help-27

[alpine hull]

what does that mean

[full flume]

Essentially you're taking the derivative like normal but anything that isn't x is going to be written in terms of the function

For ex

[alpine hull]

i sitll dont get how that works

thjis implicit stuff

[alpine hull]

huh

[full flume]

The only thing you have to do is every time you take the derivative of y you write dy/dx

And then solve for dy/dx

[alpine hull]

and then it just becomes

dy /dx

?

how does that work

[winter patrol]

$\dv{x} y = \dv{y}{x}$

[woven radish]

ℝαμΩℕωⅤ

[alpine hull]

so multiply all the y values

by d/dx?

[winter patrol]

not multiplication

[alpine hull]

huhhh

[winter patrol]

d/dx is a derivative operator

applying that to y gives its derviative wrt x

[manic plank]

https://www.youtube.com/watch?v=7BK_mmYckmI

Maybe this will help?

[alpine hull]

all this implicit stuff is sooo hard

[winter patrol]

lets start with non-implicit stuff

consider starting with something like
$$y = x^2 + x$$
and differentiating both sides w.r.t. x \
you'd be applying the derivative operator
$$\red{\dv{x}}y = \red{\dv{x}} (x^2 + x)$$
which results in
$$\dv{y}{x} = 2x + 1$$
do you have any issues with that?

[woven radish]

ℝαμΩℕωⅤ

[alpine hull]

no

so it means

to derive it

yeye i get that

[winter patrol]

and do you have any issues with applying product and chain rule, \
i.e. find derivatives of stuff like
$$(x+1)(x^3 + 7)$$
$$\ln(x^2 + 3)$$

[woven radish]

ℝαμΩℕωⅤ

[alpine hull]

uh

first one

is product

and chain

so

wait

no chain

2nd one is 1/x^2 +3

i think

[winter patrol]

second one is wrong, even assuming you meant 1/(x^2+3)
you forgot to apply chain rule there

[alpine hull]

wat why is there chain there

iis not being raised to a power

[winter patrol]

chain rule is applicable when you have function compositions

which isn't limited to just power function compositions

[alpine hull]

okk

so multiply that by 2x

[winter patrol]

yes

[alpine hull]

so 1/(x^2 +3) *2x?

[winter patrol]

yes

now the same rules essentially apply when doing stuff like implicit differentiation

you'd still use product rule to differentiate xy

and the derivative of y can be left as dy/dx

[alpine hull]

uhhh

i dont get it

[winter patrol]

xy is the product of x and y

attempt to differentiate that using product rule

like how you differentiated the (x+1)(x^3+7)

and the derivative of y is just the derviative of y

y' or dy/dx, whichever you prefer

which you had no issue with here:
#help-27 message

[alpine hull]

why r we multiplyinh

both the x and the y values

by dy dx

[winter patrol]

we're not

[alpine hull]

my teacher multiplied x by dy dx

and 1/y

[winter patrol]

that's not what you just said though

forget about what happened there

and apply what you demonstrated you were able to do

[alpine hull]

if we deffrentiate xy

[winter patrol]

(x+1)(x^3+7) is the product of (x+1) and (x^3+7)
and you were able to differentiate that applying the product rule with no issue

[alpine hull]

wont it just become x

[winter patrol]

no

similarly xy is the product of x and y
differentiate that, applying product rule the same as before

don't worry about terms like implicit, just naturally apply product rule, don't worry about other stuff

[alpine hull]

so x prime * y + y prime * x

[winter patrol]

yes

[alpine hull]

then wat do i do

[winter patrol]

what's x'

what's the derivative of x

[alpine hull]

dy/dx ?

[winter patrol]

no

[alpine hull]

oh

1

[winter patrol]

yes

dy/dx is the derivative of y, represented by y'

which is what they have for the first two terms

and then for the other derivatives of
$$\ln(y)$$
$$e^y$$
apply chain rule

[woven radish]

ℝαμΩℕωⅤ

[alpine hull]

1/y

• 1?

[winter patrol]

no

again recall what you just did moments ago

remember you're differentiating w.r.t.

[alpine hull]

1/y

*dy / dx

[winter patrol]

yes

[alpine hull]

oh my this is so complicated

[winter patrol]

just combine the ideas you've already demonstrated you know

$\dv{x} f(g(x)) = f'(g(x)) \cdot g'(x)$

[woven radish]

ℝαμΩℕωⅤ

[alpine hull]

yeah ik this one

[winter patrol]

$\dv{x} f(\this) = f'(\this) \cdot (\this)'$

[woven radish]

ℝαμΩℕωⅤ

[winter patrol]

and with $\this$ being $y, (\this)' = y' = \dv{y}{x}$

[woven radish]

ℝαμΩℕωⅤ

[alpine hull]

sortaa

[winter patrol]

perhaps the alternate representation would help. \
i'm changing the variables to how this is normally represented
$$\dv{p}{x} = \dv{p}{y} \dv{y}{x}$$
here, $p = \ln(y)$
$$\dv{\ln(y)}{x} = \dv{\ln(y)}{y} \dv{y}{x}$$

[woven radish]

ℝαμΩℕωⅤ

[alpine hull]

i dont think

i can understand this question

i give up

[winter patrol]

don't give up

do you understand that form of chain rule just now?

