help-23

[lean otter]

no x<y

[strong sentinel]

dont understand sry

[lean otter]

if x<y x-y<o then y-x > 0

ok

ok

??

[strong sentinel]

yep

thanks ❤️

[lean otter]

negative multiplication if it's 0<

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[warped lotus]

An I.I.D sample of 10000 flight reservations was collected and in this sample , 5% of the passangers did not show up.
Question: Bound the probability that if 100 tickets are sold , all 100 people show up.

The hint in this question is:
Bound the probability of both events happening simultaniously and plug in the worst case scenario for p. (it also mentions this is a frequentist rather than a bayesian question)

My attempt: Find a bound for P using the 10000 reservations sample and then plug in a value of P in the expression P^100 (which is the binomial formula that 100 people show up) but I can't get anywhere using this as I have no idea how to get rid of the Binomial (10000 , 9500) or any of those big numbers/powers in order to solve it.

[warped lotus]

(my attempt)

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<@&286206848099549185>

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[warped lotus]

bruh

[warped lotus]

An I.I.D sample of 10000 flight reservations was collected and in this sample , 5% of the passangers did not show up.
Question: Bound the probability that if 100 tickets are sold , all 100 people show up.

The hint in this question is:
Bound the probability of both events happening simultaniously and plug in the worst case scenario for p. (it also mentions this is a frequentist rather than a bayesian question)

My attempt: Find a bound for P using the 10000 reservations sample and then plug in a value of P in the expression P^100 (which is the binomial formula that 100 people show up) but I can't get anywhere using this as I have no idea how to get rid of the Binomial (10000 , 9500) or any of those big numbers/powers in order to solve it.

[warped lotus]

. my attempt

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@warped lotus Has your question been resolved?

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@warped lotus Has your question been resolved?

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@warped lotus Has your question been resolved?

[cunning trail]

does this help?
P (B ∣ A)= P (B ∩ A) / P (A)
I think you should draw a Venn diagram or a double entry table to resolve the problem (but I'm not sure I'm right :x)

[warped lotus]

The question asks me to use a frequentist approach instead of bayesian approach
so I believe I cannot use the bayesian formula for conditional probability

it says that because we dont know pior info about p we should not use bayesian formula

but mhmm even if I used this formula I don't see how I can find the answer
I would call event A - 100 people show up when 100 tickets are sold
and B - 9500 show up when 10000 tickets are sold

mhmm

[cunning trail]

sorryy idk :(

[warped lotus]

:((( its okay !! thank you anyways !!

[warped lotus]

i still need help

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@warped lotus Has your question been resolved?

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@warped lotus Has your question been resolved?

[warped lotus]

<@&286206848099549185>

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@warped lotus Has your question been resolved?

[fossil orchid]

@warped lotus you still need help?

.close

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[ornate lark]

why cant i solve this using similar figures: A steel pipe is being carried down a corridor problem

[ornate lark]

stewart book problem 54

[worthy hemlock]

A picture of the problem would help

[ornate lark]

Yes I will post wait

Why can’t I do this

@worthy hemlock here is the picture

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[ornate lark]

<@&286206848099549185>

need advice for that problem

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@ornate lark Has your question been resolved?

[sour jay]

Why is it 9-x?

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[spice beacon]

I'm stuck and I'm not sure if I did something wrong

[spice beacon]

So it's like

Y=-2x²+8

Which I think equals to just x=2

But then

Is it

[thin bridge]

your mistake is you dropped the $\pm$ sign

[flat frigate]

ℝamonov

[spice beacon]

I'm sorry?

Could you elabore a bit further

OOOH

So

8/4

And -8/4

?

[thin bridge]

yeh

[spice beacon]

Ahhh

One more question

You see in that case

Is it
-2.2²+8
-4²+8

Or

-2.2²+8
-2.4+8

??

[thin bridge]

the latter

[spice beacon]

Thanks

That's it

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[frosty oyster]

my teacher didint explain what to do and jus gave us this

[frosty oyster]

what do i do???????

nvm

found out

lol

[foggy salmon]

lol

gj

[frosty oyster]

.close

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[hexed pumice]

i need help in differentiating this function

[hexed pumice]

oh wait i think there's a more appropriate channel for this mb

.close

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[wintry mantle]

vectorspace: M = {f | f [−1, 1] → R}
Is U1 := {f ∈ M | f(x) ≥ 0 for all x ∈ [−1, 1]} a subvectorspace of M?

My friends and I have been discussing this one but we could not find a solution 😦

[wintry mantle]

Another question:

Let V be the Q-vector space of the real numbers R and W the R-vector space also of the real numbers R. By changing the basic body we get different subspace terms. Decide and justify,
which of the following subsets are subspaces of V or W:

I need help with c,d,e but also I would not mind to have a solution to check with for the other ones

[final halo]

You only have 3 things to check

[wintry mantle]

@final halo 0 is in U1, f(x) + g(x) is in U1 and n*f(x) is in U1 => should be a subvectorspace, but I was wondering whether it was a problem that f(x) can't be lower than 0

[final halo]

Why would that be a problem? You should have used that fact to prove the 3 things you listed

[wintry mantle]

@final halo ok thanks, do u have some tips for the other task?

[final halo]

Do the same thing

[wintry mantle]

@final halo what is Q-vector space of the real numbers? I'm not sure what exactly that is

[final halo]

The scalar multiplication is by elements of Q, instead of R

[wintry mantle]

@final halo so the elements in that can only be out of Q?

