#help-23
safe radishBOT
elder sparrow
what should i do after exanding the brackets?
uneven veldt
!status
safe radishBOT
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
fluid holly
Are you supposed to find the value of the expression?
elder sparrow
Are you supposed to find the value of the expression?
supposed to prove
fluid holly
Oh my bad
uneven veldt
Also, can you send your working?
elder sparrow
(sin^2 a -2 (sin a )(cosec a )+ cosec^2 a) +(cos^2 a -2 (cos a )(sec a) +sec ^2 a )
elder sparrow
so that would remove the
fluid holly
You could do it anytime
elder sparrow
sin and cosec and cos and sec?
fluid holly
Wdym remove
elder sparrow
nvm
fluid holly
Just simplify as much as you can
elder sparrow
i did, sin^2 a +COS^2 a = 1, so that makes it 1-2 sin a cosec a + cosec^2 a -2 cos a sec a + sec^2 a
fluid holly
Let me write stuff out rq
hazy elbow
i did, sin^2 a +COS^2 a = 1, so that makes it 1-2 sin a cosec a + cosec^2 a -2 c...
all correct
fluid holly
It's easy once you practice a lot
elder sparrow
all correct
after that what?
elder sparrow
It's easy once you practice a lot
understandable
elder sparrow
1-2 +cosec^a -2 +sec^2 a
hazy elbow
1-2 +cosec^a -2 +sec^2 a
Yes
fluid holly
Yed
elder sparrow
oh
fluid holly
They group out -1
elder sparrow
its +1 right?
hazy elbow
Now use the identity cosec^2x-cot^2x=1
fluid holly
Yeah
hazy elbow
and sec^2x-tan^2x=1
elder sparrow
where did cot come from
fluid holly
That's what I meant by group out lol
hazy elbow
where did cot come from
That is an identity
elder sparrow
oh
elder sparrow
oh so tan + cot -1
fluid holly
No
fluid holly
Yes
safe radishBOT
elder sparrow
lmao lack of self confidence actually did till the identity part in my mind, but felt it was too ezy so came here
👍
safe radishBOT
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elder sparrow
also, do u suggest me any kind of resouce that i can refer to practice these kind of proving sums (always lose marks in them) @fluid holly
safe radishBOT
also, do u suggest me any kind of resouce that i can refer to practice these kin...
fluid holly
also, do u suggest me any kind of resouce that i can refer to practice these kin...
I'm from India I used rd Sharma question bank
elder sparrow
I'm from India I used rd Sharma question bank
I'm from India too, i have that, and RS agrawaal too
ty
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safe radishBOT
fluid holly
I'm from India too, i have that, and RS agrawaal too
Use the arihant for advanced
fluid holly
Skills in mathematics
elder sparrow
ty
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why doesnt it close lmao
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worthy hemlock
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worthy hemlock
If you see this, you are good
grim plover
also, do u suggest me any kind of resouce that i can refer to practice these kin...
Pearson, from India as well
Pearson is tough
safe radishBOT
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summer coral
Hi I have a problem with Fourier Transform, here is a MRE:
safe radishBOT
Hi I have a problem with Fourier Transform, here is a MRE:
summer coral
import matplotlib.pyplot as plt
import numpy as np
from scipy.fft import fft
# create a sine wave
sine_wave = np.sin(2*np.pi*10*np.arange(1000)/1000) # sin(2*pi*x) with x varying from 0 to 10, period is 1, frequency is 1
plt.plot(10*np.arange(1000)/1000, sine_wave, label='sine wave')
# fourier transform of sine wave
fft_sine = fft(sine_wave)
# plot the fourier transform, we should see one peak at 1
plt.plot(np.abs(fft_sine), label='magnitude of fourier transform of sine wave')
plt.legend()
plt.show()
I'm expecting just one peak for my fourier transform
since I only gave it sin(2pix)
but I'm getting this
wtf is happening at 990 ish?
twin jetty
@summer coral I don't have much experience with Fourier transforms, but is it possible there's a problem with your definition of sine_wave?
Since np.arange(...) returns an array, the program might be getting confused
summer coral
nah it's pretty clean to me
twin jetty
Yeah that looks good. I'm not sure where the problem's coming from
safe radishBOT
@summer coral Has your question been resolved?
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crude star
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royal pivot
it looks like it is just a hyperlink or a reference to something and can be safely ignored
safe radishBOT
pure agate
That depends on how many intervals you want to break up the sum into, although I think y'all use a limit as n goes to infinity these days. 🤔
vale hollow
That depends on how many intervals you want to break up the sum into, although I...
ye
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main rivet
Someone help: A company produces two products: Product A and Product B. Each unit of Product A requires 2 hours of labor and 1 hour of machine time, while each unit of Product B requires 1 hour of labor and 3 hours of machine time. The company has 200 hours of labor and 150 hours of machine time available each week. Figure out how many units of each product should the company produce so that it uses all its available resources?
solar pike
!status
safe radishBOT
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
@main rivet Has your question been resolved?
main rivet
a = number of A units, b = number of B units
It’s different from the one yesterday
main rivet
Same problem but the maximising part of the problem changed
Wait let me show u something
That was the working out for the one yesterday
How can i do that same method to solve this new one
solar pike
Isn't it the same?
