help-23

[safe radish]

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[worldly anvil]

help

I have this so far

After rationalizing

[vital olive]

i need help with this

z-0.16z=

[elfin yew]

This is someone elses channel! Check out #❓how-to-get-help to get help 😺

[worldly anvil]

ty

<@&286206848099549185>

[safe radish]

@worldly anvil Has your question been resolved?

[thin bridge]

don't bother expanding that product in the numerator
consider multiplying the numerator and denominator by the conjugate of the numerator as well

[vagrant pawn]

yep use conjugate

[safe radish]

@worldly anvil Has your question been resolved?

[worldly anvil]

i tried

[worldly anvil]

so ur saying do the same step twice but one for the conjugate of the numerator and one for the conjugate of the denominator?

[safe radish]

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[fathom wyvern]

I managed to do the Cartesian portion

As for the cylindrical coordinates I got the limits for the dz portion in a general triple integral but I'm getting confused for the r and d(theta) portions, should I split the region for the y and x planes?
For the spherical I'm not able to proceed

[safe radish]

@fathom wyvern Has your question been resolved?

[safe radish]

@fathom wyvern Has your question been resolved?

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[mortal arrow]

what does a root of a function mean?

[fair dagger]

zeros

if f is your function, the roots are those x such that f(x) = 0

[elfin yew]

(or where y = 0)

@fair dagger quadratics are usually taught as y = ax^2 + bx + c not f(x)

[fair dagger]

Okay no idea

He asked explicitely for a function though

[elfin yew]

Oh

Well yeah for a function it'd be f(x) 😛

[fair dagger]

yes I think so 🙂

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[mortal arrow]

.repon

.repoen

.reopen

[safe radish]

✅

[mortal arrow]

so the x intercepts

[elfin yew]

Yup

[safe radish]

@mortal arrow Has your question been resolved?

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[junior wagon]

be really good at adding

[safe radish]

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[tribal cove]

I want to know if my proof is legal or not

[steel stag]

looks good!

[tribal cove]

Ok thank you

.close

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[humble plinth]

Can someone explain what they are asking in simple terms cause the word “parallel” and “m#=m#” is really confusing me
Like I know what parallels are and what angles are but I’m confused on what they want me to do

[thin token]

see

you've got 4 lines

c,d,e,f

[rich fulcrum]

so

iv

[humble plinth]

But then isn’t every angle parallel?

[junior wagon]

nvm

[rich fulcrum]

if i post

my math

in here do i get help

?

[thin token]

in every question there is a situation where two angles are equal

[thin token]

go to unoccupied channels

[rich fulcrum]

mb

[thin token]

bro this channel is occupied

[rich fulcrum]

sorry

i already

sent

[thin token]

delete maybe

[humble plinth]

As I was saying, isn’t every angle going to be parallel since it would be always parallel since there are 4 lines that are perpendicular?

[thin token]

umm, i have a few questions

[junior wagon]

wdym angels are parallel?

[thin token]

how are angles parallel?

[humble plinth]

I have no idea

It doesn’t make sense

[thin token]

lines are parallel

not angles

[humble plinth]

Like maybe lines but I have no idea why this question is like this

[thin token]

ok maybe i can help with the first one

if you want me to that is

[humble plinth]

Sure

[thin token]

so do you know all properties of parallel lines?

like alternate interior angles are equal and stuff

[humble plinth]

Like corresponding, alternative interior, alternate exterior, etc.

Yes

[thin token]

so wrt lines c and d, 2 and 7 are alternate interior right?

[humble plinth]

Yes

[flat tendon]

paralel means 2 lines that will never touch but im not sure about the m stuff

[thin token]

so therefore c and d are parallel lines

[humble plinth]

But if that is true then all the angles there are parallel lines

[thin token]

??

[humble plinth]

3 and 11 are corresponding

1 and 12 are alternate exterior

And 13 and 12 are alternate exterior

6 and 7 are are same side interior

But like then everything is parallel?

???

huh

[thin token]

wait wait

no

we can't comment about 9,10,11,12,13,14,15,16

[humble plinth]

huh

[thin token]

see

alternate interior angles should be equal

for the lines to be parallel

it won't help if they are just present

[humble plinth]

I’m confused a bit

[thin token]

ya i can see😅

[safe radish]

@humble plinth Has your question been resolved?

[misty tartan]

please

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[safe radish]

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[vestal cloud]

would it be invalid because there is no variable in the function?

[steel stag]

nah, that's fine

like the function could be f(x) = 1/4 + x - x for all that matters

[valid grove]

Yup ig it can be be defined

Because sum of f(x) = 1

I don’t know how to explain it to you

1/4 + 1/4 + 1/4 + 1/4 = 1

[vestal cloud]

oh i get it

so if there were more or less than 4 values of x it would be invalid?