[final halo]

No that's not what I said

It's the vector space R, with scalar multiplication given by timesing by elements of Q

When you write down a vector space you have to specify which field its over

[wintry mantle]

@final halo could you give an example?

[final halo]

You've been given the two easy examples

Take the real numbers, and define scalar multiplication either by timesing by elements of R or by elements of Q, this defines two different vector spaces

[wintry mantle]

@final halo ok makes sense, then b would only be subvectorspace of W right?

[final halo]

Why not of V

[wintry mantle]

.close

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[mighty phoenix]

i am solving this question with substitution
i put x^2 - 1 = t

[mighty phoenix]

after diffrentiate i got 2x dx = dt

after that i right x^3 like x^2 .x and
the put in equation so i got (t+1) .x / sqrt(t) .dt/2x

what should i do next

[grizzled fossil]

Don’t you have smth that cancels?

[peak estuary]

Cancel the x's. Split the fraction

[grizzled fossil]

I see x in numerator and denom

[mighty phoenix]

ok

then i left with (t+1)/sqrt(t) . dt/2

is this right ?? @peak estuary

[grizzled fossil]

Could for example sub again

[mighty phoenix]

what

i don't understand what you're trying to say

[grizzled fossil]

You have a new integral after your substitution

You need to solve this

So use whatever method you want, say substitution again

[mighty phoenix]

yaa

so it will be (t+1) and i can write sqrt(t) as t^1/2 and if i reciprocal that it will become t^-1/2

@grizzled fossil

[grizzled fossil]

Ok?

[mighty phoenix]

what about the 2 that's in denominator of dt

[grizzled fossil]

What about it?

[mighty phoenix]

how should i solve that

[grizzled fossil]

What?

$\int \frac{t+1}{\sqrt{t}} \cdot \frac {1}{2} ; dt$

[flat frigate]

ScapeProf

[grizzled fossil]

Is your integral

Solve this whatever way you want just like any other integral

[mighty phoenix]

ok

.close

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[lean otter]

how do you find the extreme values of a function without the graph given

[lean otter]

eg $f(x)=2x+8$ how do i find the extreme values??

[flat frigate]

miky

[turbid raven]

usually you take the derivative and check where it equals 0

[tall bough]

Derivative det to zero

[lean otter]

2x+8 has no extrema

[tall bough]

Yes

[turbid raven]

yeah, it can be shown when you take the derivative and at no point it equals zero, it's just a constant

[lean otter]

yea that’s the problem

[red tapir]

hello

[lean otter]

ive not taken derivates yet

hi

[turbid raven]

ok you can graph the function

[lean otter]

then find the extreme values?

[turbid raven]

yeah you could just point them out

[lean otter]

oh

so simple

im so sorry for the question then

[turbid raven]

just use intuition, you will see that x is a slope that goes on forever right?

[lean otter]

yea

it’ll go on forever either way

[turbid raven]

it's monotonous all the way, no extrema

then just prepare for the same, but with parabolas

[lean otter]

tysm

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[prisma epoch]

Can someone explain how to simplify 1-tan^2 theta/sec^2 theta

[bold ferry]

use $sec^2(\theta) = 1 + tan^2(\theta)$

[flat frigate]

kihei

[prisma epoch]

i got it

i had one more question

how do we simplify cos^2 theta-sin^2 theta

@bold ferry

[lean otter]

@prisma epoch ${cos(\Theta)}^2+\sin^2(\Theta)=1$

[flat frigate]

[Master Chief [117]]

[prisma epoch]

i need it in minus

[lean otter]

in minus?

Whats the question?

What are you solving for?

[prisma epoch]

cos^2 theta-sin^2 theta

[lean otter]

equals?

[prisma epoch]

i need to prove that cos^2-sin^2=1-tan^2

[lean otter]

Do you know what tan^2(theta) is equal to?

${cos\left(\Theta\right)}^2+\sin^2\left(\Theta\right)=\left(\frac{cos\left(\Theta\right)}{cos\left(\Theta\right)}\right)^2-{tan\left(\frac{sin\left(\Theta\right)}{cos\left(\Theta\right)}\right)}^2$

[flat frigate]

[Master Chief [117]]

[lean otter]

Consolidate the cos as it's an equal value on the fraction

[prisma epoch]

k i got the answer

.close

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[lean otter]

You did?

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[rare hearth]

Can I get help with this?
5.6

To find out how long a roll of 1 mm² copper wire is, the wire roll is connected to 4 V DC. Then 1 A is measured through the copper line. How many meters of wire are there on the roll?

5.7

A portable generator must supply electricity for lighting and heating to a consumer. The distance is 500 m. A 2 x 2.5 mm2 cable with copper conductors is used from the generator to the consumer. The cable carries a current of 20 A.
a) Calculate the voltage drop in the cable.
b) Calculate how high the generator voltage must be for the voltage at the consumer to be 230 V.

[quasi bison]

@rare hearth have you made any progress with either of these?

[safe radish]

@rare hearth Has your question been resolved?

[regal girder]

I believe for 5.6 you'd use this and ohm's law

5.7 seems similar too

[quasi bison]

yes

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[rare hearth]

Yeah, all I need help with now is 5.7 b

[rare hearth]

Not that I understand it though, a friend in class helped me

[quasi bison]

have you calculated the voltage drop across the cable

i.e. 5.7a

[rare hearth]

I think it's 140V

Might be wrong, but well

[quasi bison]

well, the generator voltage is the desired consumer voltage plus that.