[alpine hull]

i just know chain rule as derive the outer

and then derive the inner

[winter patrol]

yes

[alpine hull]

then multiply

[winter patrol]

yes

same here

[alpine hull]

i cant understand all the dxdy fraction respesct stuff

anyways i dont have time to understand this question

over here

when we do 6In(x-3)

u said when we do the functions

chain rule applies

[winter patrol]

its an indication of how fast one variable is changing in reference to another
i.e. how fast is y channging as x changes

y' is just alternate notation to dy/dx

[alpine hull]

but my teacher didint chain rule 6/ (x-3)

[winter patrol]

techncally chain rule is required

its just that the derivative of (x-3) is just 1, so it doesn't matter whether you explicitly write the multiplication by 1 or not

[alpine hull]

o

why does

In 4

become 0

[winter patrol]

ln(4) is just a number, a constant

derivatives of constants are 0

[alpine hull]

then what happened

on the right

i gootta go to school now

adjaifoaifhaifoh

cya

.close

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[devout snow]

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[sand isle]

,rotate

[sand isle]

i need help with d and e

for some reason, i got times in d as 11.45 am and 18.42 pm but

for sum reason its wrong

Where did i go wrong

no idea how to do e

guys i got a test tom pls

😭

<@&286206848099549185>

[edgy canopy]

helloo

[edgy canopy]

wsg

[sand isle]

hello

[sand isle]

^

[edgy canopy]

what do you need help with

oh okat

[sand isle]

yah

[edgy canopy]

wait

where did this question come from

is there a full worksheet

[sand isle]

^

[sand isle]

its a textbook question

😭

[devout snow]

@sand isle Has your question been resolved?

[strange arch]

arcsin(2/3)

first value is 0.73

(which you rounded to 0.72, but that's mostly fine)

but the second value, where do you state how you calced it?

@sand isle

I'll put the two equations here

first value: 2.78735432639

second value: 9.21264567361

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[hollow jasper]

Is this correct?

[lost laurel]

!original

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[lost laurel]

what exactly are you trying to do

[hollow jasper]

Graphically represent the vector

[stray bramble]

hot milk:

At the café, the waiter heats 220 mL of milk by injecting water vapor at 120.0°C.

The milk, initially at 18°C, is heated to 60.0°C.

Suppose that heat transfers take place only between milk and water vapor,

and all the injected steam becomes liquid and then cools to 60.0°C.

Compact statement:

• What mass of water vapor should the server inject?

Detailed statement:

1- Calculate the energy received by the milk to heat up from 18.0°C to 60°C.

2- Express, according to the mass m of injected water vapor:

a- The energy released by this steam as it cools to 100.0°C.

b- The energy released by this water vapor when it becomes liquid.

c- The energy released by the liquid water formed by being cooled from 100°C to 60.0°C.

3- Using a balance of energy exchanges, calculate the mass m of steam that the server injected into the milk.

• Data:

• Density of milk:

• ρ milk = 1.00 kg. L-1

• Specific energy of water liquefaction

• Lℓ = – 2257 kJ. kg–1

• Energy transferred during a temperature variation Δθ without change of state,

of the mass m of a body of specific heat capacity c:

-Q = m. vs. Δθ

• water (g) = 1.89 kJ. kg–1 . °C–1

• c lait (ℓ) = water (ℓ) = 4.18 kJ. kg–1 . °C–1

please help me

[lost laurel]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[lost laurel]

hmm, could you share the original question?

Which is r

[hollow jasper]

I presume that you don’t speak Slovak lol.

And the original question was what I said. Graphically represent the vector

And I just did it by this example in my classmates notes

[lost laurel]

well, what is vector a?

[devout snow]

@hollow jasper Has your question been resolved?

[devout snow]

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[sand pelican]

.close

[viscid ivy]

Hello

[viscid ivy]

I really need help

Kindly ping if you answer. Thank you!

[devout snow]

@viscid ivy Has your question been resolved?

[tough cove]

https://ibb.co/XbGDVJG

[devout snow]

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[dawn pine]

I wrote my answer for 1a as 0[1,2,3] + 0[1,0,-3] + 0[0,0,0] = 0 vector as the two vectors are linearly independent and thus have only the 0 solution

is this correct?

<@&286206848099549185>

[devout snow]

@dawn pine Has your question been resolved?

[devout snow]

@dawn pine Has your question been resolved?

[devout snow]

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[dim egret]

In a question like this: (Find the Cathetus "A" of a right triangle if β = 29° 33' and C = 10.) how do i know if im supposed to use cosine or sine

[winter patrol]

drawing the triangle helps

[dim egret]

yea but couldnt the A and β be in any spots?

[winter patrol]

did you change any of the capitalisation

[dim egret]

what do you mean

[winter patrol]

usually lowercase letters are used for sides

[dim egret]

oh yea i meant a sorry

[tame nova]

There's a right angle, so we just need to know if the 29⁰ side has the 10 or 31 in length

[winter patrol]

follow conventional labelling rules
side a is opposite angle A or alpha
side b is opposite angle B or beta
side c is opposite angle C or gamma

[dim egret]

oooh okay

so in the question i need to find "b" and using the pythagoras theorem i can find the "a"?

[winter patrol]

you can use trig to find "a" directly

[dim egret]

how would that work

[tame nova]

This might help, idk

[winter patrol]

try drawing this out

[dim egret]

is it like 90-23 and then i turn that into alpha and then calculate?