But now with equations
Instead of constraints
I mean, equations are constraints
you just don't need to maximize anything
Just find the solution
main rivet
thats why it’s confusing me
He gave us a different one but its the same thing i dont get it
solar pike
2 equations 2 variables => solution
it's not the same because here you need to find something else
main rivet
The equation will stay the same?
solar pike
The equations are the same
solar pike
Oh, you mean that yesterday to maximize you solved these equations
main rivet
yeah
that last part changed
Figure out how many units of each product should the company produce so that it uses all its available resources?
main rivet
If the company wants to maximize its profits by not wasting any resources how many units of each product should it produce?
That was yesterdays one
Why do i have to solve it again if the solution is the same
solar pike
Yesterday you had a profit
so the solution potentially could be different
If for instance you would get 100000$ for A and 1$ for B
you would produce only A's
right?
main rivet
Ye
main rivet
Im confused idk
I solved that in like 5 minutes the one yesterday after i got help
But this one idk
If i had to solve it with the new numbers i would honestly still do the same thing i done in my working out
solar pike
So would you get b=20?
main rivet
Where do u get 5 from
safe radishBOT
solar pike
and =90
solar pike
So the profit is... 90 * 100000 + 20 * 1
safe radishBOT
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rigid arch
A school's population is increasing by approximately 31% each year. If there
are currently 990 students, what was the student population 11 years ago?
safe radishBOT
A school's population is increasing by approximately 31% each year. If there
are...
rigid arch
Someone help for that exponential equation^
rigid inlet
!status
safe radishBOT
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
2
A school's population is increasing by approximately 31% each year. If there
are currently 990 students, what was the student population 11 years ago?
rigid inlet
show what you've done so far
rigid arch
Ik the equation will be something like y=990(b)^x
but I dont know if the b value would be 1 - or + 31%
because it is a growth rate, but then I have to find the population of the past
rigid inlet
it's indeed a growth rate
the implicit assumption is that this rate is constant and has been for as long as you need it to be
rigid arch
so then how would I find out 11 years ago
rigid inlet
well, if you know that the growth rate is 31% every year, and the current population is 990, what must it have been the year prior?
rigid inlet
that's not how you correctly model growth
for something to grow by 31%, you add 31% of where it is presently, not where it will be
rigid arch
1297?
rigid inlet
perhaps it would help if you precisely defined what x and y represent in the equation y=990(1.31)^x
it can't be larger than 990
rigid arch
y is the population and x is the years
rigid arch
y is the schools population for the year, and x is the number of years passed
rigid inlet
ok then
if we're asking about something that happened 11 years ago, then how many years have passed since today?
rigid inlet
indeed
rigid inlet
yes
safe radishBOT
@rigid arch Has your question been resolved?
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rain talon
find real numbers a and b such that the equation is true.
a +bi = b+ (2a-1)i
rain talon
i guessed 1 and 1 fits, but in reality im not sure how to solve this question...
how should i approach this question?
stoic dune
If that equation is true, then these are also true:
a = b
b = 2a - 1
That is, real parts match, imaginary parts match.
rain talon
That is, real parts match, imaginary parts match.
sorry but i dont get this part, what's meaning of that?
stoic dune
If a + bi = c + di
Then
a = c
b = d
fresh aspen
safe radishBOT
flat frigateBOT
Broken
fresh aspen
that much i know, but thats not gonna work because the curve crosses the x axis at x = 2
and its below the x axis before x = 2
from x = -1
touches at x = 0
safe radishBOT
@fresh aspen Has your question been resolved?
safe radishBOT
@fresh aspen Has your question been resolved?
safe radishBOT
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manic path
Can someone just help me explain the logic of the answer for question 2E) ii)?
manic path
I know how to do it but the answer is always 2.4375 which is right technically
but the answer would want it as 24.375
so what should be doing?
pastel verge
Where is 2E?
Did tou share the wrong question or is it 3E
If it is 3E I can't see part ii
pastel verge
But where is ii
manic path
its at the top, instead of it asking you 3ai, 3aii
its just find i) and ii) of all these letters
so its implied
bascially for 3E
find the variance
pastel verge
,w 1000(2.5/100)(97.5/100)
flat frigateBOT
pastel verge
Idk what you did wrong
manic path
man.
