cash gained at the moment the bonus was unlocked or after the bonus was unlocked. anything earned beforehand is unchanged

[pastel verge]

Ok then it will be linear equations for every intervals as I said

[tawny totem]

Okay

[pastel verge]

For first 0 to t=3 it will be y=1.7x
Then at 3 you add 0.02% giving a vertical line from y=1.7(3) to y=1.0002(1.7×3)
Then the other line will be from 0 to t=6
y=1.7(x-3)+1.0002(1.7×3)
And so on such linear functions

[tawny totem]

I haven’t exactly covered interval notations… or anything beyond algebra one… so is there an equation someone like me could use to see how you change slopes at a certain point in the graph, in this case doing y=1.02(1.7*3)?

totally not going to paste it into desmos and stare at it for another half hour.

[tawny totem]

I’ll figure something out eventually

.close

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[stark coyote]

arent all of these propositions?

[stark coyote]

i forgot since this lesson was like last week

[lean otter]

No they are not all propositions

Although, who wrote the answers there?

[stark coyote]

idk it was an example

[lean otter]

Did you write them or someone else?

[stark coyote]

someone else

[lean otter]

Huh well they aren’t all right

[stark coyote]

which ones exactly

[lean otter]

Well ok 3 has no meaning without defining x

So I guess I wouldn’t call it a proposition

[stark coyote]

so if "x" were given a definition within the statement it would be a proposition? Or if "x" itself was something like a number?

[lean otter]

Yea if there was a “let x be …” or whatever then it would be a coherent statement

And a proposition

[stark coyote]

what about 2?

[lean otter]

What about it? Answer is fine as is

[safe radish]

@stark coyote Has your question been resolved?

[safe radish]

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[halcyon aurora]

<@&286206848099549185>

[lost lodge]

the formula for the mean before is all the times in minutes added divided by the amount of times

let's call that a sum of all the values from the 21 year old category, like this

that weird little thing means the sum, btw

so, can you do the mean right now by adding all the times in the 21 yar old class?

then i'll explain the rest

[safe radish]

@halcyon aurora Has your question been resolved?

[halcyon aurora]

What is number of times mean?

[lost lodge]

the number of times is the amount of ''scores''

[halcyon aurora]

So we add all of these right?

[lost lodge]

so you count the amount of time people scored, and it's 8

[lost lodge]

that's right. then you divide it by 8, which is the count of scores

and you'll have the mean

so just calculate that, and i'll explain the rest

[safe radish]

@halcyon aurora Has your question been resolved?

[halcyon aurora]

@lost lodge one min

[halcyon aurora]

So for denominations I add these values ?

And divide by 8

?

[safe radish]

@halcyon aurora Has your question been resolved?

[halcyon aurora]

@lost lodge is the final answer 15.6??

Ping me please

[lost lodge]

sorry, had an internet outage, i'll double check

[lost lodge]

yup! that's correct. can confirm

[halcyon aurora]

Ohh

It’s ok

[halcyon aurora]

thank you

[lost lodge]

basically, you know the new mean of 13.6 would be the previous values plus sam's time whole thing divided by 8+1

[halcyon aurora]

Also I had few questions to what checked could u please check if u don’t mind

[lost lodge]

it's all about applying the formulae

[halcyon aurora]

I see I did the same

[lost lodge]

of course! show me them, i'll try

[halcyon aurora]

My friend got a different answer so I’m confused

[lost lodge]

just looking at it, i can tell your answer is wrong by your calculations. standard deviation basically means consistency [it's based off of how far you are from the mean in your results], so a lower standard deviation is better

i'll double check your calculations though, just to make sure

[halcyon aurora]

Is this correct then?

[lost lodge]

no, for the same reason: the lower standard deviation, the better and more consistent

[halcyon aurora]

How about the calculations?

