help-26

[scenic flare]

sure

just inserted the mentioned values

[rose flame]

thank you, something wrong my geogbra but thank u so much

[scenic flare]

np :]

whenever stuck for longer just seek guidance here, tends to be quicker

[gleaming reef]

desmoss!!

amazing

[scenic flare]

and lets you solve it quicker next time

[rose flame]

u deserve compensation for this

[scenic flare]

Nou nou

your happiness is compensation hehe

[rose flame]

can you more simple question?

its not super hard but tricky

[scenic flare]

k

[rose flame]

find the high and lowest volicty of r_a(t)=(2cost-2, 2t, sint) when t is tall [0, 2*pi],

i found the hight which is 2*sqrt(2)

but stuc on lowest velocity

[scenic flare]

by highest/lowest velocity do you mean the highest and lowest values of r_a?

or what does r_a represent

[rose flame]

the velocity vektor of r which is r' and find the highest and lowest valus for it

[scenic flare]

ah k, well first find r'(t)

and then search the t values for which it's 0

[rose flame]

found that stuck on its highest and lowest valus

[scenic flare]

well the velocity is |r'(t)|

so we want to know it's min & max in the given interval

which we can find using |r''(t)| = 0

to get the extrema

r''(t) = (-2cos(t), -sin(t))

[scenic flare]

And then solve this for t :]

[rose flame]

got that, and then?

i got error

[scenic flare]

error?

[rose flame]

t=?

and {}

[scenic flare]

|r''(t)| = |√((-2cos(t))² + (-sin(t))²)|

= |√(4cos(t)² + sin(t)²)|

= |√(3cos(t)² + 1)|

now set that to 0

|√(3cos(t)² + 1)| = 0

[rose flame]

thank u, will try to do now

[scenic flare]

So it does end up at cos(t)² = -1/3

which isn't solvable

which is correct

because that means

The second derivative is never 0

Ah no, we have to take the derivative of the absolute velocity, not r', oops

sry for the confusion lol

[rose flame]

its okey i did more mistakes

[scenic flare]

We want to find out where the velocity doesn't change

To find extrema

so we need the derivative of:
|r'(t)|

I also didn't see the 2t at first, it's 3D right

[rose flame]

yea its has x,y and z

[scenic flare]

r'(t) = (-2sin(t), 2, cos(t))

[rose flame]

y?

[scenic flare]

comma

|r'(t)| = √((-2sin(t))²+4+cos(t)²)

= √(3sin(t)² + 5)

ok so now we have the velocity function

over time

then take the derivative of that function, solve for = 0 and you have the t-values

[rose flame]

√(3sin(t)² + 5) = 0 and solv for t?

[scenic flare]

nono first derive it

since we want to find the extrema locations

the derivative of that is
(6sin(t)cos(t))/√(3sin(t)² + 5)

and we solve that for = 0

so we can multiply be the root

to get
6sin(t)cos(t) = 0

sin(t)cos(t) = 0

is true if:

sin(t) = 0

or cos(t) = 0

[rose flame]

i got k*pi

[scenic flare]

so at t=0, π/2, π, 3π/2, 2π you have zeros

k*pi for sine

and the others for cosine

[rose flame]

oh got it

[scenic flare]

Now you can evaluate |r'(t)| at these 5 values

and get min & max

🪼

[rose flame]

brooo how are you so smart?

[scenic flare]

I have a bird on my shoulder whispering what I should do, I actually have no idea what I write

[rose flame]

you are a lifesaver

[scenic flare]

Wish thee good luck with further tasks

[rose flame]

thanks

.close

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[neon iron]

I need help doing B, I know how to do a

I don’t even know what the factor theorem and rational root theorem are

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

<@&286206848099549185>

Am I on the right track with B?

[plain mist]

yes

[neon iron]

What do I do next?

@plain mist

[plain mist]

$k^3 - k = 0$

[thorny flame]

Rare fish

[plain mist]

then factor and solve

[neon iron]

Yeah, but then I moved k over

I don’t understand

[plain mist]

its like what you did in a)

with (x+3)(3x-2)=0

you want it in that form so you can solve for them individually at =0

[plain mist]

looks good

[neon iron]

Would you please teach me how to do d?

Could you teach me how to do the rest on this page PLEASE 😭

@plain mist

[plain mist]

if x-a is a factor, then we know x-a=0 or x=a

from there sub in a into all x's and solve for a

[plain mist]

im a busy man.

[neon iron]

I understand

[pastel coral]

Yo is the answer 315? This is a trick question given to me by my teacher

[neon iron]

Dude leave my channel please

[pastel coral]

ok

[neon iron]

Why did I get 2 k values here?

[plain mist]

didnt check the rest of it but it looks like you multiplied 2(-1)^4 with (k + 1)

when its 2x^4 + (k + 1)

[neon iron]

Is this one being done wrong?