I got that type of stuck, where you did it wrong originally
then when you do it again you get ti right somehow
:C
thanks though
manic path
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safe radishBOT
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tepid minnow
safe radishBOT
tepid minnow
AE = EC and BF= FD
frank imp
hi can someone help me with this question? I'm really bad at math
Simplify the following expression
tan (π + x)
safe radishBOT
@tepid minnow Has your question been resolved?
outer cedar
I forgot how can I solve $1 = 2A + 3B -4C$ ?
safe radishBOT
I forgot how can I solve $1 = 2A + 3B -4C$ ?
flat frigateBOT
OctopusToy
rich elm
outer cedar
Solve A,B and C
mystic timber
A body, initially at the origin of a Cartesian reference system, moves 5 meters in the second quadrant of the (x,y) plane along a line whose direction makes an angle equal to θ with the y axis. Then the body moves 4 meters parallel to the y-axis. Knowing that at this point the final distance d of the body from the x-axis is equal to 6.5 m, what is the angle θ?
(a) 60th Correct answer
(b) 0°
(c) 45°
(d) 30°
(e) the data is not sufficient to formulate an answer
safe radishBOT
A body, initially at the origin of a Cartesian reference system, moves 5 meters ...
mystic timber
I am supposing the body has (x,y) coordinates at the beginning then it moved 5 m so the new coordinates are (x-5,y+5) then it moved once again 4m and the final coordinates are (x-4,y+9).
what I have to do after this or is this a true path
peak lily
just forms a triangle
use herons formula or break up into some smaller right-angled triangles
safe radishBOT
@mystic timber Has your question been resolved?
surreal stratus
$-\sin \left(x\right)+\cos \left(x\right)>0$
safe radishBOT
$-\sin \left(x\right)+\cos \left(x\right)>0$
flat frigateBOT
Penca53
surreal stratus
what's the algorithmical solving process I should follow? I think I can do it intuitively, but I don't know what's the "usual" process
what I would do is
$\cos \left(x\right)>\sin \left(x\right)$
flat frigateBOT
Penca53
surreal stratus
and then, intuitively look at the cos and sin values
so, I know that at pi/4 cosx = sinx
same for 5pi/4
earnest wagon
My only option would be graphical
surreal stratus
ok, so what I'm already doing
thin bridge
i'd consider harmonic trig identities to express
-sin(x) + cos(x)
with a single trig function
viral loom
sqrt(2) cos (pi/4 +x)
surreal stratus
I don't know what they are 
but I was thinking
from what I've written, can't I just do
viral loom
sqrt(2) cos (pi/4 +x) this is equal to cos(x) - sin(x)
surreal stratus
$tan(x) < 0$
flat frigateBOT
Penca53
viral loom
you can work from here
surreal stratus
well, it doesn't make sense
but, why can't I divide by cosx the previous inequality, so that I get this?
surreal stratus
sqrt(2) cos (pi/4 +x) this is equal to cos(x) - sin(x)
but why?
earnest wagon
Because you're not sure about the sign of cosx
surreal stratus
makes sense
thin bridge
cos(x)/cos(x) isn't 0 either
surreal stratus
yeah I was thinking about this ahaha
so, if I don't know trig identities, should I learn about them, or stick with the graphical method?
pastel verge
$tan(x) < 0$
no
surreal stratus
(it would be one), but still, it's wrong yeah
so I can't just say that, since the equation
$\cos \left(x\right)=\sin \left(x\right)$
flat frigateBOT
Penca53
surreal stratus
has results:
viral loom
but why?
cos(x+Pi/4)=cos(Pi/4) cos(x)-sin(Pi/4) sin(x)
cos(x)-sin(x)=Sqrt[2] (cos(Pi/4) cos(x)-sin(Pi/4) sin(x))
cos(Pi/4)=1/Sqrt[2]
cos(x)-sin(x)=Sqrt[2] (1/Sqrt[2] cos(x)-sin(Pi/4) sin(x))
sin(Pi/4)=1/Sqrt[2]
cos(x)-sin(x)=Sqrt[2] (cos(x)/Sqrt[2]-1/Sqrt[2] sin(x))
Sqrt[2] (cos(x)/Sqrt[2]-sin(x)/Sqrt[2])=cos(x)-sin(x)
cos(x)-sin(x)=(cos(x)-sin(x))
surreal stratus
$\frac{\pi}{4} + 2k\pi and \frac{5\pi}{4} + 2k\pi$
flat frigateBOT
Penca53
surreal stratus
then the result of the inequality is
$\frac{5\pi}{4} + 2k\pi < x < \frac{\pi}{4} + 2k\pi$
flat frigateBOT
Penca53
surreal stratus
but this doesn't make much sense? Or does it? I don't like the fact that I've written that x has to be smaller than something, but also greater than something that is much bigger
$-\frac{3\pi}{4} + 2k\pi < x < \frac{\pi}{4} + 2k\pi$
flat frigateBOT
Penca53
surreal stratus
are the two results the same?
surreal stratus
sqrt(2) cos (pi/4 +x)
from this, how would I proceed?
