#help-27
orchid wasp
devout snowBOT
orchid wasp
Why is the 5 on the third point
lusty sapphire
Why is the 5 on the third point
because it is the third coordinate
ohh
I see what you are asking
It's not like this
orchid wasp
Is it suppose to be like this
orchid wasp
It's like this
I’m confuse so why is it at the third z
lusty sapphire
I’m confuse so why is it at the third z
wdym by third z?
orchid wasp
wdym by third z?
Like the bottom point is (3,2,0) so shouldn’t it move up 5 points from there
lusty sapphire
Like I said here, you should not be reading it like this. The point is in 3D space (projected onto paper), it is not in the 2D coordinates of z and y
lusty sapphire
Like the bottom point is (3,2,0) so shouldn’t it move up 5 points from there
It did.
Here is roughly what you see
orchid wasp
This what I’m doing
lusty sapphire
and here it is from a different perspective
orchid wasp
and here it is from a different perspective
Bruh I don’t get these
lusty sapphire
Bruh I don’t get these
All the red lines are parallel to each other, same for the green and blue lines
and the two black lines are parallel
the blue and purple rectangles are also parallel to each other. The blue rectangle is at z=0 and the purple is at z=5
@orchid wasp
orchid wasp
The red line is y?
lusty sapphire
The long red line is the x axis, and the long green line is the y axis
orchid wasp
Isn’t y to the right of z
lusty sapphire
Here's the same image, closer to the perspective on your paper
lusty sapphire
Isn’t y to the right of z
It's all in 3D, I just rotated it a bit
play with the 3D here: https://www.geogebra.org/calculator/mfdeddcy
orchid wasp
Here's the same image, closer to the perspective on your paper
Ok I see that the z at 0 is at -2 so when u move it up by 5 it goes to 3 but how am I suppose to know it’s at -2 using only my graph
lusty sapphire
This what I’m doing
From here, the two dashed lines at (3, 0, 0) and (0, 2, 0) are in the XY-plane and meet at (3, 2, 0) (the blu points). Then, from the blue point, you must move upward by 5 units (but thanks to 3D perspective, this will not align neatly when projected onto 2D paper. That's what the two blue long curly { are showing you, that the purple dot is 5 units above the blue dot, but at the same x and y coords, making the purple dot (3, 2, 5)
orchid wasp
From here, the two dashed lines at (3, 0, 0) and (0, 2, 0) are in the XY-plane a...
But they can just stop the { anywhere they want instead of the 3rd point at z?
How do I show that as a dashed line
lusty sapphire
But they can just stop the { anywhere they want instead of the 3rd point at z?
It's not at the third point at z
you're still looking in 2D
they're not "stopping it anywhere"
They're drawn to be the same length
Looks like you are struggling with orthographic projections
requires some mental imaging of third dimension
orchid wasp
It's not at the third point at z
So can I not draw it as a dashed line
lusty sapphire
So can I not draw it as a dashed line
in what way?
lusty sapphire
Oh. Then yes, you could draw that as a dashed line (and is the usual convention.
I think the curly braces here were used to emphasize that the separation between the blue and purple points was exactly five units
But that's not how you would normally draw it
orchid wasp
But that's not how you would normally draw it
Can u show how cus I don’t get it
lusty sapphire
Normally, it would be drawn like this
Where the little black squares emphasize right angles
And it is common to label the height
So we know that we went 5 units up
You could also add this extra dashed line to emphasize that the higher dot is at z=5
orchid wasp
Normally, it would be drawn like this
Like this?
lusty sapphire
Almost
you keep trying to draw the point so that it is horizontal to z=5
But that is the wrong perspective
orchid wasp
So how come 3 and 2 r at those exact points
orchid wasp
What but they did that
lusty sapphire
See how their dashed lines are parallel to their axies
you aren't doing that
you drew this line on the right going straight down, aligned with your sheet of your paper
But it should go parallel to this axis
You drew this dashed line correctly because it goes parallel
orchid wasp
your dashed lines need to be parallel to your axes
Ok then idk how to draw z as 5
Like what way is it suppose to dash then
lusty sapphire
Lines of the same color should be drawn parallel to each other
orchid wasp
Lines of the same color should be drawn parallel to each other
Can u draw it out like my graph
orchid wasp
Lines of the same color should be drawn parallel to each other
Cus mine doesn’t have those
lusty sapphire
Cus mine doesn’t have those
doesn't have what?
orchid wasp
doesn't have what?