It’s 5d

@plain mist

[plain mist]

why did you put (a+5) in brackets

[neon iron]

It’s being multiplied

[plain mist]

its $x \times (1-a^2)$

[thorny flame]

Rare fish

[neon iron]

Oh wtf

I thought it was the whole thing

[plain mist]

the +5 is afterwrds due to PEMDAS

[neon iron]

How do I do F?

[plain mist]

you can just multiple those factors together

[neon iron]

Like that??

[plain mist]

yes

[neon iron]

Uhh

[plain mist]

actually idk why i thought it was asking for the lowest degree of x instead of the lowest degree of the entire polynomial.

[neon iron]

Bruh

[plain mist]

the process is still right, but its technically asking for highest

just that those factors are not the only ones

so it would be degree 6 since its x^6

[neon iron]

The answer key says degree 4

[plain mist]

. . .

does it give any explanation

[plain mist]

ok thats what it means

[neon iron]

I don’t get it

[plain mist]

its cause there are repeating factors

[neon iron]

Uhh

[plain mist]

since all 3 of those factors couldve still been further factored

[neon iron]

Uhh

Okay

[neon iron]

@plain mist how do I do g?

[plain mist]

its pretty much d)

[neon iron]

@plain mist how do I do h?

[plain mist]

if x at those values = 0 then they are factors

[neon iron]

I don’t get it

[plain mist]

ex. p(-2) = 0 means x at -2 = 0

[neon iron]

Yeah

So what do I do

[plain mist]

use those as your factors then solve for the remaining

[neon iron]

?

I don’t get it

[plain mist]

idk what your textbook solution says but i would do (x+2)(x+1)(x-1) then solve for whatever polynomial multiplied by those 3 = the given function

[neon iron]

Ok uh how do I do J?

@plain mist

[plain mist]

i feel like theres an easier way that im not seeing but i think you could solve it using a system of equations since its 2 unknowns

can i see the textbook soln

[plain mist]

ok yh nvm they just did a system of eqns

since x-1 is a factor they just plugged in x=1, then arrived at two eqns

and from there you can either do substitution or elimination

it looks like they did substitution. letting -a + b = 0 -> b = a, sub into eqn 1 for b + b = -2

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[molten crystal]

hey, studying resonance with fourier series
important parts are highlighted

[molten crystal]

does this means that I can still read the ibase frequency of the input and know that the response will be a multiple of that?

I mean, if the natural freqency is a multiple of that i can get resonance

?

even if i don't know which multiple.

[short acorn]

This is math sir not physics

[molten crystal]

so I must be in the right server, this is in the MIT program to solve differential equations.

[short acorn]

Ok well maybe this is wat u call applied math, but thats just generization for math used in science

So....

[molten crystal]

hopefully someone can help me out here 🙂

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@molten crystal Has your question been resolved?

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@molten crystal Has your question been resolved?

[molten crystal]

<@&286206848099549185>

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@molten crystal Has your question been resolved?

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@molten crystal Has your question been resolved?

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@molten crystal Has your question been resolved?

[molten crystal]

https://tenor.com/view/whatever-sassy-ugh-duh-eyeroll-gif-17849793169258709107

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[slender sonnet]

1280,640... is a geometric sequance find the members number that is equal to 20

[twin surge]

do you know the formula to find nth term of a gp?

[karmic dove]

what is this?

[slender sonnet]

yes

[twin surge]

here use 1280 as the first term

common ratio will be 1/2

now put it in the formula

youll get it

[slender sonnet]

ok wait

[twin surge]

yes

[slender sonnet]

whats n tho?

[twin surge]

n is the "members number"

youre supposed to find it

[slender sonnet]

an=1280 * (1/2)^n-1?

?

[twin surge]

yess

an here is 20

20 = 1280 * (1/2)^n-1

youll get the value of n by this

[slender sonnet]

ok

[twin surge]

ok

did u get the ans

[slender sonnet]

n=7

thanks a loy

[twin surge]

yes

[slender sonnet]

lot

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[radiant lotus]

How would I show the answer here?

[topaz sinew]

@radiant lotus Has your question been resolved?

[tough nest]

you show that the vectors you find through solving that matrix equation are closed under addition and scalar multiplication

which is the condition for being a subspace

it is if and only if

the last part of the question is about the vectors themselves

what euclidean vector space are they members of as in what's the shape i think is what they're asking

ok so the answer seems rather trivial if i'm honest

[radiant lotus]

It was supposedly easy but I was not sure how to answer it

[radiant lotus]

wait how do you show if 2 matricies are a subspace? i've never done that

[tough nest]

to show a subset of a vector space is a subspace all you have to show is that the set is closed under vector addition

take any 2 vectors in the subset and show that the addition of them always results in another vector in the subset

and closed under scalar multiplication

meaning take any vector in the subset and scale it using any arbitrary number and show that the result is also in the subset

if both are true

then your subset of your vector space is a subspace

you have to show that the solutions to that equation

meaning any vector (x, y) that solves that equation

is part of a subset of the total vector space of any (x, y) vectors

R^2

that is closed under those two operations

meaning take any of the vectors that solve that equation

and add another one to it

and it must result in a vector that is also part of that subset

idem for scalar multiplication

try to first find all vectors (x, y) that solve that equation

step 1 is that

[radiant lotus]

so could i say for the 0=0 first part that <0+2(0) , (0)+2(0) , 2(0) - (0)> which equals <0 , 0 , 0> and thus <0 , 0 , 0> = <0 , 0 , 0> ?