$\sqrt{2}\cos(\frac{\pi}{4} + x) > 0$
surreal stratus
oh, I thought another thing
flat frigateBOT
Penca53
surreal stratus
so I can divide by sqrt(2)?
flat frigateBOT
Penca53
viral loom
yes, u know to do that right?
surreal stratus
not really, but I can try to think about something
viral loom
good
surreal stratus
I mean, intuitively I can
I have to set the arguments equal to pi/2 + kpi, right?
so x is
$\frac{\pi}{4} + k\pi$
flat frigateBOT
Penca53
surreal stratus
is this right?
surreal stratus
but we're solving an equation right now
viral loom
why?
surreal stratus
I honestly don't know. To find the 2 points?
viral loom
show me how you find them your way
surreal stratus
$\cos(\frac{\pi}{4} + x) = 0$
flat frigateBOT
Penca53
flat frigateBOT
Penca53
flat frigateBOT
Penca53
surreal stratus
$\frac{\pi}{4} + 1\pi$
flat frigateBOT
Penca53
surreal stratus
which are the only two different angles
then I look at the circle and see that
my solution has to be between the first and the second
clockwise
so I write
$\frac{\pi}{4} + 1\pi + 2k\pi < x < \frac{\pi}{4} + 0\pi + 2k\pi$
flat frigateBOT
Penca53
surreal stratus
but as I said before, I don't like the fact that there is a larger number of the left than on the right
and I don't know if it is even right
@viral loom
viral loom
what do you usually do when u finish an equation?
surreal stratus
mmm... I write the results?
viral loom
no, you test them to see if you got the right answer
surreal stratus
makes sense
at pi/4 sin and cos are the same
same for pi/4 + pi
because they are both negative and same values
but for the inequality, I don't know if I can write it like that
if I pick an integer number k, let's say 0, I get that x has to be smaller than pi/4, but greater than 5pi/4, which doesn't make any sense?
viral loom
what's the value of cos(5pi/4)
surreal stratus
-sqrt(2)/2
viral loom
and cos(pi/4)?
surreal stratus
sqrt(2)/2
viral loom
so x is between -sqrt(2)/2 and sqrt(2)/2
viral loom
the solution is something * pi + 2kpi < x < blablabla
i mean, you wrote a solution
in the proper way
surreal stratus
$\frac{5\pi}{4} + 2k\pi < x < \frac{\pi}{4} + 2k\pi$
flat frigateBOT
Penca53
surreal stratus
If there was a cos, I'd understand, but there is none?
$-\frac{3\pi}{4} + 2k\pi < x < \frac{\pi}{4} + 2k\pi$
flat frigateBOT
Penca53
viral loom
that's the same solution
surreal stratus
this one I understand
viral loom
cos(5pi/4) and cos(-3pi/4) is the same
surreal stratus
yeah
but the first solution doesn't make sense to me
Only because I'm setting x to be less than a value, and greater than a much bigger one
viral loom
that's because should solved in a strange way i think
surreal stratus
but I understand that since it is a trig function related thing, then I have to think differently
viral loom
the second one makes more sense and that's the one I got
flat frigateBOT
Penca53
viral loom
we have cos(pi/4+x) > 0
so the values are between -1 and 1
we got -arccos(0) + 2pik < pi/4 + x < arccos(0) + 2pik
-arccos(0) + 2pik < pi/4 +x
and pi/4 + x < arccos(0) + 2pik
x > -3pi/4 + 2pik for the first one
and pi/4+2pik for the second one
but you solved it correctly too
surreal stratus
I don't know how to solve them that way
viral loom
do the way you were tought
surreal stratus
The only time I've used arccos and friends, it was wrong because I didn't take into consideration domain changes and whatnot
viral loom
it's fine, u got it anyways
there are plenty ways to solve a problem
the thing is to solve it
unless someone ask u to do in a specific way
you're free to use your own method
viral loom
same
surreal stratus
.close
dull rapids
also the question cut off but they said <LBA is x and we have to find x
<@&286206848099549185>
please helppp
thin bridge
why 80
lean otter
shouldnt it be 80
70×2+40 = 180°
thin bridge
firstly, why did you think it should be 80
dull rapids
bcs they want LBA and so LA=LB and L is 40 degrees so 40+40
lean otter
im so sorry for asking so many questions
Triangle LBA is isoceles. Look carefully
thin bridge
so 40+40
where's that coming from
what theorem/property are you applying to justify that action
dull rapids
> so 40+40
where's that coming from
the 40 degrees
thin bridge
40 + 40 is 80
but why are you adding two 40s together
lean otter
LBA = LAB
dull rapids
what theorem/property are you applying to justify that action
none i was rushing to find a solution so i did anything
thin bridge
don't just do anything/random things
dull rapids
i was worried i wouldnt figure it out
thin bridge
there should be mathematical justficiation for what you're doing
if you don't know, just say you don't know instead of taking shots in the dark
dull rapids
okayy
thin bridge
did you have any issue with
LB=LA
Tangents drawn from a point are equal
In length
thin bridge
with two sides of the triangle being congruent
you have an isosceles triangle right?