[halcyon aurora]

So c is Ray

[lost lodge]

i got 1.05 for roy so far [which is correct in this one], i'll check ray now

are you sure you didn't confuse the table and mix up goals scored with frequency or anything similar?

it should be ray

the calculations in the screenshot [the 2nd pic you sent me] seem correct

[halcyon aurora]

Ah understood thank you

Can I ask a few more ? Please

[lost lodge]

feel free to

[halcyon aurora]

Thank u

[lost lodge]

i got 6.0444444 for the mean, just do 6. i got the same standard derivation though

[halcyon aurora]

Right

[lost lodge]

for D, did you mean 179/282?

everything else is correct

[halcyon aurora]

182

[lost lodge]

well, there's 564 unemployed people, and there's 358 unemployed females, and we're saying that the selected person is unemployed for sure, the probability should be 358/564, then simplify for 179/282

[halcyon aurora]

Ahhh ok makes more sense

@lost lodge I got few more if u don’t mind

😅

[lost lodge]

it's fine, just tell me em

[lost lodge]

LOL, i haven't done these questions for a long while. i'm probably not the guy to ask. try asking in the topic channels, because they're specialists and i'm not

[halcyon aurora]

Ah ok

Thanks a lot tho

Which channel do I ask in

[fathom pivot]

wait a second

let me see if i remember that

[halcyon aurora]

Oh ok

[fathom pivot]

just one doubt, how much time does each activity take ?

this format is confunsing me

[halcyon aurora]

The ones in brackets so example A(4) so time is 4

Does that make sense?

[fathom pivot]

aaa ok

[fathom pivot]

yess

@halcyon aurora

If i did all correctly this is the AON

AOA confuses me a lot

[halcyon aurora]

What’s this

[fathom pivot]

an excel

[halcyon aurora]

Which one will be the answer then

[halcyon aurora]

What’s AOA

[fathom pivot]

i'm trying to remeber

[fathom pivot]

sorry , i did the AOA and not AON

AOA activity on arrow

AON activity on node

[halcyon aurora]

Ahh ok

[fathom pivot]

bt if i have the variance the amount i can reduce etc etc

we can reduce it to the mimimun time possivble

[halcyon aurora]

I’m confused

U subtract start with finish?

[fathom pivot]

i subtract late finish - duration to found the late start

the slack is late finish - duration - early start

https://www.velopi.com/insights-and-resources/post/pmi-pmp-free-project-management-resource-AoA/

[fathom pivot]

AOA

sorry if i made you confused

[halcyon aurora]

Ahhh

[halcyon aurora]

Did know it was called aoa

Thanks for the info

[halcyon aurora]

No it’s ok

But like can u tell which ones of the answers are wrong?

[fathom pivot]

so early time is early start ?

and late time late start ?

[halcyon aurora]

Yes

[fathom pivot]

hmm ok

actually, i don't think it's early/late start

[halcyon aurora]

Why

[fathom pivot]

because why not early start / late finish ?

or start/ finish ?

[halcyon aurora]

Yes this

[fathom pivot]

so you just need to check the upper left and right boxes here right ?

[halcyon aurora]

Yes

[halcyon aurora]

I think so I might be wrong

[halcyon aurora]

@fathom pivot I think I grinding thanks a lot

@lost lodge @fathom pivot can anyone check this

[fathom pivot]

don't know this topic

sorry

[safe radish]

@halcyon aurora Has your question been resolved?

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[grand cave]

Does anyone follow this

[safe radish]

@grand cave Has your question been resolved?

[grand cave]

<@&286206848099549185>

[hollow mountain]

What do you need help with

[grand cave]

part 4 onwards

[hollow mountain]

You have shown Q1) i) ?

[hollow mountain]

vi) is true is called condensation lemma of Cauchy

Ok let's begin With iv)

I hope what you have done before is true

[grand cave]

me too

Sure

@hollow mountain ?

[safe radish]

@grand cave Has your question been resolved?

[glacial sage]

A car starts braking at 90km/h. It stops after 500m. What is the value of deceleration and how long did it take to stop if deceleration in constant?

[grand cave]

Just use suvat bro

And use a different chat

[grand cave]

<@&286206848099549185> anyone?

[safe radish]

@grand cave Has your question been resolved?

[grizzled fossil]

Integral test works for both series

[grand cave]

which part

[grizzled fossil]

7 and 8

6. is just using 5)

[grand cave]

Can you explain an integral test please?