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[radiant lotus]

thank you @tough nest

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[neon iron]

Hi, how can i do to get the roots of : x⁴+81

[normal tapir]

it's a difference of squares

(x^2 + 9i)(x^2 - 9i)

[neon iron]

My bad

Its a + not a -

[normal tapir]

.

[neon iron]

I know the method to do it for a difference

But with a sum idk

[normal tapir]

it's the same thing

[neon iron]

Huh

[normal tapir]

but 81 = -(9i)^2

[neon iron]

Wait

[neon iron]

Where does it come ?

[normal tapir]

just distribute this and see

[neon iron]

Yeah i believe you but how you thought about it

[normal tapir]

a^2 + b^2 = (a+bi)(a-bi) in general

[neon iron]

Ohhh i had in mind only a²-b² and not a²+b² too

So i just have to aplly it here

[neon iron]

Am i not supposed to have 3's instead of the 9's?

Found, ty

By using complexs formulas

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[keen patio]

is the question asking to reduce to RREF first?

[keen patio]

looks like they arent in the correct form yet but im not sure

[hollow drum]

No those are in REF, you don't need to make it RREF

You can solve the system in that form

[keen patio]

oooh ok

[hollow drum]

They are augmented matrices

[keen patio]

i see

i was confused because i thought they wanted me to change them first

i mean technically i can but i dont need to

[hollow drum]

Yeah you technically can make it RREF but it's not needed

[keen patio]

would it be worth the time to do that or would it just be easier to solve

[hollow drum]

I'd say just solve

[keen patio]

ok ig i was just overthinking it

thx so much

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[blissful mantle]

is this right?

[radiant marlin]

yes

[blissful mantle]

this as well ?

[normal tapir]

Yes

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[blissful mantle]

i need help with this, can someone help?

[simple bloom]

what part are you confused about?

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[blissful mantle]

why my answer is wrong

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[sweet salmon]

Could I please get a hand for (ii)

so i differentriate it to find the suprema

[worthy storm]

sounds promising

[sweet salmon]

I got n/n+1

i mean i got x = n/n+1

but i'm not sure what I would do next?

So i figured i plugged it in

[worthy storm]

what's f_n(x) for that x

[sweet salmon]

let me write up

$\frac{n^{k+n}}{(n+1)^{n+1}}$

[thorny flame]

Twitter (formerly X)

[meager dawn]

oh my god its twitter, the famous hit app for writing short, quippy blurbs of text

[sweet salmon]

@worthy storm what you think, what would we use k < 1 for?

[worthy storm]

you can try rearranging things a bit, maybe like:
$$\left(\frac{n}{n+1}\right)^n n^{k-1}$$

[thorny flame]

Bungo

[worthy storm]

the first factor has a finite nonzero limit

so this overall expression goes to zero if and only if n^(k-1) -> 0

[sweet salmon]

ah I see i get it

thank you so much

also could you please explain L2 convergence

I don't quite ge it

for part (iii)

[meager dawn]

can you state the definition of the L2 norm?

[worthy storm]

write down the definition of what it would mean for the sequence to converge to zero in the L^2 sense

[worthy storm]

ok, so specialize this to your situation:

[sweet salmon]

but i don't know what f(x) is

so k is the n right

[worthy storm]

it's the limit function

in your case zero

[sweet salmon]

so we are integrating this squared

[worthy storm]

yep

[sweet salmon]

and taking the limit

[worthy storm]

and finding out what k needs to be in order for that integral to go to zero

as k->inf

[sweet salmon]

the end point is 0 and 1 right?

[worthy storm]

yes

just square everything

integrate from 0 to 1

and see what the result is

[sweet salmon]

okay let me do the calculations and I will ost it

This i my working

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[atomic wadi]

tension are equal becuz question stated system is in equilibrium..?

[atomic wadi]

also how do i find R for iii)

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[young heron]

can I get a hint

[drifting heart]

how to do skib'

[young heron]

oh sorry I took this one a few seconds before you. can you use another help channel as I alrdy opened this one

[acoustic tangle]

Start by taking logarithms of both sides of the equation

[young heron]

like this ?

sorry for inverted pic

[acoustic tangle]

Yes

[acoustic tangle]

,rotate

[acoustic tangle]

You kind of changed what's on the left and on the right though

[young heron]

hm

[acoustic tangle]

It's supposed to be [ \log!\left((2x)^{\log2}\right) = \log!\left((5x)^{\log5}\right) ]

[thorny flame]

A Lonely Bean

[young heron]

oh

then you get this using properties of logs

?

[acoustic tangle]

Yes but I just realized we don't even need to take logarithms here

[young heron]

hm

then how do we solve it ?