dull rapids
yes
thin bridge
and from the properties of such triangles, the angles opposite those congruent sides will also be congruent
right?
dull rapids
yes
thin bridge
apply that in combination with interior angle sum of a triangle
dull rapids
okayy
dull rapids
apply that in combination with interior angle sum of a triangle
i dont know if im foing something wrong but i got 140
thin bridge
show what you're doing
dull rapids
i subtracted 180 with 40. im so sorry im a really slow learner
lean otter
Then divide it by 2
thin bridge
what are the three angles in your triangle
dull rapids
angle L angle B and angle A
dull rapids
Then divide it by 2
thats it?
lean otter
Yeah
thin bridge
well you don't know the reasoning behind that
so better actually go through the whole process
dull rapids
okayy
lean otter
well you don't know the reasoning behind that
Since both angles are equal
thin bridge
its seemingly random work without clear equations
lean otter
2x+40= 180
thin bridge
angle L angle B and angle A
ambiguous notation
<L, <LBA, <LAB
you chose to use
<LBA is x
and from
the properties of such triangles, the angles opposite those congruent sides will also be congruent
<LAB will also be x
so your three angles have measures of
x, x, 40°
dull rapids
then we do 2x+40=180?
thin bridge
after applying the above,
that comes from the interior angle sum of a triangle
then solve for x
dull rapids
and thats all??
thin bridge
if they want you to find x, and you found it then you're done
lean otter
No
lean otter
is that all i need to know
x can also be written y. It can also be written as § and ∆
Anything else you wanna know?
lean otter
Sum of interior angles of a triangle = 180° =π radians
lean otter
Yea
dull rapids
.close
safe radishBOT
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crude star
Can I rewrite this as $$S = {(x, y): xy \leq 16$$ and $$x \in [1, 9]$$ and $$y \in [1, 9]}$$
safe radishBOT
Can I rewrite this as $$S = \{(x, y): xy \leq 16$$ and $$x \in [1, 9]$$ and $$y ...
flat frigateBOT
Calc II Victim
solid timber
Its actually easier to imagine this in a coordinate plane
Basically S is the set of all the points inside a circle of radius 4 with its centre at (5,5)
x and y thus do belong to [1,9]
Not sure about the xy<16 part
safe radishBOT
@crude star Has your question been resolved?
rose estuary
hi
rose estuary
i need help
crude star
Not sure about the xy<16 part
sorry i meant x + y <= 16
lean otter
just send the question
crude star
oh mb channel is taken
rose estuary
pastel verge
!status
safe radishBOT
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
plucky elk
would you like me to send u my workings?
do it
rose estuary
pastel verge
would you like me to send u my workings?
Yes
pastel verge
Wait
rose estuary
ok sorry
pastel verge
Yes you are right
safe radishBOT
pastel verge
ok thank you very much
You're welcome dear 
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Available help channel!
misty bay
Suppose a certain quantity is computed as: discretize(K * (0.7x + y) + C), where C is one of {-1.5, 0, 1.5}, x and y are any integers. We know that all of these values are between -1.5 and 1.5. Discretize is basically the function floor(x * 8192) / 8192.
How might I efficiently test whether a certain value is part of the set of possible outputs?
safe radishBOT
Suppose a certain quantity is computed as: discretize(K * (0.7x + y) + C), where...
misty bay
Obviously, the values have to be of the form A/8192, but I'm curious whether:
- there are values of A that are not generated by this process
- if (1) is the case, then how does one efficiently determine this
one trick I've tried is pretending that the discretization doesn't exist and checking that (value / K) is close to an integer multiple of 0.1, but this doesn't work too well in practice.
K can take on the values of ({1, ..., 100} * 0.001)^2, too, but I basically figure that I can just compute all of the outputs for all (K, C) values and union them together
safe radishBOT
@misty bay Has your question been resolved?
desert marsh
safe radishBOT
desert marsh
let me tell you what I did
220/256 (0.8)
and then I did 14x12 (168).