[grizzled fossil]

Your book should have it (otherwise you can’t use it)

[grand cave]

And that will work?

[grizzled fossil]

Yes?

[grand cave]

is integral test similar to ratio test

[grizzled fossil]

Why don’t you check your book and find out

[grand cave]

I don't use a text book

[grizzled fossil]

Surely you have been taught following some syllabus

So check whatever that is

[grizzled fossil]

.

what have you done then?

[hollow mountain]

For the Riemann series the integral test is not necessary

For Bertrand séries it's more complicated

[grizzled fossil]

can't use ratio and not really comparison either. Idk what you mean with radius lemma

[hollow mountain]

If you take p>1 and u_n=1/(n)^(p-1)

[grand cave]

I think we've covered that yeah

[hollow mountain]

You know that the serie u_n-u_(n+1) converges

And if you calculate an equivalent you get the Riemann series

Question 6 can be generalised to any integer as long as the sequence is positive and decreasing

[grand cave]

@grizzled fossil how can I integrate (a)k

[hollow mountain]

You have to read your course about integral test

There is no way you have to invent it in a sort of homework paper

[grizzled fossil]

integrate a_k? Wdym? No a_k in 7) or 8)

[grand cave]

I mean

1/k

What does p' mean

[grizzled fossil]

says what p is in the question

[grand cave]

why is there a ''

[grizzled fossil]

that is a comma

[grand cave]

But why is it there

oh

I see

[grizzled fossil]

because you use commas in sentences in English

[safe radish]

@grand cave Has your question been resolved?

[safe radish]

@grand cave Has your question been resolved?

[safe radish]

@grand cave Has your question been resolved?

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[lean otter]

How do I determine the direction of a vector when a or x is 0

[safe radish]

@lean otter Has your question been resolved?

[inland ivy]

Wdym? @lean otter

[safe radish]

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[lean otter]

question

[lean otter]

32 stones, all of different weight, are given. Is it possible to find the heaviest and second heaviest stones using standard two-sided scales in 35 weightings?

my solution:

We can weigh the 32 stones in groups of 2 and then take the heaviest of those. This takes 16 weighings. From those 16 we split into two groups and take the heaviest, which is 8 weighings. We do the same thing again for 4 weighings the to the heaviest. Then we do the process one more time in two weighings to get the 2 heaviest stones. The heaviest out of those 2 is the heaviest stone out of all three. 
        To get the heaviest stone, it take 16+8+4+2+1=31 weighings. To get the second heaviest stone is a bit different. We know that the second heaviest stone in each “round” (when we take the heaviest from the groups of two) could be a potential second heaviest stone out of all 32. We have 5 of these potential stones, (the 5 “rounds”), and it takes 4 weighing to find the heaviest stone. Therefore, the total number of weighings it will take to find the heaviest and second heaviest stone is 31+4=35. Q.E.D.

is it good?

there is some wording that i dont like

<@&286206848099549185>

[lost patrol]

...?

It is okay, why?

What do you want to change in it

[lean otter]

i think the wording is bad

[lost patrol]

We can say like

We can weigh the 32 stones in pairs and take the heaviest of the two for the next pair.

[lean otter]

instead of what sentence

[lost patrol]

The first

[lean otter]

is that all?

[safe radish]

@lean otter Has your question been resolved?

[flint ledge]

@lean otter you have two channels open

close one of them

[lean otter]

ok

.close

[safe radish]

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[bronze rivet]

How do I algebraically explain why a certain exponential function has no x intercept

[bronze rivet]

I replaced the y with 0 but now what

or verbally idk I just don’t know what the next step is. Like I could simplify it but what’s the point if I know that it has no x int I just don’t know how to explain why

[dense yacht]

What it means to a function not have a x-intercept? Can you picture what is going on with this functions?

[bronze rivet]

yes

[dense yacht]

So, what is going on with these functions?

[bronze rivet]

I just realized that it wouldn’t meet x because of an asymptote?

[dense yacht]

Yes, that right... but algebrically, what can you say about these functions? Are you analysing an specific function or are you evaluating the whole class of exponential functions?

[bronze rivet]

A specific one

I made it up right now so let me show u

[dense yacht]

What are the possible values of this function?