[rare hearth]

Uhm, alright. Thank you, I'll try that

.close

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[broken wagon]

need someone to help me step by step to put these fractions together and writing it as simple as possible

[visual patio]

$\frac{a}{a^2-a}-\frac{3}{2a-2}$

[flat frigate]

ItzAine

[broken wagon]

yes

[lean otter]

that is equivalent to $\frac{1}{a - 1} - \frac{3}{2(a-1)}$

[flat frigate]

trololol !

[lean otter]

which is equivalent to $-\frac{1}{2(a-1)}$

[flat frigate]

trololol !

[broken wagon]

very confused

[visual patio]

on which part?

[broken wagon]

everything trololol said

[visual patio]

okay

[visual patio]

continuing from this

$\frac{a}{a\left(a-1\right)}-\frac{3}{2\left(a-1\right)}$

[flat frigate]

ItzAine

[visual patio]

do you understand this?

[broken wagon]

right so i have to factorize them both

yes i understand

[visual patio]

yes so it can be simplified further

[broken wagon]

understood

[visual patio]

on the left side there is $$\frac{a}{a\left(a-1\right)}$$
and that will be $$\frac{1}{1\left(a-1\right)}$$

[flat frigate]

ItzAine

[visual patio]

so $$\frac{1}{1\left(a-1\right)}-\frac{3}{2\left(a-1\right)}$$

[flat frigate]

ItzAine

[broken wagon]

one question

[visual patio]

and so it will be $-\frac{1}{2\left(a-1\right)}$

[visual patio]

sure

[flat frigate]

ItzAine

[broken wagon]

when i was factorizing a^2 i got a(a) but since there wasnt anything on the right side of - left am i supposed to add a 1 there to replace it?

[visual patio]

what exactly are you factoring?

[broken wagon]

not even sure if thats the right word for it, im not english

but making it a(a-1)

as you have it on the picture

[visual patio]

a^2+a is a(a+1)
a^2 is a(a)

it is - because from the question it is a^2-a

[broken wagon]

but there’s a^2-a

[visual patio]

a^2 - a = a(a-1)
a^2 + a = a(a+1)

[broken wagon]

how does that become a(a-1

right so its replacing the a you cross out with a 1

right?

[visual patio]

you can prove it by doing a(a-1)
a * a = a^2
a * -1 = -a

[broken wagon]

isnt it just putting a one in there instead of it being empty?

[visual patio]

if its empty then it would just be a^2

and not a^2 - a

try doing this on a piece of paper a(a-1)

what result do you get

[broken wagon]

i get a*a-a

then arent i supposed to cancel the a on the right and left of minus sign

[visual patio]

a*a is a^2

[broken wagon]

yes

[visual patio]

it doesnt cancel

it only will cancel if its a negative number multiplied by a negative number

eg. -5 * -5 = 25

[broken wagon]

alright so why’s there a 1 on the end

[visual patio]

because -a is the result of a * -1

[broken wagon]

is there a reason why it doesnt just say -a there tho

[visual patio]

like a(a-a)?

[broken wagon]

yes

[visual patio]

a(a-a)
= a(0)
= 0

a number minus itself is equal to 0

[broken wagon]

so its being replaced to not make 0

[visual patio]

its not replaced

its just math

a^2 - a is the same as a(a-1)

[broken wagon]

right i dont see how that makes sense in my head but lets just move on in the task and ill hopefully understand more

[visual patio]

alright I suggest going online and looking at some factors and examples while you go along that way you may understand it more

[visual patio]

but after this

you can pretend (a-1) is x

$\frac{1}{x}-\frac{3}{2x}$

[flat frigate]

ItzAine

[visual patio]

$-\frac{1}{2x}$

[flat frigate]

ItzAine

[visual patio]

and replace x with (a-1) again

$-\frac{1}{2\left(a-1\right)}$

[flat frigate]

ItzAine

[broken wagon]

the answer is supposed to be 1/2-2a btw

so i dont know if i have gotten to the point where im supposed to replace things with x

why does it go from 3/2x to 1/2x?

[visual patio]

this was just to simply think about things

really optional but useful in some cases

[visual patio]

its 1/x - 3/2x

[visual patio]

answer must be wrong then 🤷‍♂️

i checked calculator as well, me and trololol ! answer are correct

[broken wagon]

weird

so what exactly is the answer

1/2(a-1)?

[broken wagon]

?

[safe radish]

@broken wagon Has your question been resolved?

[safe radish]

@broken wagon Has your question been resolved?