[acoustic tangle]

It's $2^{\log2}x^{\log2} = 5^{\log5}x^{\log5}$ so you can isolate $x$ easily

[thorny flame]

A Lonely Bean

[acoustic tangle]

Start by dividing by x^log2

[young heron]

wait wouldnt that remove x

?

[acoustic tangle]

Only from the left side

[young heron]

oh ok

[acoustic tangle]

Ah and keep in mind that x = 0 is a solution

[young heron]

oh ya I forgot to mention question says x>0

[acoustic tangle]

I see

[young heron]

sorry for the messy work

where to give from here?

I am sorry a little stupid today

[acoustic tangle]

On the right you have x^{log5 - log2} = x^{log(5/2)} and you can raise both sides to the power of 1/log(5/2)

[young heron]

wait what gonna be the left side then

cause right becomes x

@acoustic tangle

[acoustic tangle]

$\left(\frac{2^{\log2}}{5^{\log5}}\right)^\frac1{\log!\left(\frac52\right)}$

[thorny flame]

A Lonely Bean

[acoustic tangle]

Hmm, I don't see a good way to simplify this

[young heron]

ya

[acoustic tangle]

Besides using change of base formula

[young heron]

wait wouldnt it be raised to ^1/log5-log2)

I could change base on one side you are right

[acoustic tangle]

log5 - log2 = log(5/2)

[young heron]

oh ya nvm

[acoustic tangle]

I mean in both numerator and denominator

[young heron]

ya

I think this is correct ?

[acoustic tangle]

\begin{align*}
\left(\frac{2^{\log2}}{5^{\log5}}\right)^\frac1{\log!\left(\frac52\right)} &= \frac{2^{\frac{\log2}{\log!\left(\frac52\right)}}}{2^{\frac{\log2}{\log!\left(\frac52\right)}}} = \frac{2^{\log_{2.5}2}}{5^{\log_{2.5}5}} \
\end{align*}

[thorny flame]

A Lonely Bean

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@young heron Has your question been resolved?

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[slender sonnet]

Equalavent pentagons neighboring sides are MN and NQ in that pentagon there is a point P so it makes MPN equalaveng triangle. Need to find angle NQP

[slender sonnet]

Bad diagram but

<@&286206848099549185>

<@&286206848099549185>

.close

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[neon iron]

hel

[neon iron]

<@&286206848099549185>

[fierce thicket]

No.1,2,4

[fallow igloo]

!status

[topaz sinew]

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

[neon iron]

thanks

[fallow igloo]

!nosols

[topaz sinew]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[fierce thicket]

what do you mean?

[fallow igloo]

Don’t give out the answer without guiding them

[fierce thicket]

ok but how do you explain this question, i found it no need to guide or idk how to guide such question

[fallow igloo]

I’ll ask where are they struggling at in the first place

If they weren’t paying attention in class, I would give them sources for them to look up prior to solving this question

It’s totally meaningless for you to give out the answer to them directly since they might ask similar basic questions again and again

[fierce thicket]

got it

[fallow igloo]

.solved

[topaz sinew]

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[topaz sinew]

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[topaz sinew]

@dark pond Has your question been resolved?

[topaz sinew]

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[topaz sinew]

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[acoustic mulch]

When doing first order differentials, say we have x^4y = x^6 - x^5, then we divide by x^4

[acoustic mulch]

since we’re integrating both sides, we get y = x^2 - x + c/x^4

but why is c divided by x^4 since its a constant

as in c/x^4 = c as c is just a constant

[topaz sinew]

@acoustic mulch Has your question been resolved?

[topaz sinew]

@acoustic mulch Has your question been resolved?

[mossy tree]

i can't see any c in the original expression

it must be y = x²-x i guess

[acoustic mulch]

sorry its d/dx (x^4y)

so you integrate both sides

[mossy tree]

wait why did we integrate

it's derivative

[acoustic mulch]

x^4y = x^2 -x +c/x^4

to get rid of the dydx

[mossy tree]

oh okay

so what is the original question

[acoustic mulch]

ill send a picture 1 second

[mossy tree]

sure

[acoustic mulch]

im just curious as to why c is divided by x^4 since c is a constant anyway , dividing it by x^4 gives a constant too

[mossy tree]

no

it doesnt gives

there is x term as you can see

c/x⁴

is not just constant

is 1/x⁴ constant?

c is constant (c = 1 in this case)

1/x⁴

[mossy tree]

but 1/x⁴ is not constant itself

1 is constant but 1/x⁴ is not

like this

[acoustic mulch]

ohhhh

that makes sense

thank you @mossy tree

.close

[topaz sinew]

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[mossy tree]

youre welcome

[topaz sinew]

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[finite panther]

How do u do the derivative?

[restive inlet]

power rule

[finite panther]

wats the power rule?

