thats correct yes
#help-13
red pumice
soft ivy
Is that the only method? Taking the integral and then substituting it into the Maclaurin format for tan^1?
Sorry if that's redundant. I just want to make sure. It didn't seem like the appropriate way to figure it out lol
red pumice
only method to integrate this?
red pumice
well you can always use riemann sums to integrate
but if youre looking for an antiderivate, there does not always exist an antiderivative composed of elementary functions
cedar kilnBOT
cedar kilnBOT
Available help channel!
light pine
cedar kilnBOT
violet night
why ?
high lance
Hello! I just need to confirm something
can I write
$$\frac{x\hat{i}+y\hat{j}+z\hat{k}}{\sqrt{x^2+y^2+z^2}}$$
as:
$$\frac{x}{\sqrt{x^2+y^2+z^2}}\hat{i} + \frac{y}{\sqrt{x^2+y^2+z^2}}\hat{j} + \frac{z}{\sqrt{x^2+y^2+z^2}}\hat{k}$$
wraith daggerBOT
nyantoki
high lance
and the curl of this is $$\nabla \times \frac{x\hat{i}+y\hat{j}+z\hat{k}}{\sqrt{x^2+y^2+z^2}} = <0,0,0>$$ is this correct?
wraith daggerBOT
nyantoki
cedar kilnBOT
@high lance Has your question been resolved?
severe edge
and the curl of this is $$\nabla \times \frac{x\hat{i}+y\hat{j}+z\hat{k}}{\sqrt{...
yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
stray palm
is the answer a and e
cedar kilnBOT
is the answer a and e
stray palm
because the other options are cusps?
cedar kilnBOT
@stray palm Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
mental mural
Hi
mental mural
Anyone know what is closed and open set mean?
weak mountain
Look in your textbook
Every point in an open set has an open neighborhood around it that’s in the set
There’s multiple equivalent definitions
For closed set
Closed set contains its limit points
mental mural
Closed set contains its limit points
Anymore simple explanation?
solid juniper
set is closed iff it's complement is open might be simpler
mental mural
set is closed iff it's complement is open might be simpler
Ic but why [ 1, inf) is close?
weak mountain
What is the complement
solid juniper
you should probably find a def for open and closed set
mental mural
What is the complement
If c is close g^-1 (C) is close
weak mountain
Are you on chatgpt
mental mural
No
weak mountain
What is the complement of your set wrt the real line?
Look at the definitions and go again
You don’t need the defn of continuous functions here
mental mural
[-inf, 1)?
weak mountain
Yes, but are you in the extended reals
mental mural
No
tropic oxide
the complement of [1, +∞) is (-∞, 1)
mental mural
the complement of [1, +∞) is (-∞, 1)
Yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
spare geyser
good day all, please how do i convert A454 from Hexa to it's BCD equivalent
tropic oxide
binary coded decimal?
convert 0xA454 into decimal, then replace each decimal digit with the four bits of its binary representation
dusk finch
I guess you will have to convert to base 10 and then just convert from base 10 to BCD
cedar kilnBOT
@spare geyser Has your question been resolved?
spare geyser
Oh! Thanks a lot!
hearty nimbus
I want to know the steps to integrate this
cedar kilnBOT
I want to know the steps to integrate this
hearty nimbus
\
violet night
u sub
and probably get the -1 gone treat the -1 in it's own integral and focus only on sqrt(x^2+L^2)/x
I think that would get you somewhere
cedar kilnBOT
@hearty nimbus Has your question been resolved?
violet night
if you mark it ❌then maybe post your working on the problem? or your attempted u sub
hearty nimbus
u sub of what
hearty nimbus
can you show me?
crimson sedge
Hey, I need help with a problem
hearty nimbus
don't hijack my session
crimson sedge
nvm
cedar kilnBOT
@hearty nimbus Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
earnest kettle
I need help
cedar kilnBOT
I need help
earnest kettle
how do I find the critical points, local minima and maxima of this question
this is what I’ve done so far
I tried using the chain rule
but I’m still unsure of how I’m supposed to extract the critical points
hidden osprey
how do I find the critical points, local minima and maxima of this question
differentiation
cedar kilnBOT
@earnest kettle Has your question been resolved?