[winter patrol]

not needed

you just need to use the appropriate trig function

you "could" do that subtraction, if you use that new angle you'd just end up using a different trig function

[dim egret]

so what would be like the easiest way

[winter patrol]

draw it out

first

then consider the position of the angle and sides you're interested in
and soh cah toa
to determine which trig function to use

[dim egret]

like this?

[winter patrol]

label your "a" as well

[dim egret]

okay

[winter patrol]

and ideally also put a square for the right angle
anyway relative to the given angle,
will "a" be the adjacent, opposite or hypotenuse

[dim egret]

according to what

to 29 33

then its adjacent

[winter patrol]

yes

and what's the position of the given side of 10

[dim egret]

eee

is this how its supposed to be done

[winter patrol]

,W cos(29 degrees 33 minutes)

[woven radish]

Results provided by WolframAlpha

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

Requested by ramonov

[dim egret]

omg

[winter patrol]

you didn't seem to evaluate your cos properly

[dim egret]

i did it wrong

yea i asked chatgpt i wasnt bothered to take my calculator out 😭

no way chatgpt lied

[winter patrol]

!nogpt

[devout snow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[winter patrol]

the latter doesn't apply here, but the initial part still stands

[dim egret]

but did i do it like correctly

except the cos part

[winter patrol]

ignoring the wrong numerical value
I suppose

ideally you'd first set your equation up as
cos(29° 33') = a/10
a = 10 * cos(29° 33')
then chuck that whole thing into a calc

it isn't as big of an issue when it multiplication by 10, but for other values, rounding too early will result in reduced accuracy

[dim egret]

okay thank you a lot!!! but did i do this correctly?

simple version but tried to make it fast

[winter patrol]

yes, that would be valid

[dim egret]

thanks a lot!!!

[tame nova]

Don't forget to '.close'

[dim egret]

.close

[devout snow]

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[stoic crystal]

I found the co-ordinates of A and B but cannot find it for C, I cannot find x or y of C from the given information so I can use the equation of the line: x+y=21 or 2y=12+x to find the other.

[robust dust]

you can find the coordinates of C from solving 2y=12+x and x+y=12 simultaneously

[devout snow]

@stoic crystal Has your question been resolved?

[stoic crystal]

oh wait yes ty

.close

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[potent whale]

My answer is right and I’m pretty sure my work is too. However, I don’t quite understand why we solve in terms of x instead of in terms of y

[torn vessel]

because the way you've oriented your function for the hypotenuse, the side of length 4 is on the x-axis.

[devout snow]

@potent whale Has your question been resolved?

[potent whale]

so could I had made the length of 4 be on the y-axis?

if i could have, how would my function looked?

[devout snow]

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[timber nebula]

hey

[devout snow]

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[lapis blade]

Integration

[sturdy sigil]

i think i know this one

[winter torrent]

,rccw

[lapis blade]

I am not sure where I am going wrong in this question

[winter torrent]

your work seems right to me?

[sturdy sigil]

can i do that command aswell?

or only u?

[winter torrent]

you can as well! there's also ,rcw for clockwise

[lapis blade]

But my system won't accept my answer

[winter torrent]

hmm have you tried distributing that - sign?

[lapis blade]

Yes

[winter torrent]

you can also check your work by finding dy/dx and verifying that the original equation is satisfied

[lapis blade]

One second

[devout snow]

@lapis blade Has your question been resolved?

[dense jay]

its -ln|2-y| no?

[lapis blade]

=sin(x)+c

[dense jay]

if the - was there, though i cant see it, then it disappeared later

2-y=e^{-sin(x)-C}

[lapis blade]

Ohhhh I think that makes sense

I forgot the negative. Let me try

Thanks

[devout snow]

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[lilac pebble]

Find the slope of the polar curve at the indicated point. r =7/θ, θ = 4π

i got -4 can someone do the problem and see what they get? it isnt one of the answers
0
Undefined
-4pi
4pi

[lilac pebble]

im pretty sure youre trying to get dy/dx so you need an x and y which is rcosθ and rsinθ

so i plugged in for r and got dy/dx then I plugged in 4π and for -4

[devout snow]

@lilac pebble Has your question been resolved?

[lilac pebble]

I FORGOT A PI IM A DUMBASS

.close

[devout snow]

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[misty sun]

Hello mathematics community, I am a bit confused on this problem specifically because it seems to imply that tangent is equal to the hypotenuse on a right angle triangle. When I looked it up as illustrated in the picture attached you can see that tangent has a vertical component of sine and a horizontal component of versin and exsec summed, not the hypotenuse. Can anyone offer any insight?

[smoky nimbus]

This is what you should apply

[misty sun]

Does this mean tangent is equal to the hypotenuse?

[smoky nimbus]

No

It says in that image that tangent of theta is equal to opposite over adjacent

It does not say that tangent is equal to hypotenuse

[misty sun]

This is true, so why are they using tan(theta) to say that's e....

It kinda clicked for me, am I correct in saying because we know 18 and y(t) are both the opposite and adjacent sides we can use tan(theta) to calculate y(t)?

[devout snow]

@misty sun Has your question been resolved?