[acoustic pecan]

x^n -> nx^{n-1}

[finite panther]

so is the answer to the first one y′ = 10x + 7 ?

b = f ′(x)=− 28/x ^5?
​

c = y ′ =− 15/2x * 1.5?
​

d= f'(x) = 7x^{5/2} + \frac{1}{3}x^{-4/3}?

e = y' = 4?

f= (f'(x) = \frac{35}{2}x^{3/2})?

[topaz sinew]

@finite panther Has your question been resolved?

[finite panther]

can someone tell me if they are right?

[finite panther]

<@&286206848099549185>

<@&286206848099549185>

[lofty jetty]

Uh

I'm sorry what was the question

[finite panther]

finding the derivatice for e d and f

im asking if i got the correct asnwer

[ebon flume]

For e

Think of simplifying

The expression

[finite panther]

so is my answer wrong?

[finite panther]

d= f'(x) = 7x^{5/2} + \frac{1}{3}x^{-4/3}?
e = y' = 4?
f= (f'(x) = \frac{35}{2}x^{3/2})?

[ebon flume]

Is that ur answer for e

[finite panther]

yea the one that say e =

[finite panther]

and is d and f right or wrong aswl

?

[ebon flume]

e is correct

f is right

Same with d

[finite panther]

ok thx very much

.close

[topaz sinew]

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[topaz sinew]

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[pale barn]

Calculate the points at which the tangent line to the graph of the function f is parallel to the abscissa axis.

[pale barn]

f(x)= x^2-4x+9

how do i start?

<@&286206848099549185>

thank for the help

.close

[topaz sinew]

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[topaz sinew]

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[topaz elm]

how do i do this

[topaz elm]

I tried doing A - λI = 0

and got

[topaz sinew]

@topaz elm Has your question been resolved?

[topaz elm]

<@&286206848099549185>

nvm im just gonna go to a tutor

.close

[topaz sinew]

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[topaz sinew]

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[fringe apex]

what do I do with the decimal point if the divisor is a decimal number? the answer is 72, but I got 7.2

[fringe apex]

I recently learned that making up a 0 means you should add a decimal before it, then drag that up

[smoky sinew]

0.5 goes into 3 evenly

also thats not how equivalent fractions are done

[still reef]

what you've done is divide by five instead of 0.5, which is why your answer is 10x smaller

[fringe apex]

yeah for divisions with decimals I was taught to assume they're whole numbers then add the decimals afterwards

but its been a while so I forgot what to do with the decimals afterwards

[still reef]

im not sure how to word what i want to say properly, sorry, hopefully someone else can answer it for you

[topaz sinew]

@fringe apex Has your question been resolved?

[dusky harbor]

Just take 0.5 as 5/10 which results 360/5 w that eqn

[still reef]

Ok, when you want to divide decimals you can count how many decimal places forward you have to move the decimal point forward to make it whole. Then in the answer you have to move the decimal point the same number of spaces forward again

@fringe apex

[fringe apex]

no the original question is 36/0.5, the .0 is a number I made up

[dusky harbor]

Either way

[still reef]

The .0 under the division has no effect on the answer

[dusky harbor]

You can again do 36/(5/10)

[still reef]

Because all numbers have .0 at the end technically

[fringe apex]

to move 0.5 to become a whole I'd move the decimal one place, it'll then become 05 (5)

72 doesnt have a decimal so theres no need to move?

[still reef]

Your answer was 7.2 so you had to move it to 72

[fringe apex]

ohh alr, since I moved to the right once for 0.5 to make it 5, I have to move to the right for 7.2 to make it 72?

@still reef

[still reef]

yeah

[fringe apex]

but since I got 7.2, isnt moving the decimal from .0 up to the answer area the right move?

[still reef]

i dont follow

ohh nvm

no, when you add the .0 it doesnt change anything because writing for example 32 is the same as 32.0 and even 32.00, they are all the exact same number

the same goes for 5.3 is the same as 5.30

you can add as many zeros after the last digit after the decimal point and the number doesn't change

[topaz sinew]

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[mortal pewter]

hi my questions is about the b1.5 because the lenght of A3C3 is 4LE/cm and i don t understand why

im sry for the poor quality and some sentences might be wrong because i was using google lens to translate it

[topaz sinew]

@mortal pewter Has your question been resolved?

[topaz sinew]

@mortal pewter Has your question been resolved?

[topaz sinew]

@mortal pewter Has your question been resolved?

[topaz sinew]

@mortal pewter Has your question been resolved?

[topaz sinew]

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[tight rivet]

How do I do this

[grand solar]

start by listing the information you have

you showed that the hyptoenuse is 15, what other informatiion do you have

[tight rivet]

Ladder=15 ft. Bottom of ladder =10 feet from wall

[grand solar]

theres another piece of information also

[tight rivet]

Derivative of something is 1/4 ft/sec?

[grand solar]

yeah but what is that something

[tight rivet]

Idk

[grand solar]

try imagining it in your head, the ladder is being pushed toward the wall

[tight rivet]

Ladder being pushed to wall

[tight rivet]

Ok what now

[grand solar]

what are they asking you to find

they are asking you to find the rate of change of something

[tight rivet]

Deriv of how fast the top of ladders moving up

[grand solar]

which side of the triagnle would that be

[tight rivet]

Left

Vertical line?