[valid grove]

Yup

[vestal cloud]

aight, thanks both

.close

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[next kayak]

If a and b are positive integers and 2019 / 2020 < a / b < 2020 / 2021 what is the minimum possible value of a + b?

[final loom]

$a, b \in \bZ^+$ Given $\frac{2019}{2020} < \frac{a}{b} < \frac{2020}{2021}$, determine minimum possible value of a + b

[flat frigate]

Ansh

[safe radish]

@next kayak Has your question been resolved?

[final loom]

$\frac{20190}{20200} < \frac{a}{b} < \frac{20200}{20210}$

[flat frigate]

Ansh

[final loom]

is it possible you can find a number between 20190 and 20200 , 20200 and 20210 that has like.. a dozen common factors?

[true egret]

Can we think like 2019/2020=2020-1/2021-1

[next kayak]

oh, now I see

then we might multiply them by 2/2

and the solution will come in between

[true egret]

Ah I got it i think so

Yeah

[next kayak]

4039/4040, which means the solution is 8080

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[lean otter]

can anyone help with part d pls

[cunning heron]

just sub 23 into T

and use trig identities

[lean otter]

but slightly confused with the arcsin of 0 bit

what are the other values that come with it?

0 and 180 or 0 and 360?

[cunning heron]

the range is 18x60

so 0 to 1080 for 18x

[lean otter]

yeah

[cunning heron]

so just solve it like a trig

[lean otter]

yeah but arcsin of 0

gives 0

so what are the other solutions?

[cunning heron]

180 360 .....

and so on

[lean otter]

wait why 180?

if it repeats every 360 degrees

[cunning heron]

cause sin180 is also 0

it repeats every 360 but crosses the x axis every 180

[lean otter]

ok what about arc sin -1?

would that repeat every 360?

[cunning heron]

time can't be negative

[lean otter]

nah its just an example

cuz im kinda lost with it

im just saying if it was arcsin 1 or -1

[lean otter]

ahhhh i got it thanks

.close

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[thick flame]

Statistics

should be very easy i just dk how to do it

:/

[copper venture]

you just line up the -5 from the x-axis to the y-column

so its between 75-80, so something like 78%

[thick flame]

oh

thought it would be easy

thanks

[copper venture]

i mean do you know hwo this works

what do you think you got confused on

[thick flame]

yes, i just dont know how to read word problems

i thought i had to create an equation

[copper venture]

oh, yeah the trick here was that the years were given in the question.

well what i would think it would be at least

[thick flame]

Well thx anyways

.close

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[latent jasper]

can someone help me with 20c? i understand a & b but can’t solve c)..

[true egret]

I think the answer will be 9×8+2(8×8)

Just take four spaces like
2 1 - -

• 2 1 -
  -- 2 1

[latent jasper]

ahh okay let me try once!

[true egret]

Yeah

[latent jasper]

ok wait wouldn’t that still be 7 x 7 x 1 x 1 ??

[latent jasper]

the final answer is supposed to be 154 btw

[tidal imp]

I would consider each possible location of 21

And do those cases separately

[latent jasper]

thx sm i finally got it

.close

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[safe radish]

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[safe radish]

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[vestal cloud]

hi

[vestal cloud]

i solved the value for k=2, but i am not sure what values to put for integration in (a) and (b)

[royal ivy]

Do you know how to relate the probability density of X with the probability that X is smaller than some value a?

[broken yew]

I would probably advise drawing a sketch graph

to get an idea of what you're meant to integrate

[vestal cloud]

i am just a little confused on whether to use f(x>3/4) or f(x_>3/4)

[royal ivy]

Well, f is the probability density, not the probability itself.

For example, P(0<X<1) is equal to the integral of f(x) between 0 and 1.

I'm assuming that this is how you calculated k=2.

[vestal cloud]

yes

[broken yew]

= and > are the same area.

[vestal cloud]

really? i think that was the part that i was confused on

[broken yew]

If you remove the exact point

the area under the graph lost a total of 0 area

it has no width

[vestal cloud]

ah

this would only apply to continuous density functions i assume?

[royal ivy]

Yes

There is such a thing as a Dirac impulsion, but it's not technically a function, and even less so continuous.

But they help to represent situation where you have a mix of discrete and continuous probabilities.

Say, you have a discrete variable X and a continuous variable Y, you want to know the probability density of X+Y.

But in your case, it's just continuous, so the probability that X=3/4 is exactly 0, and as Shuri said, you don't have to worry about it.