[safe radish]

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[lean otter]

Yo guys I'm doing a factorization exercise and I don't understand the correction :
2x² - 10x + 8 = 2(x-4)(x-1)

[wispy sentinel]

i can give you a trick for factorization

[lean otter]

Tell me

[wispy sentinel]

lets say an equation $ax^2+bx+c$

[flat frigate]

ayushch80

[lean otter]

Okay

2x² - 10x + 8

[wispy sentinel]

this equation can be factorized if $a * b = $(parts of b)

[lean otter]

2*4

[wispy sentinel]

where parts of b are x and b-x

did you got me

[lean otter]

No

[little blade]

First of all

You see that every term is divisible by 2

[lean otter]

Yes

[little blade]

Take the 2 out

And write whats left

[lean otter]

2(x²-5x+4)

[wispy sentinel]

😦

[little blade]

Now that the x squared term has a 1

You can notice how the -5 (b) is equal to -4 + -1

And 4 (c) is equal to -4x-1

[lean otter]

Yes

[little blade]

This is how you factorise it

[lean otter]

but I don't know why but on the answer key it says 2(x-4)(x-1)

[little blade]

That's what i just said

You get -4 and -1

So it becomes (x-4)(x-1)

And the 2 was already on the front

[lean otter]

Ooh okayyy

[little blade]

Try this one

x^2-7x+12

[lean otter]

Okay

(X-3)(X-4)

[little blade]

Correct

That took you a while

[lean otter]

Okay nice !

[little blade]

But its correct

So good

[lean otter]

Yes xd.

But thanks you !

[little blade]

Yeah there are no methods, a nice thing to do is write down all the factors of 12, in this case, amd seeing which ones sum to 7

And then also multiply to 12

Because for example 6 and 1 would sum to 7 but not multiply to 12

[lean otter]

Okayyyy

.close

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[light crater]

I have this set. Can it be written as a direct product of three sets?

[light crater]

.close

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[lean otter]

Hello, how can i factorize x³ - 3x² + 2x

[sonic spruce]

Factor out what’s common first

[lean otter]

X

[sonic spruce]

Factor that out first

[lean otter]

Its x ?

[pseudo path]

(x^2-3x+2)x

[peak bramble]

^

now work on LHS

[lean otter]

Idk

[sonic spruce]

Can you factor this x^2-3x+2

[peak bramble]

https://youtu.be/U6FndtdgpcA

[lean otter]

I can't

[sonic spruce]

Refer to the source HeadShotCem provided

[lean otter]

Okay

I can't find

@sonic spruce

[sonic spruce]

Did you watch this?

[lean otter]

Yes

[sonic spruce]

so what are you having trouble with?

[lean otter]

Idk just i cant.

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[lean otter]

i have a question

[lean otter]

2;-4,8,-16... is not arithmetic ?

[hardy lion]

no its geometric

[lean otter]

okey ty

[hardy lion]

check the difference between two pairs of adjacent terms

[lean otter]

yeah my exercice is to check if its arithmetic or no

[hardy lion]

2-(-4)=6, -4-(8)=-12

not the same

[lean otter]

.close

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[lean otter]

.close

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[golden hamlet]

hi. so it translates to; you get to know: find the exact value of the side length of BC on the triangle above. Anyway of helping me understand which steps to take in the start?

[rotund zodiac]

what does this mean?

[golden hamlet]

its something true

[rotund zodiac]

and what is it exactly?

[lean otter]

Dot product?

[golden hamlet]

yeah?

[plucky elk]

use this and law of cosines

[golden hamlet]

won't that just be an angle?

[plucky elk]

and law of cosines

[golden hamlet]

in which you mean?

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[mental lagoon]

how can i solve?

[safe radish]

@mental lagoon Has your question been resolved?

[plucky elk]

use the definition of continuous at x=0

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[dense dagger]

The book says bc is 12cm, I'm getting 20

[dense dagger]

What am I doing wrong

[cosmic magnet]

the answer is 0 because you're gonna use
f(x) = a+sinx
so
f(0) = a+sin(0)
f(0) = a+0
ig

[mental lagoon]

Thanks!

[cosmic magnet]

u r welcome

[dense dagger]

Oh shit didn't see thst

.close

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[lean otter]

A test taken by 20 students, consists of 20 problems. Each problem is solved by exactly 12 students, and each student solves exactly 12 problems. Show that there are 3 students, such that every problem in the test is solved by at least 1 of the 3 students.

[lean otter]

I know it involves combinatorics but Im not exactly good at that

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@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

Someone?

Its been 20 minutes

<@&286206848099549185>

Hello?

<@&286206848099549185>

One last time and I guess I will close

<@&286206848099549185>

Rip

.close

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[topaz bear]

Did I graph this right?

[vestal pagoda]

no

[topaz bear]

So I shade inside?

Or like this

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[topaz bear]

<@&286206848099549185>

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@topaz bear Has your question been resolved?

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[compact apex]

hi, i need help simplifying an expression :)

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[final halo]

Stop pinging me

Stop?

<@&268886789983436800> 🤷‍♂️

Im not paid to help you or anyone else, stop pinging me

[gilded scroll]

<@&268886789983436800>

[final halo]

In the time you wasted pinging me you could've figured it out yourself

[gilded scroll]

this is a puzzle. figure it out

i will not help you

[plucky elk]

your service deserves > 0 payment 🙇🏻‍♂️

no i don't help entitled people

you wait just like everyone else

[stable hearth]

you can’t expect people to help you for free

[plucky elk]

stop acting entitled

[stable hearth]

[final halo]

I responded to you not following the rules, and then repeatedly pinging me

[plucky elk]

no one said it's a crime. stop gaslighting

then stop being overdramatic

if you can't wait go pay for a tutor rather than waiting to get FREE help here

[final halo]

I asked you multiple times to stop pinging me and you purposely carried on

Shake your head all you want you've self sabotaged your chances of getting help

[stable hearth]

[final halo]

Grow up child

[stable hearth]

you can’t solve it either

[plucky elk]

<@&268886789983436800>

[gilded scroll]

third time the have been pinged where are they?

you could have

[plucky elk]

.

nobody needs to help

who's paying us? you?