168/-8=-21 so 0.8 x -21 = -16.8
so i got -16.8 but it's wrong
desert marsh
oh
desert marsh
p = 220 - 16^2, not 220/16^2
I mustve typed it wrong?
but can't 220 (- 16^2) can also be written like this? @austere spade
lean otter
What do you mean with the brackets
austere spade
but can't 220 (- 16^2) can also be written like this? <@347122115071442946>
yeah that doesn't change what i said though
yes it does what
thats not correct
desert marsh
but how come, people say when a minus sign is behind a number it's a negative number? example: the '-' is behind the 12f. And in the eqaution The number turns out to be a negative. 9f+10f(-12f)
lean otter
If 12f is a negative number, for example (12 x -6), then putting a minus in front makes it positive
Is that what you were confused about?
desert marsh
If 12f is a negative number, for example (12 x -6), then putting a minus in fron...
huh? putting a - infront of it makes it positive?
lean otter
Im not sure what the questipn was sorry if im confusing you 😅 but - 16^2 is negative yes but - (16)^2 would be positive
(-16)^2
I thonk thats what you were asking first
Right
worthy hemlock
but how come, people say when a minus sign is behind a number it's a negative nu...
The way you wrote 10f(-12f) makes it multiplication, it's 10f - 12f, which is the same as 10f + -12f, not 10f(-12f) which as stated, is read as 10f * (-12f)
lean otter
but can't 220 (- 16^2) can also be written like this? <@347122115071442946>
Like 220 + (-16^2). But writing 220 + (-16)^2 is totally different
Then youre multiplying negative times negative, which is positive. You have to read the first one like: 220 + (-1)*(16^2), which is negative times positive (=negative). The -x just means - 1 * x
safe radishBOT
@desert marsh Has your question been resolved?
desert marsh
The way you wrote 10f(-12f) makes it multiplication, it's 10f - 12f, which is th...
OH
But how come in 9f + 10f - 12f the "12f" is negative
<@&286206848099549185>
gleaming gull
In this example, how do I make the value of 15 - the difference between the two - explicit? Is there an expression derivable from this for that, and how would I arrive at it?
`Cody is 165cm, 10% more than before. What was his height before?
165 = 1.1h
165/1.1 = h
150 = h`
safe radishBOT
In this example, how do I make the value of 15 - the difference between the two ...
hushed minnow
In this example, how do I make the value of 15 - the difference between the two ...
You mean cody is 10% taller now?
gleaming gull
How do you show the 15 (the difference between the 165 and 150)?
I'm not particularly knowledgeable on math, so I'm hoping that this makes sense.
hushed minnow
I don't exactly follow what the question is, I suppose you mean Cody grew by 15 cm is what you're trying to prove
what you have shows is correct
gleaming gull
How do I manipulate 165 = 1.1h to explicitly show 15?
Is that possible from the starting point of 165 = 1.1h?
If not, then why? It's obviously present in a way, so why can't it be shown explicitly if so?
gleaming gull
I wanted to understand how to explicitly show the relationship between 165 and 150, that does it
mystic timber
safe radishBOT
mystic timber
what is the cross product of both
merry sleet
S3?
mystic timber
3d space*
merry sleet
so R^3?
and i j and k is the canonical basis?
if so
they are orthogonal to each other
so
so you can juyst developp the cross product and use that fact
fast sigil
1 =(x²/20² + y²/23.5²) find y that then will have a distance from the ellips to the y-axis equal to 5
safe radishBOT
1 =(x²/20² + y²/23.5²) find y that then will have a distance from the ellips to ...
fast sigil
I dont know how to solve this anymore, 1 year ago i could...
plucky elk
1 =(x²/20² + y²/23.5²) find y that then will have a distance from the ellips to ...
use distance formula and set it equal to 5
plucky elk
right. the distance is just the horizontal distance from (0, y1) on the y-axis to (x2, y2) on the ellipse
fast sigil
man sorry it just doesnt fit in my head, do i have to use a matrix after that?
plucky elk
d=√((x_2-x_1)²+(y_2-y_1)²)
you have 5 variables here.
plucky elk
right. the distance is just the horizontal distance from (0, y1) on the y-axis t...
4 here since
plucky elk
1 =(x²/20² + y²/23.5²) find y that then will have a distance from the ellips to ...
d is the other one
fast sigil
plucky elk
the only unknown is y1 and y2. but they are equal
fast sigil
this ? im trying to find
safe radishBOT
@fast sigil Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
safe radishBOT
brisk turret
ok
so whats your approach so far
distance?
wait
just find total mass of all vehicles
that should do the trick
so thats (50 * 1200 + 10 * 3000)/60
ok
ok so you cant divide into 6 equal parts
the truck part should be different
im not getting your method, its pretty late at night for me, i'd reccommend pinging helpers
someone else might be of better help
brisk turret
this says 15 minutes
coarse kelp
Find a generating curve on the xy-plane for the surface of revolution given by $4x^2+4z^2 = e^{4y}$
safe radishBOT
Find a generating curve on the xy-plane for the surface of revolution given by $...
flat frigateBOT
steamhahasteamhaha
coarse kelp
can somebody guide me on how to answer this
what I don't know is, how would I know where it revolves
like what axis
if I had to guess
maybe it would revolve around the z axis
then to find the generating curve
i will do let z = 0?
so now we have $4x^2=e^{4y}$
flat frigateBOT
steamhahasteamhaha
lean otter
$x = \pm \frac{1}{2}e^{2y}$
coarse kelp
but how would I know if it's in terms of x or y
flat frigateBOT
Ilvvus
coarse kelp
how did you know it's in terms of x?
coarse kelp
$x = \pm \frac{1}{2}e^{2y}$
why not y =
how did you choose x =
?