[grand solar]

yeah

so we have this so far

[tight rivet]

Ok

How do I know which is adjacent or opposite

There’s no theta

[grand solar]

well we don't need to know theta

we can use the information we have to solve for some things

we have x and y

that means we can solve for z

the variables were kind of confused

so I switched y and z

[tight rivet]

Sqrt125

[tight rivet]

Y=sqrt125

[grand solar]

yeah

using the information in the problem do you know what dz/dt is

[tight rivet]

It’s moving at a rate of 1/4 ft per sec

[grand solar]

thats dx/dt

the length from the bottom of the ladder to the wall is shrinking by .25ft/sec

the length from the bottom of the ladder to the wall is x = 10

z is the length of the ladder

[tight rivet]

Idk then

[grand solar]

so dz/dt is rate of change of the ladder's length

[tight rivet]

Is it 0?

[grand solar]

yep

since the ladder length is constant

the derivative of any constant is 0

so now we have all the variables values except for the one we wish to find dy/dt

[tight rivet]

What’s the point of deriving it then

[grand solar]

because we'll need that information when solving for dy/dt

and actually I made a mistake x isn't 10

x is 10 - (.25*12)

because we need to find dy/dt when it is 12 seconds after

and so that means y would be different also but z would be the same

Basically once you get those values

you'll use the pythogrean theorem and differentiate the pythregrean theorem

this will give you an equation of dy/dt, dy/dz, dy/dx, x, y, and z

and we have all those vairables except dy/dt

so we would rearrange and solve for dy/dt

then plug in values

you'll be using implicit differentiation to differentiate the pyhtogrean theorem

[tight rivet]

Bruh this is so confusing

[grand solar]

so we want to find how fast is the length of the wall to the ladder is changing after 12 seconds right, from the triangle we drew we labeled that as y

we were giving the intial value that x is 10 at time 0

and we were given that x decreases at a rate of .25ft/sec

so we want what x is 12 seconds after the intilize time 0

10 -.25(12)

the basically gave you the position equation with 10 as the intilial position

x(t) = -.25t + 10

[tight rivet]

7

[grand solar]

and t = 12

yep

so now we know that 12 seconds after, the length of the bottom of the ladder to the botton of the wall would be 7

we use this information along with that z is 15 the length of the ladder

to find what y would be after 12 seconds

and that would be the pythogrean theorem what we did earlier

[tight rivet]

Why did the signs switch

[grand solar]

the signs didn't switch -.25(12) + 10 = 10 -.25(12)

I just moved the 10 to the back

10 + (-.25(12)) = 10 -.25(12)

but its the same equation

so we got 7 for x

now you can find y

which would be the length from the bottom of the wall to the top of the ladder after 12 seconds

[grand solar]

if you meant why the did I say .25ft/sec before and -.25ft/sec now is becaus before I said it was 'decreasing' by 25ft/sec

it's important to put a negative in front of the rate of change when a problem says decreasing or you'll get the wrong answer and they'll take off points

This is what we have right now

[grand solar]

in this picture dx/dt shouldve been negative

[tight rivet]

So 7^2+y^2=15^2?

[grand solar]

yeah

[tight rivet]

Sqrt176

[grand solar]

yeah

so that's y

now we have all the values again but the correct ones for when it's 12 seconds after

now you have to find an equation where you can differentiate it and solve for dy/dt

and thats the pythagreon theorem

x^2 + y^2 = z^2

you'll have to differentiate that with implicit differentiation

[tight rivet]

Mann what

[grand solar]

did you learn implicit differentiation

[tight rivet]

So 49+sqrt176=225

I deriv that

[tight rivet]

Yeah

[grand solar]

do you remeber how to do it

how can you take the derivative of this equation x^2 + y^2 = z^2

you can't plug in the values

because we want to derive this and when we do we'll get out a dy/dt, dx/dt, dz/dt

[tight rivet]

2x+2yy’=2z

[grand solar]

close

everything is a function of time

so we can't just say 2x and 2z

it'd be

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

[tight rivet]

Ok

[grand solar]

now get dy/dt by itself

and then plug in the values we found

and that'd be your answer

[tight rivet]

2z-2x/2y with their deriv thing

?

[grand solar]

yep

[topaz sinew]

@tight rivet Has your question been resolved?

[topaz sinew]

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[topaz sinew]

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[whole igloo]

How would I get started on these?

[quaint badger]

you need to know the fundamental theorem for abelian groups

[whole igloo]

i mean

so just..

?

[quaint badger]

yes

[whole igloo]

Oh.

Okay, I see

thanks !

.close

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[devout dove]

Can someone explain to me the difference between the First Fundamental Theorem of Calculus (FTC) and the Second Fundamental Theorem of Calculus?

[glossy fable]

The second one includes chain rule

[devout dove]

When should each one be used?

[topaz sinew]

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@devout dove Has your question been resolved?