[bronze rivet]

Horizontal asymptote at 38 so it won’t go below that but like how would I explain it

That it won’t have a x int? Will I just say that it has a ha

[dense yacht]

I would explicitly say that the function has positive values. For all x, the function is a positive number (> 38).

But analytically, you could convince people of this by showing the asymptotes (using limits, if this is apropriate for what you are arguing).

[bronze rivet]

ahh I see

that makes sense thank you so much

[dense yacht]

If for all x, the function is positive, then it never crosses the x-axis.

(assuming continuity... it always coulf jump....)

[bronze rivet]

Yeah that’s true

[dense yacht]

like -1, 1, -1, 1, -1, 1 .....

[bronze rivet]

Got it! Thanks for explaining. I know the concepts I’m just horrible at communication

so ya now it’s good that I’m able to understand how and why instead of just following an order

[lean otter]

why is that necessary?

[dense yacht]

@lean otter, you are right... if it is always positive, it never has a zero value. I miscommunicated what i was thinking (in general, the existence of the x-intercept by analysing the sign of the function depends on continuity, since the functioun could jump from positive to negative, without actually crossing the axis. BUt if it is always positive, then it never crosses the x-axix at all)

Does it make sense?

[lean otter]

are you asking me?

[bronze rivet]

.close

[safe radish]

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[north raven]

will these be valid for any x or does x have to be acute or sth?

[safe radish]

@north raven Has your question been resolved?

[bright crow]

Any real number x. In tan(x) excluding the points where it is undefined

[north raven]

.close

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[hardy crater]

hi, can i get some help with this

[safe radish]

@hardy crater Has your question been resolved?

[hardy crater]

<@&286206848099549185>

[quartz delta]

Hey, I-m guessing that if the answers aren't too difficult the sqrt(7) part on the x^2 term must cancel with x

so like $2sqrt(7)x^2 = x$ which is true for $x = 0$ or $x = \frac{1}{2\sqrt7}$

but then you don't get x^4 = 7, which is sad

[flat frigate]

TC159

[quartz delta]

it doesn't have a neat solution, checked wolframalpha

[lean otter]

$x^4-2\sqrt{7}x^2+x+7=\left(x^2-\sqrt{7}\right)^2+x=0$

maybe this could help

[flat frigate]

Cüneyt

[hardy crater]

this seems good, idk how didnt thought of that

[quartz delta]

that tells you that x is negative.

[lean otter]

exactly

im supposing we are working on real numbers

[quartz delta]

it doesn't have neat solutions

[hardy crater]

i think so

i wasnt given any other info

[quartz delta]

what's left to the x^4?

there's something to the left of x^4

[hardy crater]

probably equals

i just redirected what i was sent

[quartz delta]

from whom?

teacher?

[hardy crater]

my professor

ye

[quartz delta]

This doesn't have neat solutions.

https://www.wolframalpha.com/input/?i=x^4+-+2*sqrt(7)*x^2+-+x++%2B+7+%3D+0+

you can check if you'd like.

I'd probably do a substitution for x, $x= \sqrt{7} + r$

[flat frigate]

TC159

[lost lodge]

i don't suppose any polynomial with an irrational square root in it would have a ''nice solution''

[quartz delta]

I'm including solution like $\sqrt{5} + 1$ as simple solutions

[flat frigate]

TC159

[lost lodge]

oh, alright then

[quartz delta]

$x^4 - \sqrt{7}x^2 + 7x - 49 = 0$ has a neat solution

[flat frigate]

TC159

[quartz delta]

that being sqrt(7)

[hardy crater]

.close

[safe radish]

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[mossy kindle]

I believe I have the right process on how to get the answer

but I'm not sure

Could someone please tell me if this is correct and if it isn't what I did wrong

.close

[safe radish]

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[bronze rivet]

How do the intercepts of a log and exponential relate. Assuming that the log and exponential in question aren’t inverses of each other

[safe radish]

@bronze rivet Has your question been resolved?

[bronze rivet]

.close

[safe radish]

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[lean otter]

now. explain this to me-

[lean otter]

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[lean otter]

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?