[plucky elk]

maybe if you weren't so entitled

[gilded scroll]

riemann is one of the best helpers here and is incredibly kind and intelligent.

[stable hearth]

you can ping at helpers in general not specific people

[plucky elk]

since you haven't read the rules yet

[gilded scroll]

omg

if i tell you the answer will you behave yourself

[plucky elk]

lol imagine thinking you're smarter than discord history

[warped roost]

sigh

.close

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[gilded scroll]

i have never felt a discord sigh more

[drowsy moss]

Aww, my popcorn just finished too

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[granite cape]

Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel. How old is Kevin now?

[granite cape]

just confused about the second equation, wouldn't it be 4k instead of 4d?

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@granite cape Has your question been resolved?

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[quiet barn]

How do I add this?

[quiet barn]

I genuinely can’t remember

[merry sleet]

$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$

[flat frigate]

Benjamin

[quiet barn]

Ok i got that

Whats next?

Can I add the top?

[mellow rune]

what do u have

after adding them together

[mellow rune]

they share common denominators so yes

[merry sleet]

yeah so

so a+ a =2a

[quiet barn]

Um

[merry sleet]

its the definition of multiplication by 2

its when you add a thing two times

[quiet barn]

Oh I see

[merry sleet]

so the top becomes $2 \sqrt{2}$

[flat frigate]

Benjamin

[quiet barn]

Like this?

I still don’t quite get it, how did $2 appear

[dusk iron]

What don't u get

[dusk iron]

You've cancelled 2

[quiet barn]

Where did the 2 before square root appeared

[dusk iron]

Cuz it's √2+√2

[quiet barn]

Yeah because that was the correct action but I don’t get the step before it

Does that mean anything?

[dusk iron]

Two times √2

[quiet barn]

I feel like I missed on something while in class

Ummm

[dusk iron]

I don't even learn from class lol
YouTube best

[dusk iron]

Ry

T

A+A=2A

[quiet barn]

Does it turn into multiplication if it’s square root plus square root

[dusk iron]

Put A=√2

[quiet barn]

I think I get it

[dusk iron]

No.. They're just numbers lyk the rest of em

[quiet barn]

But what if they are different numbers?

[dusk iron]

You just let them stay

The way they are

[quiet barn]

I see

So only when it’s the same number

[dusk iron]

Yup

[quiet barn]

I got it brobably

[dusk iron]

Otherwise maybe u can do smthg different

[quiet barn]

Did you learn it from that one organic teacher?

[dusk iron]

Byjus ig... Or maybe somewhere else I don't remember.... I'm in 12th rn

Long time...

[quiet barn]

Oh I see

Im in 11th lol

[dusk iron]

Ohh okay... What course r u doin

[quiet barn]

Pre calc

[dusk iron]

https://youtube.com/playlist?list=PLMnHwrPjHwJWXkpecGozL9RFAtgMsVNRv

Check thus out

[quiet barn]

Aight

[safe radish]

@quiet barn Has your question been resolved?

[quiet barn]

Haha no

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[tender mountain]

Please could we do some trigonometric substitution practice together, using $\frac{x^3}{\sqrt{x^2+4}}, \frac{1}{\sqrt{36-x^2}}, \frac{\sqrt{x^2-9}}{x^3}$

[flat frigate]

kangaroo rat

[queen parcel]

If you're trying to integrate each of those functions, start by writing down the 3 pythag trig identities. This will be the basis of your substitutions

[tender mountain]

$sin^2 θ + cos^2θ = 1.
sec^2 θ - tan^2 θ = 1.
csc^2 θ - cot^2 θ = 1.$

[flat frigate]

kangaroo rat

[tender mountain]

what next?

[queen parcel]

Try to take advantage of those identities in your substitutions

Think about the derivatives of your substitutions when finding the differential

[tender mountain]

so could we please use one of my examples?

[queen parcel]

Try thinking it through

Isolate one example and think about how you can end up with something like √(something squared)

So the sqrt cancels

[tender mountain]

use an identity

like 1+cos(x)=?

@queen parcel so for $\frac{x^3}{\sqrt{x^2+4}}$, first replace x with 2sin(theta) $\frac{2sin(\theta)^3}{\sqrt{2sin(\theta)^2+2^2}}$ then factor out 2 from denominator, $\frac{2sin(\theta)^3}{\sqrt{2(sin(\theta)^2+2)}}$ and $sin(\theta)^2+2$ doesn't have an identity?

[flat frigate]

kangaroo rat

[queen parcel]

So you'll need to use a diff substitution

[tender mountain]

what?

[queen parcel]

*different

[tender mountain]

what substitution?

[queen parcel]

Try them out

Don't just blindly try them out, think about what would happen if you were to consider a given trig function for your substitution

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[terse oxide]

If you cut off one of the angles in a triangle, how many angles will be left?

I’m confused by this question, a triangle has 3 angles so is it 2 or am I missing something

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@terse oxide Has your question been resolved?

[hallow egret]

what do you mean by cut off?

Like bisecting the angle?

[terse oxide]

i have no idea thats exactly how the question was written

[hallow egret]

Like split in half? or split in sideways?

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@terse oxide Has your question been resolved?

[safe radish]

@terse oxide Has your question been resolved?

[safe radish]

@terse oxide Has your question been resolved?