[vestal cloud]

that sounds like an interesting concept, maybe ill eventually learn abt it

thanks both

.close

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[compact meteor]

hey, i need to figure out the global behavior and symmetry of these quadratic functions, but how?

[safe radish]

@compact meteor Has your question been resolved?

[safe radish]

@compact meteor Has your question been resolved?

[safe radish]

@compact meteor Has your question been resolved?

[plucky elk]

Do you know how to plot by hand?

Zeros, critical points, inflection points, behavior at +- infinity

[compact meteor]

Do i need value table?

[magic wasp]

You don't need to plot it exactly, just an approximation is enough, that you understand the behaviour of the function

For example, understanding the shape of the curve

[safe radish]

@compact meteor Has your question been resolved?

[jovial spade]

can u translate the instructions

[safe radish]

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[lyric ingot]

How high will a 2 kg ball be if it is currently going 5 m/s after falling at a starting height of 33m ?

[lyric ingot]

How would I go about solving this problem

[pulsar condor]

write out the list of knowns and desired unknown

then apply the correct kinematic equation.

[obtuse jackal]

launched with vertical speed 5 m/s upwards, what will be its peak altitude ?

[pulsar condor]

no.

[lyric ingot]

Tf?

Well I know I need to set KE = PE

[pulsar condor]

Ok sure, we can use energy

[lyric ingot]

But how do I incorporate the 2 heights in the problem

[obtuse jackal]

I was trying to understand the question

[pulsar condor]

$E_i=E_f \
K_i+U_i=K_f+U_f$

[flat frigate]

Mosh

[lyric ingot]

Explain?

[pulsar condor]

Energy

[lyric ingot]

Ohh

I see

[pulsar condor]

You just said KE=PE...

[lyric ingot]

Yes

[pulsar condor]

Energy is conserved since gravity is conservative, and assuming no drag it's the only force present

Further assuming v_i=0 (ie dropped)

K_i=0

[lyric ingot]

So 1/2mv^2 + mgh = 1/2mv^2 + mgh
0 + (2)(10)(33) = 1/2(2)(25) + (2)(10)h

Like this?

The teacher says we can just use 10 for gravity btw

[pulsar condor]

then yes

[brave jolt]

maths

[lyric ingot]

660 = (0.5)(2)(25) + 20h

660 = 25 + 20h

635 = 20h

31.75 = h?

@pulsar condor

[pulsar condor]

,calc (660-25)/20

[flat frigate]

Result:

31.75

[pulsar condor]

yes

[lyric ingot]

Alright

[pulsar condor]

then appropriate units obviously

[lyric ingot]

Yes

I have another question

How far will a ball land from the 2 m tall table if it rolls down a ramp that is 0.13 m above the table?

So first I find the velocity after it rolls down the ramp right?

Then projectile motion?

[pulsar condor]

yes

[lyric ingot]

gh = 1/2v^2
10(2) = 1/2v^2
20 = 1/2v^2
40 = v^2
sqrt(40) = v

Then find the time it takes to hit the ground?

OHHH

WAIT

the ramp is 0.13...

Not 2...

Fuck

(10)(0.13) = 1/2v^2
1.3 = 1/2v^2
2.6 = v^2
sqrt(2.6) = v

@pulsar condor Does that look right?

[pulsar condor]

,w 0+20(2.13)=v^2+40

[flat frigate]

Results provided by WolframAlpha

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Requested by Omegabet_#9771

[pulsar condor]

yes

[lyric ingot]

Kk

Then plug in d = 1/2at^2

To get the time

[pulsar condor]

plug into the complete y-motion kinematics quadratic

[lyric ingot]

2 = 1/2(10)t^2
2 = 5t^2
0.4 = t^2
sqrt(0.4) = t

then use d = v/t?

[pulsar condor]

Yes, only cause v_x is constant

[lyric ingot]

Ya

[pulsar condor]

again w/o drag

[lyric ingot]

Ya

Ok so d = sqrt(2.6)/sqrt(0.4)

Wtf

2.55

m

@pulsar condor Is that correct?

[pulsar condor]

no clue

[lyric ingot]

O

[pulsar condor]

not doing the entire problem.

[lyric ingot]

Okie

,w d = sqrt(2.6)/sqrt(0.4)

[flat frigate]

Results provided by WolframAlpha

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Requested by Breeziboi#0672

[lyric ingot]

.close

[safe radish]

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[safe radish]

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[solar dock]

currently doing a problem on vaccines using bayes theorem, i found the P( disease | positive test ), but my teacher asked what would the probability of disease be if they took the test again and it was positive, what do i do?