[topaz sinew]

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[sick kestrel]

Im not really sure what i should do after finding the first derivative

[eternal cave]

Antiderivative

These term helps u with C term

[topaz sinew]

@sick kestrel Has your question been resolved?

[sick kestrel]

i bit confused

[simple bloom]

what did you get when you found the first derivative

[sick kestrel]

i tried to make it equal to f'(0) = 2

and solve for C

[simple bloom]

yes that’s the right idea
what did you get for the first derivative though?

you can find the first derivative by taking the anti derivative/ integral of f’’(x)

(ping me when u have an answer)

[sick kestrel]

@simple bloom

[simple bloom]

mm not quite

so you’re taking the integral of -4sin(2x)

are you familiar with u-substitution?

[sick kestrel]

i dont think so

[simple bloom]

do you know how to take the anti derivative / integral of something ?

[sick kestrel]

yea i kinda need to do the reverse of finding the derivative

[simple bloom]

mhm, so u-substitution is a method you use when solving for integrals i would recommend watching a video explaining u-sub

and once you can get the integral of -4sin(2x) we can move onto the next step

(or i can try explaining it, i think a short youtube video might help though)

[sick kestrel]

if you could try to explain the process that would help since i can ask you questions directly

if u want of course if not i can try to find a video then come back later if thats easier for u

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[delicate viper]

https://cdn.discordapp.com/attachments/903486480985489478/1230011139367112735/Screenshot_2024-04-17_at_12.24.32_PM.png?ex=6631c424&is=661f4f24&hm=5442f1bb3a0f9a492263c1d8f360b664270f490f9828b4d8beaed991b74970b0&

[delicate viper]

.close

[topaz sinew]

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[south phoenix]

all i know is f(x) = x^ln(x)

[neon iron]

Try doing logarithmic differentiation both sides, first take ln..then do it

[south phoenix]

i figured

1/x ln (x)

[radiant sparrow]

gonna be 1

[topaz sinew]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[south phoenix]

1/x * 1/x

or i mean

1/x * ln(x)

= ln(x) / x

1/1

= 1

[neon iron]

Now differentiate it since 1/x*(lnx) =ln(f(x))

You need f'(x)

[south phoenix]

derivative of this?

[neon iron]

Yess and also derivate of the LHS..that would be derivative of ln(f(x))=ln(x)/x since you took ln() both sides

[south phoenix]

i got

ln(x) - 1 / x^2

.close

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[neon iron]

Yess and on the LHS you be get smt else

That would be f'(x)/f(x)

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[slender sonnet]

on a circle race track there are 2 cars that are moving. they meet each other every 40 mins when they go the same way and they meet in 10 mins when thy move the oppisete way. what time would it take for each car to go around the whole track

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[quasi socket]

x/4 + 5/2 = 3/4 - 5/2

[quasi socket]

Solve

It

[verbal crater]

all unknowns on one side, all constants on other side

simplify and solve

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[sonic ibex]

Annette is a senior typist and makes an average of 2.5 mistakes per letter, if she writes 80% of all the letters what’s the probability a randomly chosen letter contains exactly three mistakes

[sonic ibex]

Why is this not just P(X=3) x 0.8

[sonic ibex]

Poisson Dist.

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.close

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[misty mica]

Use a calculator or spreadsheet program to investigate the existence or otherwise of the limits for the functions below. Write the limit, if possible.

lim x^2/2^x
x - infinity

[misty mica]

help i'm stuck on this question

i haven't tried anything because i have no idea where to start

[west ocean]

Positive infinity?

[misty mica]

yeah

a limit

x -> infinity

[west ocean]

It's 0

I think

[misty mica]

yeah you're correct

[knotty ledge]

Try using a calculator like they suggest

[misty mica]

but idk how it works

[west ocean]

Use L hopital rule

[knotty ledge]

Plug in bigger and bigger values of x

[west ocean]

This is what I used

[misty mica]

ohh

aight i see

[misty mica]

thanks

[strange topaz]

blud what

[west ocean]

L'Hopital's rule

[misty mica]

idk that yet

[strange topaz]

why u need that

[misty mica]

it's harder limits

we aren't taught that in our books

[strange topaz]

i know what it is

[misty mica]

uh ok

[west ocean]

You basically just need to get the derivative

[strange topaz]

its obviously 0 why would u need that. though

[west ocean]

To evaluate the limit

If it's need solution

To prove it

[strange topaz]

oh

wait

is it baically. inf/inf/0/

inf/inf=0/0

[west ocean]

Yeah

Common limit

[misty mica]

my calc says error lmao

[strange topaz]

bro u dont plug in infinity

u put in random numbers

bigger and. bgiger

[west ocean]

Yeah put 9999999

[strange topaz]

and see what number it approaches

[knotty ledge]

Use wolfram or desmos

[west ocean]

Table of values

[misty mica]

i did that

[strange topaz]

oh

[misty mica]

i tried 900

and it says error

💀

[strange topaz]

u dont have g raphical calc

yeah use what EAC s aid

[misty mica]

kk

i'll use desmos

ohh

ok i got it

thanks

.close

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[obsidian pawn]

if i have a augmented matrix in a general solution. does free variables mean i can put what ever value i want into it and the solution stays the same?