[honest vine]

dang bro u been waiting for help sorry idk mabye ping the helpers

[ember sphinx]

yes it would be 2

[obsidian nest]

I need someone to help me

This is so hard

[fierce trench]

My take would be 4

[terse oxide]

This is the answer but can you draw an example pls? I have a hard time visualizing this cause is it just a square then?

[manic jackal]

here i can try drawing it

@terse oxide does this work

[safe radish]

@terse oxide Has your question been resolved?

[warm bear]

This makes sense

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[north hornet]

I need help in solving this problem using the limit definition

yas

I have nothing so far

I was told to use the limit as x approaches to 1

limit of P(x) -P(1) / x-1 as x approaches to 1

and then?

[split ether]

That's the first limit, there's also the second limit

In the second limit you could multiply the top and bottom by the conjugate (in this case, sqrt(1 + h) + 1)

And you'd get h/h(sqrt(1 + h) + 1), h's cancel out and you're left with the limit being 1/2

So what you have is 1 + B * 1/2 = 3

[north hornet]

wait I have a question, from our previous chat where do you get the (-1-B)

[split ether]

That's -P(1)

[north hornet]

wait can we start over hehe

[split ether]

$$\lim_{h\to{0}}\frac{P(1 + h) - P(1)}{h} = 3$$
$$\lim_{h\to{0}}\frac{(1 + h)^2 + B\sqrt{1 + h} - 1 - B}{h} = 3$$
$$\lim_{h\to{0}}\frac{(1 + h)^2 - 1}{h} + B\lim_{h\to{0}}\frac{\sqrt{1 + h} - 1}{h} = 3$$
$$\lim_{h\to{0}}\frac{h(2 + h)}{h} + B\lim_{h\to{0}}\frac{(\sqrt{1 + h} - 1)(\sqrt{1 + h} + 1)}{h(\sqrt{1 + h} + 1)} = 3$$
$$\lim_{h\to{0}}(2 + h) + B\lim_{h\to{0}}\frac{h}{h(\sqrt{1 + h} + 1)} = 3$$
$$2 + B\lim_{h\to{0}}\frac{1}{\sqrt{1 + h} + 1} = 3$$
$$2 + B\cdot{\frac{1}{2}} = 3$$
$$\frac{B}{2} = 1$$
$$B = 2$$

[flat frigate]

A Lonely Bean

[north hornet]

so the possible values for B is 1 and 2?

[split ether]

Just 2

[north hornet]

or just 2

ah yeah I really got it

thank youuu

.close

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[raw pivot]

how can I get ?

[raw pivot]

.close

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[zenith glen]

Need help with (a) here. Please and much thanks

[steep dove]

since (x-4) is a factor of that cubic

plugging in x = 4 should yield 0

use that to get p

[zenith glen]

I thought I had to use long division here…

Many thanks

[shut inlet]

no need to

[zenith glen]

I'll close this channel

.close

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[icy forge]

hi

[icy forge]

,tex $f(x) = -2x^{2} +(m-5)x+4-m^{2} \newline $ is invertible if $x\in(-\infty,\frac{1}{3}] $

[flat frigate]

j0sephTheA

[icy forge]

how to find m

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@icy forge Has your question been resolved?

[icy forge]

<@&286206848099549185>

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@icy forge Has your question been resolved?

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@icy forge Has your question been resolved?

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[dense frost]

Hi, I have a question about probability but I don't live in an English speaking country so I will try my best to translate
A survey of the use of Mastercard, Bancontact and Visa payment cards reveals the following: 86% have at least 1 payment card. 14% have 3 payment cards. 38% have a Visa card. 53% have a Mastercard. 80% have Bancontact. 85% have at least Mastercard or Bancontact. 84% have at least Bancontact or Visa.
How many respondents have at least 2 payment cards?

[safe radish]

@dense frost Has your question been resolved?

[safe radish]

@dense frost Has your question been resolved?

[dense frost]

I think I have to make a Venn Diagram but I'm not sure

[light shoal]

one way would be to find how many have exactly 0 or exactly 1 payment card

then the number with 2 or more would be 100% minus that

finding how many have 0 is easy, you're given something that allows you to know that immediately, do you see it?

btw, this question is worded quite ambiguously, is it assumed that a person can have at most one of each type of card, or could they have two visas for example (I do!)

[dense frost]

yes, they can only have one type of each card so no two visas for one person

so if I find out how many have 0 exactly, I have to find out how many have 1 payment card too, right?

[light shoal]

yes

[dense frost]

but I don't know how to do that, finding out how many only have 1

[light shoal]

the 0 is easy, the 1 less so

the most straightforward way to proceed would be to list the individual outcomes

for example, i could use upper case to indicate that the person has that card and lower case to indicate that he does not have that card, then an example outcome would be MBv (he has a mastercard and a bancontact but not a visa)

how many different outcomes are there?

[dense frost]

85%

[light shoal]

no i mean how many possible combinations of cards

if a person can have 0 or 1 of each of 3 types of card

[dense frost]

sorry, I really don't know

[safe radish]

@dense frost Has your question been resolved?

[empty gyro]

@dense frost you still stuck?

[dense frost]

yep

[empty gyro]

So I would do, like Bungo suggested, would be to try to write down every fact you can determine

So something easy, 86% of people have at least one card, what percentage must have no cards?