🙏
please
<@&286206848099549185>
lean otter
thats just how it is
coarse kelp
DUDE
lean otter
the change is described in the x axis
coarse kelp
why do x = instead of y =?
lean otter
because thats how I resolved it, you could probably do the same for y
coarse kelp
oh
coarse kelp
because thats how I resolved it, you could probably do the same for y
it would still be correct?
lean otter
Yes, it would describe it in the y axis instead
safe radishBOT
coarse kelp
.reopen
safe radishBOT
✅
lean otter
$y = \frac{1}{4}\ln(4x^2)$
coarse kelp
would it still be correct?
flat frigateBOT
Ilvvus
coarse kelp
**Ilvvus**
yep
lean otter
this is the previous problem
coarse kelp
yes ik
lean otter
give me a sec.
coarse kelp
okay
lean otter
im pretty sure yes
flat frigateBOT
Ilvvus
lean otter
ok yeah
lean otter
because in the solution they wrote y =
i'm not sure why they did this
coarse kelp
aww okay no problem
lean otter
$y^2 = \frac{20 - 4z}{5}$
flat frigateBOT
Ilvvus
lean otter
$z = \frac{20 - 5y^2}{4}$
flat frigateBOT
Ilvvus
lean otter
**Ilvvus**
this is the same thing as the solution that you provided
coarse kelp
this is the same thing as the solution that you provided
okok
i have to move on to the new lesson
i am 1 lesson behind
lean otter
alright good luck
safe radishBOT
@coarse kelp Has your question been resolved?
green bane
find the volume in cubic inches
safe radishBOT
find the volume in cubic inches
green bane
no clue on how to start
safe radishBOT
@green bane Has your question been resolved?
green bane
<@&286206848099549185>
green bane
<@&286206848099549185>
flint prairie
The formula for a triangular pyramid is 1/2Bh. first you would need to calculate the area of the base= B...
the base is the triangle at the bottom
@green bane
green bane
no...
flint prairie
no?
green bane
can you draw where you are getting the base
flint prairie
green bane
so how does the 6 delate
flint prairie
6 is the height of the triangle
green bane
it is?
flint prairie
The formula for a triangular pyramid is 1/2Bh. first you would need to calculate...
my bad the forumla is 1/3Bh not 1/2Bh. typo
flint prairie
the 8 is the height of the pyramid, h which you would plug in to 1/3Bh
green bane
yeah but it goes though the shaded region
flint prairie
shaded region?
green bane
this???
flint prairie
this???
yeah thats the base. it doesnt have anything to do with the height
i just circled the triangle that was the base
flint prairie
no it just looks like that because the pyramid is 3d. the line is dashed showing that it does no intersect with the height line
flint prairie
the dashed lines are behind the solid lines. the dashed lines do no cross the solid lines. it just "looks" like they are crossing because a pyramid has three dimensions
im not really understanding ur question here
green bane
6 is the height of the triangle
no it isnt
safe radishBOT
@green bane Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
warm compass
Could someone please help me with this problem?
safe radishBOT
Could someone please help me with this problem?
safe radishBOT
@warm compass Has your question been resolved?
warm compass
<@&286206848099549185>
safe radishBOT
@warm compass Has your question been resolved?
velvet nebula
you need to be a bit more accurate with those angles, I would think. Originally there is 20 degrees 52 minutes and 22 degrees 45 minutes and you can calculate in terms of that, then you repeat the calculation with AB found with that with 20 degrees 53 minutes and 22 degrees 46 minutes
warm compass
How to would I do that exactly? I am not to familiar with including minutes to the calculations of triangles
velvet nebula
one minute is just 1/60 of a degree
so $22^\circ 45'=\left(22+\frac{45}{60}\right)^\circ$
flat frigateBOT
Element118
warm compass
So the angle for this is 91/4? (22.75 degrees)
velvet nebula
So the angle for this is 91/4? (22.75 degrees)
yeah you can write it that way
just do the same for the other angles
warm compass
Okay, Thank you. Do you mind if I text you the problem when I am finished so you can look over it?