I’m confused how u draw the z as 5 on my graph
Like I only have these circled parts
supple knot
just extend the z axis to -z direction
orchid wasp
just extend the z axis to -z direction
What so it’s going down?
orchid wasp
that blue line has tick marks at z=-1 and z=-2
What bruh I’m so lost
supple knot
what's wrong
supple knot
That makes it z as 5
what is "it"
orchid wasp
that blue line has tick marks at z=-1 and z=-2
This
supple knot
that blue line has tick marks at z=-1 and z=-2
there's no 5 in this picture
supple knot
oh i see i misunderstood your question
you move the point (0,0,5) that's on the z axis
to whatever (x, y, 5)
first shift (0, 0, 0) to (3, 2, 0)
red = x axis and green = y axis
after you shift (0,0,0) to (3, 2, 0), then you go vertically 5 units
both ways arrive at the same destination point (3,2,5)
rotund umbra
supple knot
your dashed lines need to be parallel to your axes
your dotted line should be parallel to the z-axis
orchid wasp
you can click around with it
Ok these things r confusing can u draw it like my graph
Using only this
supple knot
this line has to be parallel to
rotund umbra
Ok these things r confusing can u draw it like my graph
no, because you can't draw 3d on a piece of paper
supple knot
this one
orchid wasp
They did on YouTube
supple knot
all we're telling you is that your lines are slanted
sinful rover
no, because you can't draw 3d on a piece of paper
yea you just draw like a normal xy-plane graph then put a line going diaganol
from the bottom left to the top right
orchid wasp
all we're telling you is that your lines are slanted
Wym I made the z line straight
sinful rover
rotund umbra
yea you just draw like a normal xy-plane graph then put a line going diaganol
no, that's a diagonal line. you'd need to draw a line coming out of the paper
sinful rover
no, that's a diagonal line. you'd need to draw a line coming out of the paper
lmao ok
orchid wasp
Bruh what so what’s the point of this thing if I can’t draw it
sinful rover
its called drawing 3d on 2d, if your tv can do it so can you
supple knot
plotting 3d in IMAX 
sinful rover
Bruh what so what’s the point of this thing if I can’t draw it
you can... just add a third line like i said
is that better?
that one is a little hard to see
orchid wasp
you can... just add a third line like i said
They did it like this
But I wanna know how to draw it as a dashed line like the bottom (3,2,0) is
And I don’t understand where it’s suppose to stop
sinful rover
OH
you just estimate
i mean they did the lines so they could see it better
draw a line on the y axis parallel to the x axis and the same for the x line and where they intersect put a point
orchid wasp
draw a line on the y axis parallel to the x axis and the same for the x line and...
So how I draw the z axis
Cus this what I did but it’s wrong
sinful rover
So how I draw the z axis
sinful rover
Cus this what I did but it’s wrong
how is that wrong?
rotund umbra
Cus this what I did but it’s wrong
looks fine to me
lusty sapphire
@rotund umbra @sinful rover it's wrong Because this dashed line on the right should not be going straight down, it should go parallel to the x axis
sinful rover
<@211475256689426432> <@761784400643096618> it's wrong Because this dashed line ...
omg bro its an estimated line no one is getting introuble for that
its a drawing
orchid wasp
so my answers right??
sinful rover
so my answers right??
theyre just being picky; yes
lusty sapphire
omg bro its an estimated line no one is getting introuble for that
In normal circumstances, I would never point this out, or criticize it, but the root of the whole problem here is that dellungi is not making the jump from 2D to 3D, or understanding how the perspective changes as you move orthogonal to paper. The fact that it goes straight down is making me concerned that it's the same problem, but transfered to another axis now.
sinful rover
In normal circumstances, I would never point this out, or criticize it, but the ...
yea but they drew a line its not like they dont understand
lusty sapphire
theyre just being picky; yes
Yes. I am being picky, I want to be certain dellungi truly understands the task here so they're not sent off with incomplete information, and then get even more frustrated when their teacher becomes not satisfied.