[dense frost]

14%

[empty gyro]

yes

and if 14% have 3 cards, what percentage must have 1 or 2 cards?

[dense frost]

but I can't find how many people only have one card

86%

[empty gyro]

not quite

if 14% of people have 3 cards, then you can only say that 86% people of do not have 3 cards (negation)

not having three cards does not guarantee that they only have 1 or 2 cards

Some of them may have zero cards

In fact, we know how many have zero cards, we just figured it out

[dense frost]

72 % then?

[empty gyro]

yes

14% have 0, 14% have 3, and 72% are left who must have either 1 or 2

Now it's time to move to the trickier stuff

I'm just thinking out loud here, so let's hope this works

[dense frost]

i appreciate your help :)

[empty gyro]

np

stats is fun but I'm admittedly not very good at it

Okay, so we know that 38% of people have a visa. But let's exclude the 14% of people who we know have three cards. So how many people own one or two cards and one of the cards is a visa?

[dense frost]

24%

[empty gyro]

yup

And then same thing for master card and bancontact

[dense frost]

so 39% mastercard, 66% bancontact and 24 % visa

[empty gyro]

yeah. And these are factoring people who own just 1 or 2 cards

[dense frost]

what now?

[empty gyro]

thinking

I need to ruminate on these "at least" scenarios

This, admittedly, is a tricky problem

[dense frost]

yeah

[empty gyro]

Okay allow me a little while to really think on this, I suggest you do the same

[dense frost]

yeah, i've been thinking for a few hours now lol

[empty gyro]

Hah

I overthought it hard

[dense frost]

oh really

[empty gyro]

Okay let's remove percentages and say there are just 100 people

How many cards must there be in total?

[dense frost]

300?

[empty gyro]

Only all if all 100 people owned 3 cards

Instead of 38% of people have a visa card, it's now just 38 people have a visa card

[dense frost]

yes

[empty gyro]

and then there are 53 mastercards and 80 bancontact cards, right?

[dense frost]

yes

[empty gyro]

so how many cards is that total?

[dense frost]

171

[empty gyro]

yup

Okay.

Now here's what we know.

There are 100 people and 171 cards between them

But we know 14 people have zero cards

So there are really 171 cards between 86 people.

We know 14 people have 3 cards each

So how many cards does that remove?

[dense frost]

we have 129 cards left then

[empty gyro]

yup

and how many people left?

[dense frost]

72

[empty gyro]

so there are 72 people holding 129 cards total. Each person is either holding 1 or 2 cards

[dense frost]

yes

[empty gyro]

say x is the number of people holding 1 card

How many people are holding 2?

[dense frost]

wait i have to think

how do I do this?

[empty gyro]

In terms of x, how many people are holding 2 cards?

[dense frost]

72-x

[empty gyro]

yes exactly

So if x people have 1 card, and 72-x people have 2 cards, how many cards total is that?

[dense frost]

x+72-x

[empty gyro]

nah that's just number of people

remember, 72-x people have 2 cards

So how many cards is that?

[dense frost]

129

[empty gyro]

nah that's how many cards total between the 72 people total

Here's a hint, of the x people holding 1 card, there are x cards total.

[dense frost]

72 then?

[empty gyro]

So of the 72-x people holding 2 cards, how many cards are there among just them?

[dense frost]

55?

[empty gyro]

Let's try it a different way

[dense frost]

oh no

[empty gyro]

First, super simple

[dense frost]

57?

ok ok

[empty gyro]

If one person is holding two cards, how many cards are there total?

[dense frost]

2?

[empty gyro]

yeh

[dense frost]

hahah

[empty gyro]

And if 2 people are holding 2 cards each, how many total?

[dense frost]

4

[empty gyro]

and if x people are holding 2 cards each?

[dense frost]

2x?

[empty gyro]

yes exactly

So, finally, if 72-x people are holding 2 cards each?

[dense frost]

2(72-x)

[empty gyro]

precisely.

So x people are holding x cards

And 72-x people are holding 2(72-x) cards total.

So how many cards is that altogether among the two groups (in terms of x)?

[dense frost]

x+2(72-x)

[empty gyro]

yup

But, we know that the total is actually 129

You know what to do now?

[dense frost]

find x?

[empty gyro]

yup

[dense frost]

ok let me try

uhh my answer is negative, i think i'm doing something wrong

[empty gyro]

can you show your work?

[dense frost]

129 = x+2(72-x)
= x+144-2x

oh wait

found it i think

[empty gyro]

sweet

[dense frost]

is it 15?

[empty gyro]

yes

nice

[dense frost]

:D

[empty gyro]

Remember what x represented?

[dense frost]

yes, people with only one card

[empty gyro]

yup

So, finally, to answer your question, how many people have 2 cards?

[dense frost]

so it's 100% - 14% - 15 % = 71%

[empty gyro]

You're missing another 14%

One for 0 cards, and one for 3 cards

[dense frost]

but if the question is how many people have at least 2 cards, isn't the 14% also part of the at least 2 cards?

[empty gyro]

oh you are right

I thought it asked for exactly 2

good job

[dense frost]

:)

thank you so much :D

[empty gyro]

np

funny that the rest of those percentages didn't help at all.

Perhaps this is just part 1 of a problem?

[dense frost]

no, that was the only question

[empty gyro]

wild

Well congrats

Rest easy my child

[dense frost]

my teacher probably made it like that to make it harder

[empty gyro]

or perhaps they had another approach

[dense frost]

now i'm wondering, do you live in the us?