[devout snow]

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[quasi rune]

Lydia and Alan wanted to make a rectangular box with integer length sides out of plywood. At the lumber yard, they realized that they had forgotten the dimensions of the box. Lydia remembered that one of the sides had an area for 40 square cm. Alan remembered that the other sides had areas of 150 and 60 square cm. What is the length of the longest side of the box?

[steep sinew]

let's call the sides a b c

we know

• abc are integers
• three side lengths

[quasi rune]

Okay

[steep sinew]

of course, abc are positive and non zero

and let's randomly assign them

ab = 40
bc = 60
ac = 150

[quasi rune]

Okay

[steep sinew]

to solve further, we have to annihilate a variable

we know: a×b = 40

so a = 40 ÷ b

[quasi rune]

Okay

[steep sinew]

and ac = 150

(40 ÷ b) × c = 150

c = 150 ÷ (40 ÷ b)

let's define x' = 1 / x because I have no ^-1

c = 150 × (40 × b')'

= 150 × 40' × b"

= 150 ÷ 40 × b

c = 3¾ b

now

bc = 60

b (3¾b) = 60

3¾ b² = 60

b² = 16

b = 4 (because it obviously isn't negative)

[quasi rune]

Okay

[steep sinew]

the rest should be trivial, because we have the formulae

[steep sinew]

You just need to substitute ad absurdum for these kinds of questions

[quasi rune]

Okay

Is this able to be solved by prime factorization?

[craggy sequoia]

ad absurdum?

[quasi rune]

.close

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[lost plinth]

Does

[lost plinth]

How does the chain rule apply to this term x*y?

Is it y’(x’y + yy’x) Or y’(x’y + y’x)?

[vivid kite]

Product rule right

Implicit diff?

D/dx of y = y’ or dy/dx

[lost plinth]

uhh yes

[lost plinth]

Why isn’t it yy’?

Since y is a function of x

the product rule is $$ (f(x)g(x))’ = f’(x)g(x) + g’(x)f(x) $$ My concern is what happens when $$ g(x) = g(h(x))? $$

[woven radish]

Nerdy_Coder

[lost plinth]

<@&286206848099549185>

[eager lodge]

You don't have g(x)=g(h(x)) though

[devout snow]

@lost plinth Has your question been resolved?

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[covert root]

So why don't you do it?

[plucky kernel]

idk how to lol

[devout snow]

@plucky kernel Has your question been resolved?

[covert root]

So do you know how to sketch 1/x

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[surreal prism]

I chose to calculate the normal using OG and OA

Should i have used something else ?

OG = <0,1,1> OA= <1,0,0>

then you cross product

which left me with <0,1,-1>

OH WAIT

LOL I ALREADY HAVE THE ANSWER

.close

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[weak flare]

is this graph unimodal or bimodal or trimodal?

[devout snow]

@weak flare Has your question been resolved?

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@weak flare Has your question been resolved?

[wheat pawn]

recall the definition of mode. What does it state?

[devout snow]

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[hollow blaze]

Can I split a fraction into smaller piece and then apply L'Hospital to the one satisfies the condition?

[onyx rune]

give an example

[hollow blaze]

I'm typing on phone so it will take a while, please wait.

[onyx rune]

ill wait

[thick knoll]

cant you write it on a paper and send a pic of it

[onyx rune]

yeah that also will be easier to read

especially a fraction

[thick knoll]

yea

[hollow blaze]

For example: $\lim_{x\to w}\frac{1-\frac{x}{w}}{4(1-x^a)}$ $(w^a=1)$

[woven radish]

EphemeralEuphoria

[hollow blaze]

So I divide $\frac{1}{4}$ to calculate l'hospital and then multiply it back

[woven radish]

EphemeralEuphoria

[thick knoll]

yea

but isnt it the same thing

as you differentiate the Nr and Dr seperately

[hollow blaze]

Instead of 1/4, what if it was a another l'hospital and multiply both together

[thick knoll]

in both the limits are in 0/0 or inf/inf then yes

[hollow blaze]

Thank you so much.

[thick knoll]

welcome

[hollow blaze]

Just to be sure, the one I'm talking about is another function with respect to x. So can I still do this?

[thick knoll]

yeah with the condition i said before

[hollow blaze]

thanks

.close

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[edgy prairie]

hi

[edgy prairie]

i need help calculating derivatives

im rly confused

[long pasture]

what have you tried?

[edgy prairie]

nothing rly

im just looking at diffrent rules

like chain method and stuff

but idk what to use for this one

[limber atlas]

Well you should generally attempt the question before asking it as a doubt

[limber atlas]

ah

[long pasture]

this indeed requires quite an amount of chain rule

[edgy prairie]

what are all the rules?

the important ones

oh

[limber atlas]

we should be asking you

have you studied the entire part of differentiation

[edgy prairie]

yeah

[limber atlas]

because all of them are taught, theres just 3 "important" ones

[limber atlas]

then i think you should know what rules to apply here

what exactly is the problem

Do you know IF we can do this?

[edgy prairie]

so the 3 important ones would be
power rule
product rule
chain rule

is quotient rule important or nah

[edgy prairie]

ohhh

[limber atlas]

it is

everything is important

[edgy prairie]

i gota look at is as 2 seperate things

ok

[limber atlas]

if you want to make it easier

yes

it can also be done as a whole

but if you arent comfortable with that, just solve it in 2 parts

[edgy prairie]

so

i use chain rule on first part

then power on second correct

[limber atlas]

how

[edgy prairie]

hm

is it only if the number is raised to a 2?