[solar dock]

.close

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[frank elbow]

Hi I need help

[frank elbow]

Stat question

Probability

Any Juan know how to do it? One answer right one answer wrong

[pastel verge]

,rotate

[pastel verge]

Which one is right

[frank elbow]

Idk

I’m more confident in a being right

[pastel verge]

Ok so you need help on both then

[frank elbow]

Basically. We can try solving B first see if get diff answer

[pastel verge]

B can be solved if you understand A

[frank elbow]

Okay let’s do a then

[pastel verge]

So you know 10 of 21 answers

[frank elbow]

Ye

[pastel verge]

And teacher will choose 14 of 21 questions

Which can be done in how many ways?

[frank elbow]

21c14

[pastel verge]

Yeah

Now you want 7 out of 10 and 7 out of 11
So how many possible ways can that be done?

[frank elbow]

10P7, 11p7

?

[pastel verge]

Since you did those 10 , to get 7 right there need to be 7 questions form those 10

[pastel verge]

C*

[frank elbow]

right.

[pastel verge]

So let's use wolfram and see what we get

[frank elbow]

Alr

[pastel verge]

,w (10 choose 7)×(11 choose 7)/(21 choose 14)

[flat frigate]

Results provided by WolframAlpha

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Requested by yes sam#5028

[pastel verge]

Right?

[frank elbow]

Ya

[pastel verge]

So first one was right

[frank elbow]

Ya

[pastel verge]

What we basically did is
Let X be the random variable
X :- number of answers you get right

[frank elbow]

Ok

[flat frigate]

fäf

[frank elbow]

Wolfram that shit

[pastel verge]

Now for next question tell me what are the values X can take?

[pastel verge]

We already did

[frank elbow]

oh..

[pastel verge]

.

[pastel verge]

I'm asking this now

[frank elbow]

uhhh idk. 1-7?

How do I figure that out

[pastel verge]

Read the question

How many right answers do you need to pass?

[frank elbow]

7

7

[pastel verge]

But we don't stop at just 7

[frank elbow]

Okay

14

[pastel verge]

Think what other values X can take

[frank elbow]

14-7

[pastel verge]

Why do you write it backwards

7-14 right

[frank elbow]

Oops

[pastel verge]

But there's a problem in this too

Can you see it?

[frank elbow]

Ya

Need 8 too pass?

Nvm

Don’t think im@stupid

[frank elbow]

no I don’t see it

[pastel verge]

How many questions right answers can you get

[frank elbow]

At least 7

[pastel verge]

How many questions are you prepared for?

[frank elbow]

10

[pastel verge]

Right

So is it possible that we get 11,12,13 or 14 questions right

[frank elbow]

no

i mean by luck. But by this question . No

[pastel verge]

Good reflexes

[frank elbow]

thanks

[pastel verge]

We don't give shite to luck

So the values that X takes such that we pass are 7,8,9,10

[frank elbow]

Yep

14c10

or am I dumb

[pastel verge]

Just as I did here you have to find all those probabilities and add them

[frank elbow]

Damn can u wolfram that shit

[pastel verge]

You gonna do the rest

[frank elbow]

shite

k walk me thru it

[pastel verge]

Start , I'll correct if u gp wromg

[frank elbow]

Okay

So X=4

Ok im stick

Stuck

Do I use the same numbers or

[pastel verge]

X=7,8,9,10

[frank elbow]

10c4 x 11c4 divide by same denomination

?

[pastel verge]

What's 4?

[frank elbow]

Uh because there are 4 x possibilities my brain said make it a 4

[pastel verge]

[frank elbow]

halp me become not stupid

[pastel verge]

How did u answered part correctly

[frank elbow]

Had brain then lost brain

[pastel verge]

We r doing the same thing here too

[frank elbow]

Ok

[pastel verge]

Check part a again above

[frank elbow]

Ok so X=7.8.9.10

And

14c7

[pastel verge]

And

[frank elbow]

hint

[pastel verge]

What will P(X=8)=?

[frank elbow]

14c8

[pastel verge]

No

[frank elbow]

im dum

[pastel verge]

10C8 × 11C6/21C14

[frank elbow]

ok I understand denomination

how’d y get the 2 numerology

numerators

[pastel verge]

10 are the question we know

11 are the ones we don't

[frank elbow]

Ok I see.

[pastel verge]

So we get 7 out of 10 we know means 10C7

[frank elbow]

So p(X)=7 will have different value

Yea

[pastel verge]

We already did that bove

[frank elbow]

ya

so p(X)= 9 will be I see what ur doing

so like… we add all the p(X) 7.8.9.10 ?