[empty gyro]

mhm

[dense frost]

at what age do they teach this kind of stuff?

[empty gyro]

Well this was just algebra.. so... 10-18 years depending on skill of student?

[dense frost]

oh ok, well, i had a hard time understanding the whole thing lol

[empty gyro]

what class you in?

[dense frost]

i just turned 18 and i live in belgium so it's different

i'm in my last year of high school

[empty gyro]

sounds like a first or second year algebra course

I thought it was stats, but just tricky algebra

Pretty standard compared to when I was in high school

[dense frost]

it's in my stats exercises, so maybe there was a different way to solve it

stats means probability right?

[empty gyro]

essentially

[dense frost]

thanks for all the help again, it has finally been solved :)

.close

[safe radish]

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[bold bramble]

@tepid gust im having trouble with this again

[safe radish]

Please don't occupy multiple help channels.

[tepid gust]

I dont have long but whats the trouble

[bold bramble]

what do i do with this to make it vertex

[tepid gust]

If vertex is the same as completing the square which I think it is, then find it from your second line, simplify your first coefficient and then go as normal

#help-21｜아리스킨충1 message

[bold bramble]

where is the other x if its squared

[tepid gust]

Ah I forgot to add something

x^2 + (b/a)x +c/a = y
y = 0
x^2 + (b/a)x +c/a = 0
( x + ((b/a)/2) )^2 - ((b/a)/2)^2 + c =0

So your final form will be (x + a)^2 + b

[bold bramble]

okay i will try this

[tepid gust]

Gl

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[rapid lantern]

can someone help me with the algebra here

how did it become d = from 30 =

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[lean otter]

Can someone help me understand how I should approach solving this question?
Equation: $$ z^5 + 4z^3 - 2z^2 -8 = 0$$

I know how to reduce it to $z^3 = 2$ with the help of long division but what I am failing to understand is that why the solution becomes:
$r = | z | = 2^(1/3)$ instead of using de movier's formula: $$ z = r^n (cos\theta + i sin\theta)^n$$

[flat frigate]

SillyRaccoon

[lean otter]

Why is the text not broken into several lines instead of mashed into one large line in that generated image?

We are trying to find all possible solutions in above question

• is it possible for me to determine how many $\pi$ I need for a whole rotation without graphing the function?

[flat frigate]

SillyRaccoon

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

.closed

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@lean otter Has your question been resolved?

[lean otter]

.close

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[sly mirage]

Can someone help me pls

[safe radish]

Please don't occupy multiple help channels.

[dusk iron]

2 power12

×

3 power 8

Ig

[plucky elk]

You have a channel. Stick to it

.close

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[balmy hemlock]

Guys i need help

[balmy hemlock]

Find the measure of the other angles

[lean otter]

Pain

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@balmy hemlock Has your question been resolved?

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@balmy hemlock Has your question been resolved?

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[fluid condor]

Hi - this is mathcounts 2019 school sprint round last problem and I am unsure of how to go about solving this

the answer is 2 to the 5th if it helps

[solar hazel]

lol i think i helped someone with this problem before

or maybe it was just similar

[fluid condor]

could you explain the process behind what goes into solving this?

[solar hazel]

the person i helped last time was not very happy with my method but i'll try :c

[fluid condor]

any help is appreciated - thanks

[solar hazel]

it will involve a little bit of educated guessing that the answer is 32

[fluid condor]

so its just guess and check?

[solar hazel]

no haha

[fluid condor]

oh haha

[solar hazel]

soooo

so first let's try to imagine what the graph of that function would look like

it's going to be a convex function (yk what that is?) because it's a sum of convex functions

[fluid condor]

i don't... sorry

[solar hazel]

i basically want to say the graph will look like a U

well a sharp U

but a U

[fluid condor]

ok

[solar hazel]

when x is a large negative number or a large positive number, the expression will be a large positive number

and it's convex so it will look like a U

here's what it actually looks like

but really the point i want to make is that if you know roughly what the graph looks like, you can guess where the low point is

in an educated way, not just total guess lol

[fluid condor]

so to solve problems similar to this, i should learn how to mentally visualize a graph and then from there guess?

[solar hazel]

well, not necessarily

but if you have the picture in mind, there's going to be one point where the function changes from decreasing to increasing

and that will be where the minimum is

[fluid condor]

is there some sort of way to find the vertex of this?

[solar hazel]

also we're still not guessing

yea, you can reason through it

[solar hazel]

with this

[solar hazel]

it might help to write all 11 terms out to better see what i'm going to say

but think about the first 5 and the last 5

when you're just changing x when it's near 32 (|x-32| is the "middle" term), the change from the first and the last 5 cancel out

[fluid condor]

thank you so much

[solar hazel]

there's probably a more reasonable way to do this but that's what i came up with lol

[fluid condor]

ok lol thanks so much

.close

[safe radish]

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[lean otter]

Solve the formula for the indicators variable. B(a+c) = ac, for a

[lean otter]

I have my answer and I don’t think it’s wrong but I don’t know how I am supposed to rewrite this

I got a = (ac/B) - c

I think I am supposed to write it all in a fraction but I’m just not sure how I would do that or why my answer isn’t right

Maybe I am supposed to express it solely in terms of B and c?

I never learned all these properties of equality 🙁

I think I have the answer but I want to understand