marsh pond
cedar kilnBOT
marsh pond
is this the same thing as log_3[(-6x)/(x-4)]?
muted bear
Yes
marsh pond
in this case would you prefer ln or log_3?
log_3 seems easier, but maybe there is still good reason to use ln?
floral forge
at a certain point you will likely completely abandon anything other than the natural log, there really is not much reason for them other than plotting. so the reason to not use log is just that there isnt all that much reason to do so. but theres nothing wrong with it that i know of at least
i guess half life is technically more related to log 2 but again you just toss in a ln 2 somewhere and its fixed
cedar kilnBOT
@marsh pond Has your question been resolved?
earnest kettle
differentiation
I knew that 🧍♀️
hidden osprey
cedar kilnBOT
cedar kilnBOT
Available help channel!
polar umbra
Y and V are the midpoints of the legs, XZ and UW, of trapezoid UWXZ.
If WX= -2p+31, VY=5p–43, and UZ=3p–18, what is the value of p?
cedar kilnBOT
Y and V are the midpoints of the legs, XZ and UW, of trapezoid UWXZ.
If WX= -2p+...
@polar umbra Has your question been resolved?
cedar kilnBOT
@polar umbra Has your question been resolved?
distant cedar
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
tropic pilot
in this question i marked with blue, the answer should be doesn't exist because 1.5 not equal -1, so i saw that someone solved it removable discontinue, so can someone explain why (note: i am beginner at calculus)
dire geode
in this question i marked with blue, the answer should be doesn't exist because ...
what's the question
tropic pilot
i just want know why it is removable disc.
dire geode
i just want know why it is removable disc.
tropic pilot
.close
merry tinsel
the integral would have to be larger
for it to diverge
cedar kilnBOT
the integral would have to be larger
for it to diverge
merry tinsel
sum diverges becuz the integral that is larger than sum also diverges?
same for here right?
the sum diverges becuz the integral is bigger
And then for Question B
When it sum coverges
the integral COnverges
because the sum is greater than the integral
.close
cedar kilnBOT
@merry tinsel Has your question been resolved?
merry tinsel
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
marsh pond
cedar kilnBOT
marsh pond
asking in regards to the inequality table:
this is what the inequality table looks like without the +13 added
dull oxide
Yes, you need get a new polynomial again and find new zero product, otherwise, you would be able to solve the unsolvable quintic z^5+pz=1 by solving z^5+pz=0.
mighty drift
Note: this polynomial is awful, don't try to solve it
cedar kilnBOT
@marsh pond Has your question been resolved?
torpid urchin
how could i compare the first series?
cedar kilnBOT
how could i compare the first series?
torpid urchin
i figured we can’t use limit test since this isn’t always positive
but i’m not sure what i can compare to?
.close
lapis vigil
cedar kilnBOT
lapis vigil
As I integrate it
power of X becomes 0
so X is 1 now
How do I apply limit?
sage forge
Integrate correctly
crimson delta
the power rule doesnt work in this case because you would also have to divide by 0
instead the integral of 1/x is ln|x|
cedar kilnBOT
dire geode
write out a few terms. n=3, 4, 5
wraith daggerBOT
donut
dire geode
it'd help if you didn't simplify the numbers
if you compare the ratios, $a_{n+1} / a_n$, what does this approach as n gets large?
fringe hollow
cedar kilnBOT
fringe hollow
i need help on part b
latent bloom
Ayoo structure lesss gooo
fringe hollow
i suck at mechanics
latent bloom
Well
Let's look at the question slowly
First
They tell you the whole beam weighs 150 N
fringe hollow
yeah
fringe hollow
ah im so dumb lmao
fringe hollow
i just overthought it cuz part a was way harder
latent bloom
Wait
We're gonna prove part a
So they give you lengths for the parts of the beam
AC = 1 and AD = 2.5
So CD = 1.5
Now
fringe hollow
yeah
latent bloom
Let's remember that whole weight
fringe hollow
150N
latent bloom
They did not mention what it behaves like so we will assume that it works like a concentrated load.