sinful rover
i think they understood what they were doing and now youre making them doubt themselves in an unnecessary manner
rotund umbra
lusty sapphire
@orchid wasp, overall, it's up to you. Do you trust that you understand this now?
orchid wasp
so where is the z suppose to go up to if its not 5 i dont get it
orchid wasp
so it does go up to 5 in z
sinful rover
so where is the z suppose to go up to if its not 5 i dont get it
whatever the coord says
(x,y,z)
if z is 0 just dont move it
orchid wasp
whatever the coord says
it says 5
sinful rover
ok then 5
orchid wasp
but this isnt
rotund umbra
so it does go up to 5 in z
Like this, if you want to have your z axis at 60 degrees
orchid wasp
Like this, if you want to have your z axis at 60 degrees
That bottom point is (3,2,0) so the z is suppose to go up 5
So it becomes 3 at z??
I’m boutta tweak out
rotund umbra
That bottom point is (3,2,0) so the z is suppose to go up 5
no 5 at z
you've just said that
the z is suppose to go up 5
lusty sapphire
so where is the z suppose to go up to if its not 5 i dont get it
It's not going to be at some fixed height relative to your sheet of paper. The z=5 position, when projected onto your flat piece of paper, will have different relative heights
All those higher points have z=5
None are at a fixed height (relative to the screen) because the perspective projection is warping the points to make it viewable in 2D
orchid wasp
It's not going to be at some fixed height relative to your sheet of paper. The z...
so for z i can stop it anywhere i want???
So I can just say this is (3,2,5)
lusty sapphire
so for z i can stop it anywhere i want???
Not "anywhere you want. Gimme a minute to draw something again
The really fat purple line here goes from the origin, to 5 units up, along the z axis. So it starts at (0, 0, 0) and ends at (0, 0, 5)
Every black line in this graphic must be exactly that length of the fat purple line
It is that specific length that signifies that you are translating 5 units up, in the positize z direction.
If you draw your line shorter, then you would end up at a z less than 5. Likewise, draw it longer, and you are at z greater than 5
orchid wasp
The really fat purple line here goes from the origin, to 5 units up, along the z...
How am I suppose to draw it to scale
I can just use that { strategy then??
lusty sapphire
yeah
lusty sapphire
again, "anywhere you want" is not how you want to think of it. Stop it so that it is the appropriate length
lusty sapphire
Actually what if I don’t cus u said it’s not normally used
what's normally not used?
lusty sapphire
Don't "hope", just try your best to make them the same length.
They don't have to be exactly perfect. No ones expects that of you when drawing by hand
Just make it reasonably apparent that you drew to the correct height
does that make sense?
orchid wasp
again, "anywhere you want" is not how you want to think of it. Stop it so that i...
I meant that if I show the length of z as { then I can make the point of (x,y,0)s { as long or as short as I want
lusty sapphire
I meant that if I show the length of z as { then I can make the point of (x,y,0)...
No. You cannot
You should make it reasonably the same size as the original
Dang. Why don't I have any paper?
Dang. I lost my good pen
lusty sapphire
Is this right
no
lusty sapphire
no
You are making the same problem, you are extending your line until it is horizontal aligned with 9 as marked by the z axis
All of these telephone poles are the same height (in 3D space). They are presented as different sizes on this sheet of paper so that the perspective view matches what our eyes see in real life. Likewise, the tracks on the the railroad are parallel (in 3D space), but the converge into the same spot as they meat at the horizon. If the tracks were drawn parallel on this paper, then in 3D, it would look like they are separating from each other. And the house on the right. The window, the door and the wall containg them are all rectangles, but they look like trapezoids because the perpspective is slanting the lines away from right angles. On paper, the lines are not parallel, but they represent parallel lines of 3D space.
This building has a flat roof, and therefore a fixed height. But these highlighted ends of the roof are at different heights on the paper. But does that mean they are at different heights in real life?
@orchid wasp this red line does not represent z=9
does that make sense?
lusty sapphire
They’re similar length now
yes
you've done it
Keeping them the same length keeps the perspective correct.
orchid wasp
So I don’t need to write out any points for z like I did x and y?
lusty sapphire
(This is actually known as orthographic projection, which is just one way to represent 3D space, but it's the easiest way)
lusty sapphire
So I don’t need to write out any points for z like I did x and y?