[limber atlas]

no

no

man

you need to revise/study your theory before solving calc questions

please watch a video on differentiation if you dont know when and where to apply which formula

[edgy prairie]

can u recomend me a video

or plz help me i rly want to understnad

[stable storm]

you can only use the power rule if the exponent is a real number, not a variable

[edgy prairie]

oh

so what would i use here

[limber atlas]

okay wait

https://youtube.com/playlist?list=PLF797E961509B4EB5&si=xr6zkCDf10CuvzUh

watch what you want

[devout snow]

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[crude radish]

Help

[devout snow]

Please don't occupy multiple help channels.

[crude radish]

Can I use law of cosin to solve the missing side in question 3?

[wheat pawn]

,rotate

[wheat pawn]

you can, but it's not needed

[crude radish]

Than is this triangle congruent

[wheat pawn]

recall your definitions. You have two sides and an angle. If you have to sides and an angle, what needs to happen for them to be congruent?

[crude radish]

SAS

But it’s not

@wheat pawn

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[cosmic gust]

It means that it's continuous and the area under the curve is finite

There can be undefined points though*

[cosmic gust]

Continuous might not be the correct word there, I take that back. More generally it means that you can find the area under the curve.

So there can be immediate jumps in the graph

[devout snow]

@restive river Has your question been resolved?

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[feral agate]

I’m talking about the third question, I couldn’t crop the picture more

,w plot arccos(cosx)

[woven radish]

Results provided by WolframAlpha

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

Requested by shikhargupta1207

[feral agate]

This graph follows this jagged tooth pattern forever, and the other graph y=|x^2-a| will have to cross y=pi at some value

So how can this possibly be inconsistent at all? Unless I’m misunderstanding something

[lost laurel]

$y=x^2+10$

[woven radish]

Why am. I here

[feral agate]

Ah, right.

[lost laurel]

so any a>3?

[feral agate]

Not exactly 3

[lost laurel]

π

my bad

yeah

[feral agate]

It can be a little lower actually

We just need the two lines y=x and y=-x to be tangent to the parabola

[lost laurel]

ok, yeah

[feral agate]

Then any parabola above that will cause inconsistency

[lost laurel]

true

[feral agate]

My book says a=-0.5, which makes sense now

But it seems pretty low

Oh wait to consider that I can just take cos^-1 cosx to be equal to x and then set the discriminant equal to 0

[lost laurel]

a=-0.3 works too

[feral agate]

Yeah I think a=-0.25 would cause the tangency

So anything below that works

Okay, thank you for that!

[lost laurel]

which book is this from , just out of curisoity

seems like a nice, fun problem

[feral agate]

It’s a jee preparation book

[lost laurel]

ah, ok

[feral agate]

We’re given booklets of like 30-60 pages for each chapter with theory and questions

This is actually the last question for inverse, so I’m done now lmao

[lost laurel]

ah, coaching material

[feral agate]

Yep

[lost laurel]

cool

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[karmic hatch]

Given numbers from 1 to 16,put them in the square,the rarity of chance to appear all column and row got sum is an odd

[karmic hatch]

My last solution given the result of 32/715 but the answer is 8/515

16! case

8!8! for the reposition of the odds and evens

4!4! for column and row reposition

[karmic hatch]

I think the problem is here since some case r repeating but i cant solve them

oh nvm I get it now

.close

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[glass radish]

Help

[devout snow]

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

[glass radish]

1

Help

[drowsy peak]

Height = √3/2 x Side for an equilateral triangle

[glass radish]

I am not solving for height tho

[drowsy peak]

Substitute in your value for Height and rearrange for Side

[devout snow]

@glass radish Has your question been resolved?

[devout snow]

@glass radish Has your question been resolved?

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[half tulip]

Can someone help me figure out why I got this wrong?

[devout snow]

@half tulip Has your question been resolved?

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[brave trench]

Not quite sure where to go from here. It’s question 3b. How can i apply the induction hypothesis the Fk+5?

[dapper tiger]

Fn+5 = 4Fn+2 + Fn-1

you assume the hypothesis for both Fn+6 and Fn+5 and deduce for Fn+7

[brave trench]

Awesome thank you!

one more question

Is this right?

[devout snow]

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[half tulip]

.reopen

[half tulip]

.reopen

[sour falcon]

Can anyone help me with this related rates problem? I don't get what formula I'm supposed to use I think its deltaY/deltaX but I'm not sure here's my work and problem: I've been trying to figure this out all day. I have one more attempt before the software locks me out of the problem.

[sour falcon]

<@&286206848099549185> anyone?

[sour falcon]

It has been 15 minutes

[sour falcon]

Well it has been 15 minutes now so it doesn't really matter

Can someone just help me I'm stuck

[sour falcon]

I tried using the pythagorean theorem with the deriviative and I tried using the distance formula y2-y1/x2-x1 with the derivitative but none of those are it

Unless I'm just doing it wrong

I can show another page of my work but it doesn't really go anywhere

[half tulip]

Hey, can anyone help me with finding the poison distribution if there’s an average in it?
Like “The cafe has an average of 12 customers every 20 minutes.Whats the probability that in 3 hours, exactly 50 customers will come in?”