Which acts in the center of gravity
And the center of gravity of the 4 meters is 2 meters
Which is inside part CD
latent bloom
Yep
Now we draw the force there and label it as 150 N
Great now that's a force done with
Let's now focus on that new particle with weight W
And is away from point A by x meters
But here's the catch
Reaction at point C is equal to reaction at point D
fringe hollow
Let's now focus on that new particle with weight W
but we dont know where W is placed
latent bloom
Yeah
fringe hollow
so can i take moments from any point
latent bloom
We know it is somewhere along the rod
latent bloom
so can i take moments from any point
Well you have the liberty to take moments anywhere you want, but you must apply equilibrium on the vertical forces in the end
So $\sum M_o = 0$ and $\sum F_y = 0$
wraith daggerBOT
VulcanOne
latent bloom
You have two equations
I suggest taking moments around point A because that acts as your origin point.
And since you already know that the reaction at C equals the reaction at D, then that makes it possible to do some factoring
So
We take moments around A and make it at equilibrium
So the moment equation is
fringe hollow
oh i see
latent bloom
$150\text{N} (2\text{m}) + W\text{N}(x \text{m}) = R\text{N}(1\text{m}) + R\text{N}(2.5 \text{m})$
wraith daggerBOT
VulcanOne
latent bloom
Right?
Imma just write the numbers and symbols without their units but we should keep the units in mind
$150(2) + xW = R + 2.5R$
wraith daggerBOT
VulcanOne
wraith daggerBOT
VulcanOne
fringe hollow
so Wx + 300 = 3.5R?
latent bloom
Yep
fringe hollow
whats the next step
latent bloom
This gives us an equation for R
latent bloom
Yeah
fringe hollow
2R= 150 + W
wraith daggerBOT
VulcanOne
latent bloom
262.5 + 1.75W = 300 + Wx
Rearrange and solve for W
W*(1.75-x) = 37.5
Or we can make it all in fractions
So
latent bloom
$W * \left(\frac{7 -4x}{4}\right) = \frac{75}{2}$
wraith daggerBOT
VulcanOne
latent bloom
Now we proved that $W = \frac{150}{7-4x}$
wraith daggerBOT
VulcanOne
fringe hollow
wasnt it just 0 < x > 4
latent bloom
7-4x should not be equal to 0 at all times
latent bloom
Well we are focused on not making the denominator 0
Because it will make the W undefined
fringe hollow
so we do 7-4x > 0?
wraith daggerBOT
VulcanOne
latent bloom
Yepp
latent bloom
150/0
But yeah
Division by 0 is bad
So we avoid it by making 7-4x not equal to 0
And we get from that that x should not be equal to 1.75 at all times
fringe hollow
i see
latent bloom
Now I think we need an additional constraint, but I think this works for now
x should be between 0 and 4 but not including 1.75
fringe hollow
yeah
latent bloom
Also not sure if W is allowed to be negative
ie. Being an upward force like the reaction forces
latent bloom
Oo
fringe hollow
so 4x < 7
latent bloom
Yep
fringe hollow
x < 1.75
latent bloom
Mhm
latent bloom
So 0< x < 1.75
latent bloom
cedar kilnBOT
Available help channel!
gaunt glacier
cedar kilnBOT
gaunt glacier
I dont know where to even start here
obsidian coral
You want to find the best fit curve
obsidian coral
Can you use a calculator/software?
obsidian coral
What kind of calculator?
gaunt glacier
pretty much just anything short of a graphing caculator
obsidian coral
I suggest looking up some videos
cedar kilnBOT
@gaunt glacier Has your question been resolved?