You should. Ad you did
orchid wasp
I’m saying these
lusty sapphire
I’m saying these
The ticks count as marks, it shows me that your x is 3 and your y is 4, since your dashed lines intersect the corresponding axes at those marks
orchid wasp
Yeah so I don’t need for z cus idk how long it actually goes up ?
lusty sapphire
This line here, the z axis, that line represents all the points whose x and y coordinates are zero. So only the z changes on this line. Any (0, 0, 1), (0, 0, 2), (0, 0, pi), whatever, they'll all be on this axis.
lusty sapphire
Yeah so I don’t need for z cus idk how long it actually goes up ?
You should know how long it goes up. You don't need markings on the z axis in this particular example because you marked the point (0, 0, 9) on the z axis, and you make it apparent to me.
So, say you had the point (2, 4, 3). How would you plot that now?
orchid wasp
You _should_ know how long it goes up. You don't need markings on the z axis in ...
I only know that it goes up the same length as z from (x,y,0) tho not the point it stops at at z
lusty sapphire
I only know that it goes up the same length as z from (x,y,0) tho not the point ...
you were plotting (3, 4, 9), so you know it stops at wherever 9 units up your z axis would be. You marked where 9 units would be on your z axis, so that works. You don't not know it in the plot you shared
orchid wasp
you were plotting (3, 4, 9), so you know it stops at wherever 9 units up your z ...
I know it the 0 in (3,4,0) goes up 9 unit but idk to which z. Like the z has 1,2,3,4,5,6,7,8 to 9 and idk which of the number it is at?
orchid wasp
So, say you had the point (2, 4, 3). How would you plot that now?
This what I’m talking about
So it stops in middle of 1 and 2?
lusty sapphire
You did this exactly perfect btw.
lusty sapphire
So it stops in middle of 1 and 2?
Oh. I see what you are asking now. This is irrelevant. Where it stops has no meaning, and it will always be different based on the perspective
orchid wasp
Oh. I see what you are asking now. This is irrelevant. Where it stops has no mea...
Yeah so I don’t need to put those marks at z?
lusty sapphire
Yeah so I don’t need to put those marks at z?
No. it can help to mark the units of z like you did for the x and y axes, but as long as you mark the desired z height on the z axis, that is sufficient
Here, I have used 3D software to plot a point in space
But, it is really hard to tell exactly what point this is
In fact, it is impossible
If I rotate the plane space ever so slightly...
You see that it was sever points all on a line
orchid wasp
Here, I have used 3D software to plot a point in space
Ok whatever I’m just not gonna label but urs know it between 1 and 2 but idk mine
lusty sapphire
Ok whatever I’m just not gonna label but urs know it between 1 and 2 but idk min...
between 1 and 2? No. It's not anything like that. There is zero correlation in your idea here
orchid wasp
Wym ur point is between 1 and 2 in the z axis
lusty sapphire
Ok whatever I’m just not gonna label but urs know it between 1 and 2 but idk min...
This will never be a fixed fact
You're not supposed to be thinking "Oh, for (2, 4, 3), I have to draw the height somewhere between 1 and 2. That's where it belongs". There is absolutely zero relation between those two things
Here's the same point in a very esoteric perspective
These are all representations of the point (2, 4, 3)
Do you know why it looks weird? Because I'm not drawing the dashed lines that help give the perspective
Here, I drew the guidelines, which helps a bit. It's still hard to see, but that's because I am attempting to get the point across that there is no fixed location for your point in 2D space. It depends on how your axes are drawn.
Play with this link here
https://www.geogebra.org/calculator/ynjhgcp5
That graph is interactive, you can move it around
Just because the blue dot is somewhere different on your screen does not mean that it's no long (2, 4, 3). The axes move too. They are all moving in a way so that the same abstract concept of plotting a point in 3D space, and then showing you that plot in a 2D image is equivalent
devout snowBOT
@orchid wasp Has your question been resolved?
hard badger
devout snowBOT
hard badger
can someone explain part d for me please?
where did we get -1 for x and y from?
i get that horizontal tangent line is where y = 0 but i don't get how to go from beyond there
Is it bc we known when horizontal tangent line, the derivative is 0
so we set 0 = to numerator of dy/dx?