[pastel verge]

Yes

[frank elbow]

shit that’s gonna take me awhile

lemme get me pen and paper

or does wolfram do that

[pastel verge]

Can do that but do it yourself

[frank elbow]

F

Ok

[pastel verge]

No F

Do it

[frank elbow]

i like u

as in ur attitude

[pastel verge]

Me too

[frank elbow]

no gay shit

alr ima get to this

[pastel verge]

I like me I mean

[frank elbow]

same bro

[pastel verge]

Bro who

[frank elbow]

same , female

[pastel verge]

Ok sissy

[frank elbow]

If I show u my work will u wolfram it

just cuz I don’t wanna make a rounding error

[pastel verge]

Ok

[frank elbow]

Epic

plz rate my handwriting at the same time

[pastel verge]

21C4?

[frank elbow]

14

[pastel verge]

2/10

[frank elbow]

Wolfe

Summon the 🐺

[pastel verge]

Do it

Use ,w in bots

[frank elbow]

Idk how to

U do that, I’m doing manual

compare after

[pastel verge]

,w (10 choose 7)×(11 choose 7)/(21 choose 14)

[flat frigate]

Results provided by WolframAlpha

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

Requested by yes sam#5028

[pastel verge]

Take this and change numbers

[frank elbow]

Can’t I have 1 more calc

Plz

[pastel verge]

Wdym?

[frank elbow]

Like u do it

I’m solving it manually rn

[pastel verge]

Nah i won't

[frank elbow]

Got it

[pastel verge]

Ok

[frank elbow]

Thx for ur help

[pastel verge]

Welcome

[safe radish]

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[inland frigate]

hi! can anyone help me with this math problem? So we have a right angled triangle, and we are supposed to find the angle that is made by meeting the bisectors of two acute angles external angles. I hope its clear

[true egret]

Answer is 135

135°

[inland frigate]

Can you explain?

[true egret]

Ok

Did u draw any figure?

[inland frigate]

Yes the right angled triangle

And the bisectors

[true egret]

Can u put it here?

It'll be easy to explain

[inland frigate]

Ok

[true egret]

It's a wrong figure

[thin bridge]

its correct

[true egret]

It's wrong

[thin bridge]

its correct

[true egret]

Those are obtuse angle

[thin bridge]

reread the question carefully

bisectors of two acute angles external angles

you can start by introducing variables to represent the two acute angles inside the right triangle

and then do some angle chasing

[inland frigate]

I tried that but it didn’t give me anything new

[thin bridge]

what exactly did you do

[thin bridge]

,rotate

[true egret]

@thin bridge I've a doubt aren't those bisectors bisecting the obtuse angle?

[thin bridge]

yeh that's what they wanted

[inland frigate]

Yes

[true egret]

Ok ig

[thin bridge]

you're ~2 steps away from the answer

[inland frigate]

Oh i just solved it

Thanks

.close

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[lean otter]

can someone please explain to me like i am a child why this equation because x/2 specifically i want to know why the X becomes the numerator everything else i understand, thank you!!

[thin bridge]

multiplication involving fractions

$\frac ab \cdot c$ can more nicely and simply be represented as $\frac{ac}{b}$

[flat frigate]

ℝamonov

[zinc crown]

so like ramanov said

$\frac 18 \cdot x^3 = \frac{x^3}{8}$

[flat frigate]

Yottachad

[zinc crown]

then remember that the power distributes over a quotient (dividing)

so

$\qty(\frac{x^3}{8})^{\frac 13} = \frac{\qty(x^3)^{\frac 13}}{8^{\frac 13}}$

[flat frigate]

Yottachad

[zinc crown]

then from here it should be pretty simple to see that this is x/2

[safe radish]

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[covert bough]

there are 13 people in the room if each handshake with each other how many total handshakes? pls help thank you

[covert bough]

i first thot its 13!

but its not the answer

[ember bough]

for every 2 people

there's 1 handshake

[covert bough]

yes

[ember bough]

then, basic combinatorics

[covert bough]

ic ok ty

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[vagrant pawn]

how do you determine how the domain of a function changes when converting from rectangular coordinates to polar coordinates?

[vagrant pawn]

for example in these questions

i see in 1. the polar form of the equation is $r = 2\cos \theta , \cos \theta > 0$

[flat frigate]

sean

[vagrant pawn]

i tried doing that conversion myself

but i dont see why its restricted

there wasnt any cos thetas under a square root or anything, maybe i got my calculations wrong

but i got to the same answer

and for number 2, i feel like there should be some restriction

since i end up to a point where the equation is $r^2-r\cos \theta = |r|$

[flat frigate]

sean

[vagrant pawn]

but apparently there isn't?

weird

feel free to ping me if you wanna help show me where i got smth wrong or where im not understanding this right 😄

like i see why number 3 works though, that one is obvious

still working through number 4

i also see why number 4 works

its just 1 and 2 thats a bit confusing

[safe radish]

@vagrant pawn Has your question been resolved?