Like something like the example

Oh shit

[sour falcon]

This channel is already taken

[half tulip]

I though I was in the help chat

Sorry about that

[sour falcon]

So I guess no one is willing to help?

[urban harbor]

start out by writing an equation for d, distance in terms of time, d(t); what would that be?

[devout snow]

@sour falcon Has your question been resolved?

[sour falcon]

Yes but that doesn't really help me since I only have d/dt = ____

[devout snow]

@sour falcon Has your question been resolved?

[sour falcon]

Debating pinging Helpers again since no one is helping me

[devout snow]

@sour falcon Has your question been resolved?

[devout snow]

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[uncut crow]

this came up in the wild so not expected to have a nice answer. fix a positive integer $M$ and positive rational $m$. is there a nice (we can say that means computationally speedy) way to express $$S:=\frac{1}{M}\sum_{k=1}^M\lfloor mk\rfloor?$$ it is easy to bound it between 2 consecutive integers (namely $\left(\frac{1+M}{2}\right)m-1$ and $\left(\frac{1+M}{2}\right)m$) by killing the floor, and estimating $S$ as the average of those is good enough for my purposes but i'm curious if there is something better

[woven radish]

chmonkey #1 simp

[runic prawn]

m = p/q

then some number theory stuff

[devout snow]

@uncut crow Has your question been resolved?

[uncut crow]

oops i misspoke, doesn't change the problem at all but i meant bound it between two numbers differing by 1, not consecutive integers

i do not know what number theory stuff is

[weak cove]

number theory is the study of numbers particularly integers and the natural numbers

[uncut crow]

austin you probably can’t even prove the quadratic reciprocity law

[weak cove]

You probably don’t even know how to bound the sum of 1/M floor mk between two positive integers by killing the floor and estimating S as the average

[uncut crow]

actually as i stated i DO know how to do that

nice try

[weak cove]

Ok u win

[devout snow]

@uncut crow Has your question been resolved?

[heavy current]

analysis 😵‍💫

[uncut crow]

probably not analysis

[heavy current]

I see bounds, I think analysis

[uncut crow]

did anyone even read the question

the bounding thing i wrote just gives a very easily evaluable estimate for the sum

i am wondering about a computationally easier (compared to just adding everything up) way to find the exact value

[heavy current]

I'm not intelligent enough to know where to even begin tbh

sorry

[devout snow]

@uncut crow Has your question been resolved?

[uncut crow]

.close

[devout snow]

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[heavy current]

did you solve it?

[uncut crow]

no

[heavy current]

[uncut crow]

tis ok, was just a curiosity

the estimate is good enough

[devout snow]

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[rugged musk]

hiii im up to A. I got an answer but it wasnt right

my working was 2x^3 = 16x then i divided both sides by x

2x^2 = 16

2x^2 - 16 = 0

(x-4)(x+4)=0

x = 4, -4

but that was wrong

[visual hazel]

you missed x = 0

[rugged musk]

wdym

?

[visual hazel]

x = 0 is a solution of that equation

so if you divide both sides by x, you're dividing by 0

[shrewd thistle]

This is why your answer to "a" was wrong

You tried to factor where there were no factors

[rugged musk]

omg yeah i see

aha i wasnt even thinking

okay so x^2 - 8 = 0

what should I do to get x

[visual hazel]

2x³ = 16x

move the 16x to the left

2x³-16x = 0

factor out an x

then you'll get x = 0 to be a solution

and the rest is as above

[rugged musk]

yeah i see

[shrewd thistle]

Why'd you move the 8 back to the left? Just take the square root of both sides

[rugged musk]

oh yeah

wait u both saying two diff things

[visual hazel]

nah he's explaining how to solve x² = 8

im explaining how you missed x = 0 is a solution

[rugged musk]

yeah just start from the start

[shrewd thistle]

It's sort of the same thing, since x^3 means you have 3 potential answers.. when you factor out an x, x * 0 = 0, so one of your x values has to equal 0

[rugged musk]

okay if i factor out an x there

x(2x^2 - 16) = 0

[visual hazel]

indeed, but they just divided x in their first step, missing x = 0 as a solution, so im explaining how to get that

[shrewd thistle]

... = 0

[rugged musk]

yup

[rugged musk]

ummm what should I do after this

[shrewd thistle]

x(whatever, doesn't matter) = 0 means
x = 0

[rugged musk]

yeah i got that

so for 2x^2 - 16 = 0

just solve for x?

[shrewd thistle]

And you're left with x^2 = sqrt(8) that we just talked about

[rugged musk]

yeah

so x = sqrt8

then x = +- 2sqrt2

[shrewd thistle]

Remember.. there are two values here

[rugged musk]

yeah +- sorry forgot to add

[shrewd thistle]

np

[rugged musk]

ahh okay thank you

now i got the right answer just made a simple mistake then got everything jumbled

thank you!!

.close

[shrewd thistle]

best of luck!

[devout snow]

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[hexed ocean]

can someone please help me with this

[hexed ocean]

forgot to add the dx

but yea

[covert root]

Have you tried an integral calculator

[hexed ocean]

well yea

but I want to know how to do it

[covert root]

There may be numerous ways to do it. An integral calculator can walk through multiple ways of approaching the question

[blissful ocean]

Idk if this will help you, but you can walk through this

[covert root]

Maybe a u-trig substitution or u = x(1-x)

[hexed ocean]

damn wtf

so you can use inverse trig

[blissful ocean]

It is just wolframs answer Im not too sure, didnt look into it

[hexed ocean]

i mean it looks fine

im following it rn I just wish the question was shorter 😔

[devout snow]

@hexed ocean Has your question been resolved?