crimson sedge
Can someone please explain this working complete for me? I don't understand how it works like rules and stuff that are needed
buoyant perch
multiply the top and bottom by the complex conjugate
crimson sedge
multiply the top and bottom by the complex conjugate
How does -1 over the two become -(1/2)
buoyant perch
because -1/2 = -(1/2)
crimson sedge
because -1/2 = -(1/2)
How does the cos(-pi/4) become over 2 in sqrt2/2
I know that cospi/4 is sqrt(2)
buoyant perch
cos(pi/4) is 1/sqrt(2)
buoyant perch
cos(x) =< 1 so idk how it could equal sqrt(2)
crimson sedge
No cause z1 is actually sqrt2 + sqrt2i
buoyant perch
you factored out the -1/2 already tho
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
$4\sqrt[3]{16x^4y^6}\$
4\sqrt[3]{2}\sqrt[3]{8}\sqrt[3]{x^4}\sqrt[3]{y^6}\
4\4\sqrt[3]{2}\cdot 2 \cdot x\sqrt[3]{x}\cdot y^2
wraith daggerBOT
okokok
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
crimson sedge
how many things do i multiply by 2 ?
is this work right ?
im simplifying
<@&286206848099549185>
cedar kilnBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
spring copper
³√2³ won't cancel out each other
crimson sedge
³√2³ won't cancel out each other
?
spring copper
Oh it's already done okay
sick mirage
cedar kilnBOT
sick mirage
Does this fail the 0 identity for addition and multiplication because b != 0 ?
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
gray blade
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
cedar kilnBOT
@gray blade Has your question been resolved?
sage forge
Try to use Lagrange error 🙂
gray blade
Try to use Lagrange error 🙂
yeah but how
like i don't fully understand the concept of "maximizing the next derivative"
i know the first 5 terms of e^(-x) is
but then how do I use the lagrange bound error formula
it's all confusing
please just work through it for me
sage forge
gray blade
yeah I'm trying to use that
gray blade
like i don't fully understand the concept of "maximizing the next derivative"
_ _
also i can't read that language lol
sage forge
n = 5 and x =2
sage forge
The n+1-th derivative of e^(-x)
sage forge
And what is the 6th derivative of e^(-x)?
sage forge
You can bound it above by using the xi ? is in [0,2]
gray blade
what is xi?
sage forge
You can bound it above by using the xi ? is in [0,2]
Do you know why this has to be?
gray blade
well I think the formula says it must be between x and c
so x = 2
and i assume our center is 0?
sage forge
Yes
sage forge
Yes
sage forge
👍
gray blade
there is no way it was this simple
lmao
hold on
should n = 4? @sage forge
because it says 5 terms
but the first term is 1?
sage forge
Oh, no. It starts at k= 0. Thank you for pointing out my mistake.
gray blade
👍
so now the 5th derivative is -e^(-x)
so is the max at -1/e^2
cuz that's greater than -1
sage forge
To calculate the error we're dealing with absolut values
sage forge
Yes, we want to maximize the error
gray blade
soo is f^(n+1)(z) = -1/e^2 or -1
cuz the abs value of -1 is greater than abs value of the other one
but isnt that only after we plug it all in
sage forge
What is your 5th derivative?
gray blade
-e^(-x)
sage forge
Ah, okay. You already plugged in the 2. I was wondering why there was a z in the left side
sage forge
So now if we minimize -e^(-x), we'll be off by the biggest difference
sage forge
sage forge
Since we know that the RHS is negative we can say that T is bigger than e^(-2x). Now if we increase epsilon the RHS will go more towards 0, so the error gets smaller
sage forge
That's an epsilon
gray blade
I'm sorry I don't get a lot of things you're doing
what is T?
why are we using e^(-2x)?
what is epsilon?
sage forge
what is T?
That's our Taylor Approximation. It is a short writing for it
sage forge
That's f(x)
sage forge
what is epsilon?