[stoic dune]

@vagrant pawn
You're right, the restriction isn't necessary, in this context. Once you get into integration though, it becomes necessary. You want the polar form to touch every point exactly once, which the restriction causes.

[vagrant pawn]

ah i see

ok thank you

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[near steppe]

Pls help me

[near steppe]

PLEASE IM BEGGING YAL

[lyric ingot]

Is this a test

[near steppe]

uhm

its this

[lyric ingot]

It is...

A test...

[near steppe]

well YEA

[umbral meteor]

If it’s a knowledge check and u dont know it then why do u wanna lie

[lyric ingot]

Bruh

[near steppe]

uhm

IDKQ

can yall pls help me

its due like hjtfbcmn

[lyric ingot]

No

[near steppe]

🥲

i-

what

[lyric ingot]

We won't help you cheat on your test

[near steppe]

😕

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[severe linden]

Hey, I'm actually stuck at this equation where I cant' decide which one of these logarithm expression is correct? I'm thinking it was just the styles of how they write it, or is there any differences in writing the logarithm rules? And if possible, how do I write the logarithm in MATLAB? Thank you so much!

[safe radish]

@severe linden Has your question been resolved?

[severe linden]

<@&286206848099549185>

<@&286206848099549185>

[dense veldt]

hmm I think the two log notations mean the same

First two

When the base is not written, base 10 is assumed

But it'd be best if someone more knowledgeable commented as well

[severe linden]

is the 10 is a separate value from the log?

[severe linden]

and according to this, which one do you think is the right one?

[inland ivy]

lg typically means log_10 afaik

[dense veldt]

I don't understand the question

The right one according to what

[severe linden]

according to this equation, the first/second

if you don't know it's fine! I'm just doubtful to myself 😅😅

well then, thank you so much for the answers! /peace out

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[dense bronze]

hi guys does anyone know how to solve this question

[dense bronze]

im stuck here

<@&286206848099549185>

[broken yew]

refer to arctan formula... that should suggest a substitution to you

[dense bronze]

is it like this?

[final loom]

(@_@;)

[dense bronze]

i have nvr use this formula b4

[final loom]

Ahahaha

[broken yew]

no

uh

[final loom]

Yeah though.. Your integral is of the same form as derivative of arctan

[broken yew]

you should sub x = 5tan u

thats what i was tryna hint at

[final loom]

$(ax^2 + b^2)$ form.. whenever $ab > 0$, refer to the trig formula: $\tan^2 x + 1 = \sec^2 x$

[flat frigate]

Ansh

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[lime temple]

would the answer not be d? when i entered it, it says it was incorrect

[pulsar condor]

It would not

Reverse chain rule

[lime temple]

why does the chain rule have to be used can you not just convert from cos to sine

[broken yew]

differentiate d...

you will not get f

thats not how differentiation works

[lime temple]

hmm ok

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[tawdry salmon]

What happens here?

is it 2 * 2 * 2 = 8 and cube root = 2?

[ancient escarp]

more of a $(\sqrt[3]{2})^3=2$ but that works too

[flat frigate]

a disappointing son

[tawdry salmon]

what about here?

[ancient escarp]

same concept

except there's also some simplification with the fact that $$\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{a\cdot b}$$

[flat frigate]

a disappointing son

[tawdry salmon]

and thats in the 2 * 3 right?

[ancient escarp]

mhm

[tawdry salmon]

whats confusing this time is

3 * 3 * 3 = 27

oh I see

so cube is also 3?

[tawdry salmon]

Is there any rule as to what kind of radicals you can multiply?

Like only numbers with the same radicand or anything?

[ancient escarp]

this

[tawdry salmon]

So it only requires the same index?

[primal helm]

yes

[tawdry salmon]

Okay thanks

[primal helm]

you're welcome 🙂

[tawdry salmon]

.close

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[tawdry salmon]

All of square root 27 is removed right? the cube in the end is from the index in the 6

[ancient escarp]

it's the cubed root of 27

they just evaluated it

that cube is from the index of the root of 6, yes

[tawdry salmon]

Okay thanks

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[tawdry salmon]

$\sqrt{x}$

[flat frigate]

geoxcaliber

[tawdry salmon]

The index is 1 right?

[ancient escarp]

2, it's a square root

[tawdry salmon]

Oh ok thanks

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[clear crest]

how can i solve this

this is what i have

[safe radish]

@clear crest Has your question been resolved?