[hexed ocean]

alr I understand it now

thanks for the screenshots

[blissful ocean]

Np good luck

[hexed ocean]

.close

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[hexed holly]

hi all, im super duper confused about how this is solved

[hexed holly]

could someone like,, write what happens please

[opaque haven]

this is a proof using induction, very useful for dealing with any identity we want to prove that only works for natural numbers

to prove that a statement is true for all natural numbers n, we have to do the following:
prove that it holds true for n=1
and assuming that it holds true for n, prove that it also holds true for n+1

[hexed holly]

mm

[opaque haven]

think of it as a domino effect, if we prove those two then what do we know:

its true for n=1, so it must also be true for n+1=2
then, its true for n=2, so it must also be true for n+1=3

and so on, covering all the natural numbers

[hexed holly]

ah okay

[opaque haven]

well in ur class i guess you take n=0 as a natural number which isnt typical, but it doesnt change anything

you just start by n=0 instead of 1

[hexed holly]

yeah it was a bit weird lol

[opaque haven]

so what the proof does there is exactly that, prove that its true for n=0, then prove that if its true for n=k, this its also true for k=n+1

so now that the methodology is clear, do u have any issues with the algebra used?

since thats really the only other component of the solution

[hexed holly]

yeah i think im stumbling in the algebra

i understand until the 2nd line

with the (5+6)?

someone said it was because of the need for a multiple of 5

but then i dont know how it develops into the 3rd line

[opaque haven]

well on the third line, we just multiply 2*11^k with 5 and 6 respectively, expanding into the 2 last terms of the expression
on the 4th line, we factor out a 5 from the first 2 terms, since we can
on the 5th line we notice that (5^k +2 x 11^k) is the original expression we had, which we set equal to 3m, then the rest just stays as is
and then, on the 6th and final line, we factor out a 3 to turn it into the form of a number divisible by 3

is it clearer?

[hexed holly]

where does the 2*11^k come from?

[opaque haven]

on the left of the parentheses we have a 2, on the right we have the 11^k

[hexed holly]

oh im sorry brb - one sec sorry sorry

[opaque haven]

since in multiplication we can do our operations in any order we can, we are allowed to just do 2*11^k x (5+6)

[hexed holly]

okay back

oh so you just multiply the 2 before with the 11^k after? so its like (5+6)(2*11^k)

how would you know to do that?

oh no

wait

so its like

((2* 11k^)* 5)+((2* 11k^) * 6)

[devout snow]

@hexed holly Has your question been resolved?

[devout snow]

@hexed holly Has your question been resolved?

[devout snow]

@hexed holly Has your question been resolved?

[frozen aurora]

okay so

what exactly is confusing you here

[frozen aurora]

yes

[frozen aurora]

also yes

[hexed holly]

ohh okay

[hexed holly]

thank you :)

why does it then put 11^k inside the brackets on line 4?

[frozen aurora]

they factored out 5 from $5\cdot5^k + 2\cdot5\cdot11^k$

[woven radish]

artemetra

[hexed holly]

how?

[frozen aurora]

wdym how

$\pmb{5}\cdot 5^k + \pmb{5}\cdot2\cdot11^k$

@hexed holly

[woven radish]

artemetra

[hexed holly]

so they took the 5's from the equation?

[frozen aurora]

yes

they factored it out

[hexed holly]

ah okay

[frozen aurora]

to get $5(5^k + 2\cdot11^k)$

[woven radish]

artemetra

[hexed holly]

ohh

i get it now

in the last line everything was factored by 3 but the 11 was whole? do u know why this is?

[frozen aurora]

yeah that's fine

look

if you have 3*4*5, then this is definitely divisible by 3

but 4*5 will remain "unaffected"

$5(3m) + 12 \cdot 11^k = \pmb{3}\cdot 5m + \pmb{3}\cdot 4\cdot 11^k = 3(5m + 4\cdot 11^k)$

[woven radish]

artemetra

[frozen aurora]

if that helps, imagine you just had x instead of 11^k

[hexed holly]

ah okay

tysm for your help!!

[frozen aurora]

no problem

[frozen aurora]

once you do a couple of these yourself you'll quickly get the hang for them

[hexed holly]

haha yeah a bit tricky for the first one :)

tysm tho for real

have a good one!

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[amber birch]

so i need to find the domain of this function. from trial and error, i found the x to be greater than 3 but less than 4, or greater than 4 or less than equal to 6. but i got this answer rather difficult and took a long time. is there an easier way to solve a problem like this without trying to input multiple values in trial and error?

[manic plank]

Your square root can't be negative and you can't have values that make your denominator zero

[amber birch]

yes im aware of that, as it would make the function undefined

[manic plank]

That's what you'll need to find the domain restrictions

Right

[amber birch]

but when it's like

only one phrase

like sq rt of x-2

or a multiplication of roots

it's rather easy

but since it needs me to answer something that is root minus root

[feral agate]

The root - root doesn’t matter

All you need to make sure is that the argument in EACH root is strictly positive

And that the denominator can’t be zero

[manic plank]

Right, that's the same thing I said

but they're asking what about when it's a complicated equation

like the one above (I think)

[amber birch]

assuming that, i can understand the non neg values for both roots

but the

undefind point..?

my english is bad

[feral agate]

It’s not complicated, that’s the point

[feral agate]

You mean when the denominator equals 0?