That's a value in [0,2]
sage forge
gray blade
ohhhhhhhhhhhhhh
so u have to get the absolute value of the max value
so should we really be turning -e^(-x) to e^(-x)?
and then getting the max?
cedar kilnBOT
@gray blade Has your question been resolved?
ember python
cedar kilnBOT
ember python
for part(d)
I can see how the matrix satisfying M^2 = 0 and having y = 2x as a line of invariant points is consistent with it representing a reflection in the line y = 2x
but I don’t see how those 2 pieces of information imply that it represents a reflection in the line y = 2x
still barn
It doesn't. You need information from the eigenvectors as well.
cedar kilnBOT
@ember python Has your question been resolved?
ember python
It doesn't. You need information from the eigenvectors as well.
what information from the eigenvectors would you need?
cedar kilnBOT
ember python
.reopen
cedar kilnBOT
✅
still barn
The question is guiding through the entire transformation. So basically all the parts
ember python
(1 2) was an eigenvector with eigenvalue 1, but I don’t see how that corresponds to anything other than y = 2x being a line of invariant points
the eigenvectors being perpendicular might have something to do with it?
still barn
You should consider the action of M applied to an arbitrary vector in R^2 by decomposing it into a linear combination of eigenvectors.
ember python
oh right that makes more sense
the other eigenvalue was -1 and so since the eigenvectors are linearly independent we can represent every vector going into the matrix as a linear combination of them, and therefore when applying the matrix to that vectors the resulting vector will be reflected in the line y = 2x, since it was remain invariant parallel to y = 2x, and will be reflected across the origin along the line y = -(1/2)x?
vector* not vectors
rather just reflected across the line y = 2x parallel to y = -(1/2)x, not across the origin
still barn
The point is that the component corresponding to eigenvalue 1 is invariant, and the part corresponding to eigenvalue -1 alternates since M is a self inverse. So you just need to map the points along the second eigenvector to each other to describe the transformation.
ember python
yeah
basically using the fact that matrices distribute so M(ax + by) = ax - by where x is the eigenvector corresponding to 1 and y the eigenvector corresponding to -1
that is much more convincing
although nothing like this has ever been touched on so I think they did just expect us to pattern-spot, and not prove it, but this is way better
thank you that was super helpful
still barn
I don't know how you would describe it any other way.
ember python
alright yeah I see
still barn
The main problem is that without that linear combination machinery, you can never be sure the transformation is just a reflection
ember python
yeah that’s what I thought, it didn’t seem like enough, just that those 2 pieces of information were consistent only with a reflection across y = 2x out of all the transformations that have been encountered before in the curriculum, which wasn’t convincing
but I searched it up and found that other ones like shears exist so it seemed unconvincing
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
silent arch
cedar kilnBOT
silent arch
Can someone explain to me -3cos45
I got that 2sin2(60) is 0, i dont understand -3cos45
Ping me please
south tundra
I got that 2sin2(60) is 0, i dont understand -3cos45
How come 2sin^2(60) is 0?
silent arch
How come 2sin^2(60) is 0?
well i assume 2sin^2(60) = 2sin(3600), right? and sin(3600) = 0, so 2*0 = 0
south tundra
No, $\sin^2(x)\ne\sin(x^2)$
wraith daggerBOT
A Lonely Bean
south tundra
Generally it is helpful to keep in mind that sin(60) is sqrt3/2
silent arch
ya
south tundra
what does sin^2 mean
It means the sine value squared
south tundra
**A Lonely Bean**
There is a difference between those two
silent arch
Oh. so u get the sin value FIRST, then square it
south tundra
The first means taking sin of x and then squaring
silent arch
gotcha thanks.