velvet nebula
you can post your attempt here
copper pewter
CD is found easily then use that with the 70° <ACD to find AD, use 68° to find BD then do AD-BD
velvet nebula
CD is found easily then use that with the 70° <ACD to find AD, use 68° to find B...
gotta be careful, they didn't use the minutes earlier when they did their rough work
copper pewter
U could use sine rule but that also works
Oh
That's bad
Finish your proper labelling first then
safe radishBOT
Available help channel!
brazen helm
$(\sin(x))^{tan(2x)})’$
safe radishBOT
$(\sin(x))^{tan(2x)})’$
balmy mist
You meant to write sin(x)?
balmy mist
!status
safe radishBOT
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
bigpufik
brazen helm
Yeah that
flat frigateBOT
NieStachu
balmy mist
Can you show what you got
flat frigateBOT
bigpufik
balmy mist
Well, now just take the derivative
balmy mist
Do you know how to find derivative of e^f(x)?
brazen helm
I don’t think I do
balmy mist
Chain rule
balmy mist
Yep
brazen helm
and I use e^x as g and f as the ln thing?
balmy mist
Indeed
brazen helm
ok ty
balmy mist
You will still have to use the multiplication rule and the chain rule to finish the calculations
quick latch
Hi, I need help approaching this question any help is appreciated 🙂
quick latch
<@&286206848099549185>
safe radishBOT
@quick latch Has your question been resolved?
quick latch
<@&286206848099549185>
balmy mist
!status
safe radishBOT
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
2
balmy mist
Well where are you stuck then
quick latch
t3 onwards
balmy mist
Solution wise?
quick latch
yes
balmy mist
Just write down all the legal words with length 3
Then you can also calculate the t_3, this way you have 3 equations which should be enough to find a b c
quick latch
wydm calculate t3
balmy mist
Find out how many legal words of length 3 there are
quick latch
8
balmy mist
Does that solve the problem you were having?
quick latch
nope
balmy mist
What's the problem then
quick latch
the next bit
balmy mist
Then you can also calculate the t_3, this way you have 3 equations which should ...
.
I meant T4 there
quick latch
.close
umbral grove
safe radishBOT
umbral grove
im confused on question njmber 12 becuase
I don't know what math skills we learnt to cover this question
i don't think i can comvert this to any eqaution (standard, x int, vertex) that would make sense
safe radishBOT
@umbral grove Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
fickle trail
safe radishBOT
fickle trail
Why is m allowed?
Seems like commutative multiplication which is a no no for matrices
fickle trail
Oh so a is not a matrix at all
buoyant shadow
yeah
fickle trail
Just a constant
So when you distribute B it stays on the left
But to the right of the constant
And also to the left of the constant?
Could it be BaC or no?
Without any brackets at all
<@&286206848099549185>
Could m) be BaC with no brackets?
safe radishBOT
@fickle trail Has your question been resolved?
final halo
Could m) be BaC with no brackets?
it could yes
scalars (1x1 matrices), like a, commute with any matrix
fickle trail
Interesting.. so does that mean aB is the same thing as Ba?
final halo
when a is a scalar yes
final halo
dont confuse scalar with constant
fickle trail
Scalar = constant?
final halo
a matrix can be constant
fickle trail
a matrix can be constant
How so?
final halo
$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$
flat frigateBOT
ΣAC
final halo
thats constant
there is no variable in there
constant refers to things that do not change, they're constant
scalar refers to 1x1 matrices (numbers)
safe radishBOT
@fickle trail Has your question been resolved?
empty gyro
(m) a(BC)=(aB)C=B(aC)=(BC)a
In fact, they're missing scalar commutativity in general
(n) aB=Ba
@fickle trail something to consider
fickle trail
Thanks, good to know.. scalars can go on left or right of matrices
lean otter
(a-b) ² is the same as (b-a) ²
sign is squared so it will always be positive.
right?
sand minnow
Try expanding both and see for yourself
safe radishBOT
@lean otter Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
odd topaz
quasi bison
!onechannel
safe radishBOT
Please stick to your channel.
pale remnant
safe radishBOT
pale remnant
How is this done?
the mean of the 16 packets is 497.1874
but I am unsure on how to process this information
grizzled fossil
figure out distribution of the sum of 16 packs
pale remnant
Uhh could u elaborate
I'm trying to do a normal distribution with mean of 500 and standard deviation of 5
but not sure where to go from there
fair hound
Let X be the mass of a pack
X ~ N(500, 5²)
So if I have 16 packs X1, X2, ..., X16
X1+X2+...+X16 ~ ?
Once you know the distribution, you can directly conduct your test
pale remnant
Let X be the mass of a pack
X ~ N(500, 5²)
So if I have 16 packs X1, X2, ..., X1...
dont really get what u mean by "X1+X2+...+X16 ~ ?" but I guess ill search it up