[amber birch]

i only got it by inputting trial and error values

but would there be a faster route?

[feral agate]

Just set it equal to 0, find out what x is, and remove those values from the domain

[amber birch]

so the denom when x=0

[feral agate]

$\sqrt{x-2}=\sqrt{6-x}$

[woven radish]

kheerii

[amber birch]

so square both sides

[feral agate]

The value of x here is what you need to remove from the dominion

[amber birch]

then solve

[feral agate]

Yeah

[amber birch]

x-2=6-x

which yields 4

which makes it a zero denom

and makes it undefined

[feral agate]

Yes

So x=4 needs to be removed from the domain

[amber birch]

okay so i understood why it cannot include 4 as x value

and that it cannot be greater than 6

[amber birch]

thank you. one last thing, i understood the x cannot equal to 4, and also has to be less than 6 since in order to keep the function defined

but why does it have to be greater than or equal to 3?

i only got this value from trying to apply different x values but can't seem to understand why the answer i got is greater than or equal to 3

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@amber birch Has your question been resolved?

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[real cove]

Learning about First Order Logic and Prenex normal forms. Int this example I don't understand why the variable was changed in line 3

[real cove]

When the negation of the existential quantifier associated with x is turned into a universal quantifier the x is substituted by z

[devout snow]

@real cove Has your question been resolved?

[tough cove]

idk

this is weird

i have no clue

[devout snow]

@real cove Has your question been resolved?

[real cove]

Could be a typo

The third example of this video its the same as this but with the quantifier refering to z from the beginning
https://www.youtube.com/watch?v=vOfZ6LPAy3E

[worn lantern]

hi

i need help with this

[visual sundial]

always plug the value in first to check

in this case we get sin(pi/2) / (pi/2) which is not indeterminate

simply evaluate

[worn lantern]

give me a sec

sorry i still dont get it

can i just put it in a calculator

[visual sundial]

bruh 💀

limit means x is very close to the number

try to put pi/2 instead of x into the expression

what do we get?

[worn lantern]

ohhh

wait let me put it in the calc

[visual sundial]

bruh

[worn lantern]

cant i?

[visual sundial]

let's not endorse bad habbits

sin(pi/2)

which is sin(90)

which is?

[worn lantern]

1?

[visual sundial]

i mean you probably should know that

yeah

1 / (pi / 2)

dividing by a fraction is like multiplying by its inverse

= 2 / pi

[worn lantern]

oh thats it

[visual sundial]

yeah

[worn lantern]

thanks man

[visual sundial]

you're luck that the limit doesnt give us an indeterminate form

its like a trick question supposed to waste your time

[worn lantern]

lucky me

thx for the help

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[desert estuary]

Is this accurate?

[desert estuary]

im having trouble doing this, i think it might be because im setting it up wrong

its where I calculate the partial derivative of f/g or like h/r is where it goes wrong

[devout snow]

@desert estuary Has your question been resolved?

[cinder bobcat]

this setup looks right to me yep

[desert estuary]

could I also write it in terms of like f/x, f/y, f/z

i think just all the leters are confusing me

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[sour meteor]

Is the definition of choice function on a set of sets equivalent to the definition on choice function on the powerset?

[sour meteor]

https://proofwiki.org/wiki/Definition:Choice_Function

My book states that a choice function is a function $f: \mathcal{P}(S) -\left{\right}\to S$ such that $f(A)\in A$, for $A\subset S$.

[woven radish]

tales

[sour meteor]

But the usual definition is the first one in here

its easy to show that (1) => (2)

Now (2) => (1) I couldn't do

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[plush cove]

can someone do these rq? i know they're basic but I wasn't paying any attention in class

question 2,3 and 4

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[whole grove]

whats an easy way i can solve this:

Assume we have three 6-sided fair dice and two 4-sided fair dice. We roll all
five dice.

question: What is the probability that exactly 2 dice are showing 5, and that all the other dice
are showing values < 5?

[whole grove]

is this correct interpretation

i got 5.5 percent

is this right

it seems right logically

[dense lynx]

your process seems right yeah

though with rounding it would be 5.6%

also normally probability questions with well-defined sample spaces are answered with fractions unless you're asked to give a decimal

[amber valley]

Aren't the 4 sided die redundant? Since they will always show numbers <5

[whole grove]

basically is

[whole grove]

also for this question

What is the probability that 6 is the highest number showing?

is the 4 sided die still useless

its not right

[dense lynx]

the 4-sided dice cannot show 6 so they need not be considered

[whole grove]

is this the same as just checking the probability of getting 1 six

just reworded in a trickier way

[dense lynx]

seems that way

[whole grove]

yeah its weird

id assume its that

unless theres a hidden motive

idk lol

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[whole grove]

so would the probability be like 34 percent

[whole grove]

does 34 seem to high

[amber valley]

Are you counting the probability of getting two 5?

[whole grove]

nah just getting 1 six

question says What is the probability that 6 is the highest number showing?

im assuming that means prob of getting 1 six