south tundra
With a dot
silent arch
.close
crimson sedge
Hi
crimson sedge
The root of 3 x root is equal to
U are asked to give an explanation
My teacher says its X^1/3 multiplied with X^1/2
Thats equal to X^5/6
Why did she pick X^1/3 multiplied with X^1/2
buoyant latch
because when you add the exponents you get 1/2 + 1/3 = 5/6
crimson sedge
Ik but my questions is why she did pick x 1/3 and x1/2 why not x1/100 or x1/44
buoyant latch
because 1/100 + 1/44 is not 5/6
crimson sedge
Why does those two explain the previous question
buoyant latch
ok
tropic oxide
$\sqrt[n]{x} = x^{1/n}$
wraith daggerBOT
Ann
buoyant latch
$\sqrt[3]{x}\cdot\sqrt{x}=x^{1/3}\cdot x^{1/2}$
wraith daggerBOT
Frosst
tropic oxide
^
buoyant latch
i dont know why you split your question into 2 separate pictures for question and answer
but that kinda confused me on what im looking at
tropic oxide
@crimson sedge does this all answer your question
silent arch
how would i solve this?
cedar kilnBOT
how would i solve this?
tame wraith
crimson sedge
cedar kilnBOT
crimson sedge
47.(a, b, c, d) Write the formula of the linear function if:
Or atleast one like a
Example
I am lost
split jetty
,rotate
wraith daggerBOT
upbeat dune
From the line
Can you tell the gradient?
upbeat dune
Hmm
Do you know the form of a linear function?
upbeat dune
Yes
And that k
Do you not know what it is or represents ?
crimson sedge
I only know if it's >0 it goes into I AND III quarters
And if it's less than 0 it goes to II AND IV quarters
upbeat dune
Hmm
Its it is basically the steepness of the line
cedar kilnBOT
@crimson sedge Has your question been resolved?
worthy ridge
cedar kilnBOT
worthy ridge
so it is/
gilded elm
gcd is a linear combination is the bezouts lemma or whatever
gilded elm
.close
cedar kilnBOT
gilded elm
yeah
worthy ridge
sorry]
gilded elm
no worries
worthy ridge
I thought they autoclosed
gilded elm
yes after a long time
cedar kilnBOT
Available help channel!
gloomy vine
HELP PLEASE EXPLAIN THIS FOR ME I HAVE A MATH EXAM TOMORROW ITS VERY URGENT THANK YOU
cosmic steppe
Parallel-transversal theorems and vertical angle properties
half forge
Alternate angles
cedar kilnBOT
@gloomy vine Has your question been resolved?
fair mortar
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
lime nest
Find the values of m and n
cedar kilnBOT
Find the values of m and n
lime nest
<@&286206848099549185>
split jetty
post the full question
lime nest
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
lime nest
I just need help with this last one I don’t know how to solve it.
fair mortar
whats the equation of the line and the coordinates of subway
hot iron
You don’t need the equation of the line
Find the coordinates where line q and p intercept and then find the coordinates of where the subway is
Then use this equation
(X2-x1)^2+(y2-y1)^2
Then square root the overall answer
lime nest
Ok appreciate it I’ll try it
inland ocean
$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
wraith daggerBOT
ColdTee
hot iron
@inland ocean cheers
inland ocean
i knew neon would look better than pink
anyways i just wrote it so it was easier for you
lime nest
Thanks
fair mortar
i knew neon would look better than pink
heheh lol
lime nest
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
restive plover
cedar kilnBOT
cedar kilnBOT
@restive plover Has your question been resolved?
restive plover
<@&286206848099549185>
cedar kilnBOT
@restive plover Has your question been resolved?
loud hornet
claim
fair mortar
claim?
loud hornet
im claiming this channel so i can ask my question
fair mortar
you can just ask no need claim
loud hornet
Use an addition or subtraction formula to find the solutions of the equation that are in the interval [0,pi]. cos5tcos2t=-sin5tsin2t
I know but I dont want someone else to ask their question before Ive finished typing mine
autumn fox
Use an addition or subtraction formula to find the solutions of the equation tha...