[clear crest]

actually...

wait

could this work

[plucky elk]

Plug in 1/2, a number slightly smaller than 1/2, and a number slightly larger than 1/2 into both sides of your starting inequality to check

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[jagged sparrow]

how do I do this

[jagged sparrow]

<@&286206848099549185>

[inland ivy]

Try dividing the top and bottom by x

Keep in mind you can transfer x's into roots as x^2's

[jagged sparrow]

Like this?

[spice grove]

Mhm.

[jagged sparrow]

And then I take the conjugate?

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[safe radish]

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[thin stone]

How can i prove or disprove that this function is one to one

[safe radish]

@thin stone Has your question been resolved?

[vague urchin]

one to one means no two inputs should ever have the same output

[thin stone]

I know that but i cant prove or disprove it

[vague urchin]

think about how this function is defined and try to convince yourself first

what do you think, is it or isn't it?

[thin stone]

I convinced myself that the function is not one to one

[vague urchin]

do you have an example of two inputs with the same output here?

[thin stone]

No

But I tried to find it and couldn't

And I can't prove that it is one to one either

[vague urchin]

What convinced you of this?

[thin stone]

Well, It was the easier one to proof

The problem is that i cant prove that when x is a subset of irrational that fx is true or not

I already now that fx is True when x is a subset of the rational numbers

[safe radish]

@thin stone Has your question been resolved?

[vague urchin]

sorry, my internet went out!
ok, so let's try breaking this down. Is f(x)=x+1 one to one? what about f(x)=2x?

Let's assume that we have two different numbers, a and b, such that f(a)=f(b)=x. If we can find such a and b, then we know f can't be one-to-one

One possibility is that a and b are both rational, in which case f(a)=a+1=f(b)=b+1. But if a+1=b+1, then a=b, which contradicts the assumption that they're different.
Similarly, if a and b are both irrational, then f(a)=2a=f(b)=2b which again means a=b, a contradiction

Finally assume a is rational and b is irrational. Can a+1 be the same as 2b? No, because a+1 is rational while 2b is not. So f(a) can't be the same as f(b), another contradiction

So it is in fact impossible for different inputs to have the same output! Which means f is in fact one to one!

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@thin stone Has your question been resolved?

[safe radish]

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[warm river]

I'm not sure how to do this fast

[eternal mica]

what 2 numbers = to -11 and multiply to 30

x + y = 11 and xy = 30

[worthy hemlock]

Quadratic formula if you want to be fast

[eternal mica]

no

[warm river]

???

[eternal mica]

well i mean sure

but you dont need the quadratic for this

[worthy hemlock]

Don't solve for the person

[eternal mica]

im not?

Im guilding him

nvm ill just stop helping

[worthy hemlock]

Guiding by giving the steps

[warm river]

oh ty

that makes it a lot clearer than running it through my head

[eternal mica]

Np

[warm river]

.close

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[fresh hill]

so

[fresh hill]

is it undefined or infinity im confsued

[stoic dune]

Where are you seeing this example from? Lol

Seems like bs to be

[fresh hill]

professor butler

heard hes one of the best professor in this one uni

https://youtu.be/gRM5pFdVtiU?t=845

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@fresh hill Has your question been resolved?

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@fresh hill Has your question been resolved?

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[lean otter]

a is 11

but i cant get b right fsr

wait it could be simplied further

ohh

1/2

ok

/close

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[lean otter]

claim

[lean otter]

12 workers dig the foundation in 20 hours. How much will it take 8 workers to dig the foundation? (The 8 workers equally dig)

[ancient escarp]

what have you tried

[lean otter]

I tried 20/8 but then i figured it wouldnt be so simple then i spent 10mins googling to try to find an answer and from my perspective its probably 12:20=8:x but im asking you for reasurrencd

Reasurrence"

[ancient escarp]

can confirm that's correct but google won't be there for your exams

[lean otter]

True

Thank you son

/close

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[hard folio]

Can I get help

[hard folio]

<@&286206848099549185>

<@&286206848099549185>

please

Anyone

[heady basin]

Suth what

[mortal meteor]

@hard folio as you might read in #❓how-to-get-help : Don’t ask permission to ask a question, or ask if anyone knows how to solve a type of problem. Just ask your question.

[hard folio]

bro I just need help w homework

[mortal meteor]

you have to post the particular exercise you need help with. What do you expect to receive if you don't ask something that can be answered?

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[worthy hemlock]

What times by 5/3 equals 0?

So what's the trouble then?

Simplify -1/1

So then what do you have now?