[knotty ledge]

Wdym "stays the same"?

If you have free variables it means you have infinitely many solutions, coming from picking whatever value you want for those free variables

[obsidian pawn]

like
equations = some number
equations = some other number

what ever value i say the free variables are the, rhs is always the same?

[narrow wyvern]

what's free variables?

[obsidian pawn]

wdym, do u want to me show the example or just asking what they are

[narrow wyvern]

if you can show a simple example it would be nice

[obsidian pawn]

its basically a variable that doesnt have a pivot in the matrix

so it has infintely many solutions

[narrow wyvern]

like if -2x = 0; -2 + z = 0; then a basis could be {0,1,0}?

y would be the free variable you are talking about

[obsidian pawn]

why are u asking me this

[narrow wyvern]

trying to make sense of your question, since linear algebra is taught in different ways

[obsidian pawn]

ok hang on ill just give an example

[narrow wyvern]

I think I know what you're talking about but we probably describe things differently

[obsidian pawn]

lets just say i have the augmented matrix
1 0 0 2 | 3
0 0 1 7 | 2
0 0 0 1 | 9
in this case x_2 is the free variable
what im asking is, if i set x_2 to be any number, then will the 1st equation still always = 3, 2nd = 2 and 3rd = 9

[narrow wyvern]

yes that's exactly what I was talking about

x_2 can be any number

[obsidian pawn]

ok yeah i understand that x_2 can be any number, im asking what affect it has on the system

so if x_2 is any number, it will effect what x_1, x_3, and x_4 are. But does the effect the solution to the equations?

[narrow wyvern]

no it won't have any effect

think of it like these

you get the general solution as an 3-by-1 matrix

in order to get that 3 by 1

you are using the 3x4 matrix times the 4x1 matrix

the 4x1 matrix would be (x_1,x_2,x_3,x_4)

since the second column of 3x4 matrix are all zeros

x_2 just zero out

[obsidian pawn]

oh ok

and conversely, chaning x1, x3 and x4 would have an effect

[narrow wyvern]

1 0 0 2 | 3
0 0 1 7 | 2
0 0 0 1 | 9

Can be written as

1x_1+0x_2+0x_3+2x_4=3
...... etc

[obsidian pawn]

yeah got it

thanks

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[obtuse quail]

part b?

i thought it should be:

(4!+4!+3!)/5!

[honest current]

a.1 is 4!, and a.2 is 3!

here's trash drawing

A = anna, and X is where anna is not

drawing these tables make it really easy!

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[obtuse quail]

Thank you @honest current

[obtuse quail]

Would you agree that b is this ?

The answers in the booklet say (4!+4!-3!)/5! But that doesn’t make sense to me

[honest current]

i think it means 4! (anna on left) + 4! (elena on right) + 3! (both anna and elena on left and right) divided by how many people there are?

sorry i am not sure

[obtuse quail]

Yes that is what I thought

The answer booklet must be wrong (it has errors from time to time)

[obtuse quail]

.close

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[arctic rock]

LIKE

[arctic rock]

how do I do this

[swift grove]

use the unit circle

or just transform the inner angles

for example

[arctic rock]

i dont get it but im following

[swift grove]

,tex $ \sin \frac{3\pi}{4} $

$ = \sin (\pi - \frac{3\pi}{4}) $

$ = \sin \frac{\pi}{4} $

$ = \frac{1}{\sqrt 2} $

[thorny flame]

math X meth ✓

[swift grove]

or you can also think of it as

,tex $ \sin \frac{3\pi}{4} $

$ = \sin (\frac{\pi}{2} + \frac{\pi}{4}) $

$ = \cos \frac{\pi}{4} $

$ = \frac{1}{\sqrt 2} $

[thorny flame]

math X meth ✓

[swift grove]

@arctic rock

there are some useful tricks

but its too long to explain here

[arctic rock]

I don't get it, why did you do (pi - 3pi/4)?

[arctic rock]

tricks? is there like some video?

these are the following questions

i dont get these nor the prev ones

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[native cedar]

Question is:
Find the number of solutions. x∈Z

[native cedar]

I don’t know what I did wrong but answer is 3
(I found only 1 solution)

[solid dagger]

you should multiply by $9^{0.5}$ instead of dividing by it

[thorny flame]

Valsorim

[solid dagger]

in line 2

[native cedar]

Oh yeah…

My bad

thanks

.close

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[ornate magnet]

!status

[topaz sinew]

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

[ornate magnet]

@delicate viper [ABTP]=[OBT]-[OAP]

Where [] represents area enclosed

Remember the formula of area of right triangle

[delicate viper]

is it a= 1/2 x base x height

??

[ornate magnet]

Yep

[delicate viper]

.. how do i do it

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[pine sonnet]

does anyone know what this means?