Do you recall any trigonometric addition identities that might be useful here?
autumn fox
Yes. And which of those two match up with what you have?
loud hornet
cos(u-v) because its cos(5t)cos(2t) + sin(5t)sin(2t)
autumn fox
Exactly
loud hornet
I'm just not sure how to actually find the correct solutions. When I work through the problem I end up with cos(5t-2t) so cos(3t)=0. The answers, however, are pi/6, pi/2, and 5pi/6. I'm not sure how to get there from cos(3t)=0
autumn fox
Do you have any suggestions on how to get 'rid' of the cos in cos(3t) = 0?
autumn fox
Yes
crimson sedge
Perhaps this?
loud hornet
?
crimson sedge
(b)
loud hornet
so 3t = 2pi? Then t = pi/6...oh
crimson sedge
Um i think no
loud hornet
and because it's 3t it goes up in increments of pi/3? That would get me the correct answers
loud hornet
0
crimson sedge
Right
loud hornet
and then 3t = 1, so pi/3 which is added and subtracted from pi/2 to get the answers pi/6, pi/2, and 5pi/6?
is this correct?
crimson sedge
Hm
Cos3t=cospi/2
Hence 3t is 2npi±pi/2
T is 2npi/3 ±pi/6
This is the general solution
loud hornet
ah
crimson sedge
And the question have asked for solutions btw 0 to pi
loud hornet
so t = 0 would be pi/6, t = 1 would be pi/2, t = 2 would be 5pi/6
crimson sedge
Mhm
loud hornet
that makes sense
stable helm
cedar kilnBOT
wraith daggerBOT
BunkerBaby
cedar kilnBOT
@stable helm Has your question been resolved?
cedar kilnBOT
@stable helm Has your question been resolved?
lethal jackal
that's basically it, but you probably should simplify it a little
stable helm
yeah the question asks to simplify it
i was just wondering if thats the right equation before i simplify
u always come to my rescue
u either hate me or love me for always asking questions but i love you for always helping me
lethal jackal
lol thanks
stable helm
lol thanks
i will most likely be back later today with more questions
see u around brother
.close
limber snow
$\int \frac{-7}{x+x^{\frac{1}{3}}} , dx$
cedar kilnBOT
$\int \frac{-7}{x+x^{\frac{1}{3}}} \, dx$
wraith daggerBOT
Calc II Victim
limber snow
My progress:
I factored x^1/3 in the bottom to get $\frac{-7}{x^{\frac{1}{3}} (x^{\frac{2}{3}}} + 1)$
shit
dire geode
I factored x^1/3 in the bottom to get $\frac{-7}{x^{\frac{1}{3}} (x^{\frac{2}{3}...
in principle this is right
wraith daggerBOT
Calc II Victim
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
limber snow
idk whats wrong but
dire geode
just u sub after that and you're done
limber snow
then
I did u sub
where
u = x^2/3 + 1
and du = 2/(3x^1/3) dx
but like
my slow ass is kind of stuck
now
dire geode
your du is wrong
limber snow
oh how
dire geode
2/3 - 1 = ?
limber snow
2/3 - 1 = -1/3 ?
thats why
I moved
x down
to get
x^1/3
I searched it up it says the same
dire geode
i don't know what you mean by "i moved x down"
limber snow
no like
negative power
i moved it to the denominator
so that the power
becomes
positive
dire geode
well that's unnecessary
limber snow
write your integral in terms of u and du
do I like solve for dx here and then plug that in?
oh wait a min
shittttt
is it
dire geode
there are many ways to do the problem. yours is fine
dire geode
nah
dire geode
never write an integral in terms of both x/dx variables and u/du variables
when you mix, it becomes nonsense
wraith daggerBOT
Calc II Victim
dire geode
you have to substitute all x/dx with u/du
limber snow
there
dire geode
,w -7 * int 1/(x+cbrt(x))
wraith daggerBOT
dire geode
i would think you can assume x > 0
but if not, then your problem is a little more complicated
cedar kilnBOT
cedar kilnBOT
Available help channel!
flat lance
So uhm, i have a vector based assignment and uhm this one task is searing my mind because idk how to do it, There are four dots in the coordinate system A(3, 0), B(−2, 4), C(−5, −1) and D(3, −5). I have to find out whats the lenght of a vector name X which he equals 2(AB)+(DC), (AB) and (DC) are both separate vectors that define the X Vector, like the (AB) is made out of two dots A, B which u can respectfully find for both.