No

That's $x \cdot -1 = -14$

[flat frigate]

dldh06

[worthy hemlock]

x times -1

Not x minus negative 1

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[ebon rock]

something?

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[sly quarry]

If i know the largest possible outcome and the smallest. On any symmetrical distribution what is the average outcome.

[sly quarry]

E.g. I know the highest possible time something will take is 14 minutes

And the longest is 60

How long will it take on average

[fair dagger]

The average of both

I am not sure if you also want to see a proof of this.

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[low nest]

so i have a continuous function $f:[a,b)\to\mathbb{C}$. i also have that the function is square integrable (i.e. $\int_a^b|f(x)|^2dx$ exists). how do i show that $f$ is integrable, that is show $\int_a^b f(x)dx$ exists

[flat frigate]

Beous

[low nest]

like there are 2 cases

when $\lim\limits_{x\to b^-}|f(x)|<\infty$ and when $\lim\limits_{x\to b^-}|f(x)|=\infty$

[flat frigate]

Beous

[low nest]

i also have the inequality $\left|\int_a^b f(x)dx\right|^2\leq(b-a)\int_a^b|f(x)|^2dx$

[flat frigate]

Beous

[low nest]

so consider the first case when |f| converges to some value or does not exist as x approaches b from the left

i've already shown that this means f is bounded on [a,b)

ok so now i've show $\int_a^b |f(x)|dx\leq(b-a)M$ (where $M$ bounds $|f(x)|$ on $[a,b)$)

[flat frigate]

Beous

[low nest]

is this sufficient to show that $\int_a^bf(x)dx$ exists?

[flat frigate]

Beous

[fair dagger]

Woah that is a lot of text.

[frigid geyser]

It's basically cauchy-schwarz

And yes, i'd say it's sufficient

[low nest]

ok cool

[frigid geyser]

And i actually think you didn't need to differentiate cases cause you could just cs right from the start

[fair dagger]

If you want to show f is integrable

you should show int |f| dx finite

[frigid geyser]

Ah yes that is true

My bad

[fair dagger]

Cauchy Schwarz works but there is another even simpler way

you can estimate

|f| <= 1 + |f|²

(directly from binomial theorem)

[low nest]

oh damn

[fair dagger]

with this you get a simple integral bound.

[low nest]

yeah that would've been nicer

thanks

.close

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[ashen edge]

https://i.imgur.com/blh8592.png what steps is the tutor taking? I think he sets K = 0 because its homogenous and then subtracts R2 from R1 to get 4x-6y = 0, then R2 - R3 to get 6y-7z. He then defines x and z but not y? Why did he substitute into the last equation? What's going on here?

[safe radish]

@ashen edge Has your question been resolved?

[tame charm]

He wants to get x and z in terms of y

And then substitute those expressions into the last equation to get y in terms of k

Which would then give you x and z in terms of k

And then you can find the minimum integer k such that all three are integers

[ashen edge]

so could he have substituted into the other equations instead? Why did he choose the third one?

[tame charm]

Not sure why he chose the third one

But yeah you can sub into any of the three

(All three equations are true, so you can substitute all you like and it will remain true)

[ashen edge]

when k = 131 gives the minimum positive integer because the denominator is 131 so he cancels out k to get it

[tame charm]

Right

[ashen edge]

the arbitrary parameter is K because its what the original system was solving for?

[tame charm]

Wdym

The key here is that x,y,z can all be expressed in terms of k. Then it becomes trivial to find an integer solution

[ashen edge]

K is arbitrary because it depends on x,y,z?

[tame charm]

x,y,z depend on k

But yeah I mean k is arbitrary because you can choose what it is, and it affects all the other values

But so is x — choosing something for x would give you something for k, in turn deciding what y,z are

I guess I’m wondering what you mean by arbitrary

[ashen edge]

I see so at least 1 variable is arbitrary here?

[tame charm]

For integer solutions, k is arbitrary

Well

Again like

Wdym by arbitrary lol

[ashen edge]

well I don't actually know either, because the question asks to show the solution set has one arbitrary parameter so I was thinking by arbitrary they mean its not known without the others?

the value of K isnt known without x,y,z

[tame charm]

In standard mathematical language

Arbitrary means “any”

Like “this theorem holds for arbitrary scalar k”

Meaning for any scalar k

Ohhh

Arbitrary parameter

x, y, and z are all functions of k

They are parametrized by k

So K is the arbitrary parameter

[ashen edge]

the equations are x1 x2 x3 = k so that means they are all functions of k then?

Okay well I understand how he got the answer now thank you @tame charm

.close

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[azure burrow]

Pls Help Me

. close

.close

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