south tundra
And what is troubling you here?
flat lance
How do i found out the lenght of the Vector X
south tundra
First I would evaluate the components of the vector X
south tundra
For that you would need to know the vectors AB and DC
Do you know how to generally compute components of a vector going from one point to another?
flat lance
Like With the singluraity distance of i and j ?
south tundra
Yeah, you can use those
flat lance
im still lost ; _ ;
can i uhm
send u a drawing
like paint
lol
i can upload files here ?
south tundra
You can upload an image, sure
flat lance
Okay
so basically this
but u have to do it thru math calculation
not just like "looking" into the graph
lenght meaning this
south tundra
Sorry, I am back
The drawing isn't really necessary
E.g. to get the components of the vector AB you need to take the coordinates of B and subtract the coordinates of A from them
south tundra
So, here, AB = (-5, 4)
flat lance
I know but
south tundra
How can u subtract dots ???
You are subtracting coordinates, which are numbers
south tundra
Basically AB vector gets you to from point A to point B, right?
flat lance
yeah
south tundra
So, if we add its components to the coordinates of A, then we should get the coordinates of B
Should sound intuitive
flat lance
Yeah but AB = (-5, 4) Isnt a lenght
south tundra
Yes, we will get there soon
flat lance
its how much power of x and y
south tundra
Should I continue on explaining why we are subtracting coordinates or do I go back to the main course?
south tundra
So, if we add its components to the coordinates of A, then we should get the coo...
Let's say (A_x, A_y) are the coordinates of A and (B_x, B_y) are the coordinates of B
And we have a vector AB with components (a, b) which get us from point A to point B
flat lance
yes the vector would be axbx+ayby ?
south tundra
No, that's the dot product
flat lance
the lenght ?
south tundra
Visually the dot product is the length of the shadow one vector leaves on another
But that's off topic
south tundra
And we have a vector AB with components (a, b) which get us from point A to poin...
Like I said, we want to get the coordinates of B by adding the coordinates of A and the components of the vector, right?
south tundra
I am headed towards explaining that
south tundra
Like I said, we want to get the coordinates of B by adding the coordinates of A ...
I need to make sure you understand this
flat lance
I dont get the terms
south tundra
Ah
south tundra
That's pretty much the main idea of a vector algebraicly
flat lance
what is
south tundra
That you get from some point A to some other point B by simply adding the components of the vector
south tundra
Okay
south tundra
Like I said, we want to get the coordinates of B by adding the coordinates of A ...
My point is, this means that we want A_x + a = B_x and A_y + b = B_y to happen
south tundra
Yes
Here you can rearrange the equations and get that a = B_x - A_x and b = B_y - A_y
Do you now see why we subtract coordinates to get the vector?
flat lance
but we dont have to do that
south tundra
What do you mean?
south tundra
What do you mean by the dot?
south tundra
Yeah, it just looked like you were confused about how I got AB = (-5, 4)
Just in case, that is equivalent to AB = -5i + 4j
south tundra
Right
flat lance
What next
south tundra
Okay
Now add 2AB and DC
That happens by adding the corresponding coordinates
(First note that 2AB is -10i + 8j)
flat lance
2*(-5i+4j)+-4i ?
south tundra
And, generally, the length of a vector can be calculated by adding the squares of its components and taking the square root of that
So, in this case, |X| = sqrt((-14)^2 + (8)^2)
flat lance
thats 2 sqrt(65) ?
flat lance
so why could i not get the |AB | and |DC | By using that square root method
and then doing something with them then
south tundra
Because |2AB + DC| =/= 2|AB| + |DC|
You can prove an analogy with numbers right here
south tundra
E.g. |-4 + 1| is not the same as |-4| + |1|
south tundra
No problem, and close the channel if you don't have any more questions
flat lance
.close
brisk ferry
How do I get this problem's range. I've solved for the domain already