.close
devout snowBOT
devout snowBOT
Available help channel!
restive river
Assesments =50%. Grade is 117/120. Assignments = 25%. Grade is 87.9/90. Classwork = 25% grade is 85.9/91. what is the lowest grade i can get on an 100 point test and still maintain an 84 in the Assesments category
devout snowBOT
Assesments =50%. Grade is 117/120. Assignments = 25%. Grade is 87.9/90. Classwor...
restive river
im pretty sure this is easy but idk how to do it
someone pls help ,e
me
!close
devout snowBOT
@solid hollow Has your question been resolved?
rough hatch
how do you know when to use shell, disk or washer method
devout snowBOT
how do you know when to use shell, disk or washer method
sonic parrot
how do you know when to use shell, disk or washer method
What
spare zealot
Problem context and whatever variable you decide is easier to integrate
Do you have a specific problem or just general question?
rough hatch
rough hatch
Do you have a specific problem or just general question?
also gerneal question ig
but thats the one that im working on
spare zealot
What do you think about it right off the bat
I assume that interval is of y and not x
rough hatch
What do you think about it right off the bat
thats what im assuming too
also it rotates around the y axis?
spare zealot
So we have the blue shape here rotating around the orange
And goes no higher than the purple
Just to help visualize
This could be done with an integral with respect to y or wrt x depending on preference. Remember any key differences between those?
rough hatch
wym key differnces
spare zealot
That was worded weirdly on my part
Start with just the area under the purple curve, for example
If you integrate with respect to x, you're adding up slices that are dx wide (really small) and a height of 1-2x^3 (purple - blue)
If instead you integrate with respect to y, you're adding up slices that are dy wide (really small) and a height of the inverse of f(x), which is cube root of x/2
The variable that you choose to integrate changes the method that you use
Notably, if the slices are parallel to the axis of rotation (in this case axis is y axis, slices are parallel to it in the dx case) you use the shell method, and if slices are perpendicular to the axis of rotation (in this example, the dy case), you use disk or washer depending on whether there's a hole in the middle of the shape
Does that make any sense or am I rambling too much lol
rough hatch
Does that make any sense or am I rambling too much lol
i think so
if its y i should generally use shell?
rotating around the y axis
spare zealot
Depends on what the axis of rotation is
if you're integrating in y, you do shell if the axis of rotation is parallel to the x axis
Because the slices that are formed by the riemann integral when integrating are horizontal when integrating y, and vertical when integrating x
In the case of x, you're integrating these regions
If you recall the riemann sum definition of the integral, it's really the limit of the areas of a bunch of rectangles that get smaller and smaller
When doing it in terms of x, the rectangles are really tall and their long sides are parallel to the axis of rotation. Whenever the long sides are parallel to the axis, you use the shell method. (If the shell method isn't possible, you should integrate in terms of the other variable)
IN the case of y, it looks like this
In both cases the axis of rotation is the orange line. In the first image, those rectangles (or I guess lines... infinitely thin rectangles) are rotated in a way that makes each of them into the side of a cylinder, thus shell method
In the second image, they're rotated in a way that makes each of them into a circle, thus disk method
spare zealot
Where the washer method comes in is in a case like this
Notice how it's similar to the case where the disk method is used, but there's a hole in the middle of the shape once its rotated upont the axis
rough hatch
yes
spare zealot
For the points up until that hole starts, you use the disk method, but for the rectangles where that hole exists you need the washer
rough hatch
so how would i determine where the lines point
spare zealot
You get to choose, which is part of what makes it difficult lol
In any given volume of revolution problem, you can do it with the rectangles in either direction
rough hatch
oh
spare zealot
Though usually one way is easier to do than the other
rough hatch
yea
spare zealot
In the case of that third image I sent, if you did it in terms of x you would only need the shell method instead of both washer and disk
Which would result an a more simple integral
rough hatch
so they should all give the same anwser?
just one is harder?
spare zealot
Yes
rough hatch
i see
spare zealot
It all depends on the problem itself. Sometimes both ways are about the same complexity, sometimes one is incredibly complicated and the other is really easy in comparison
But as far as identifying which method you're using, if you choose the way the rectangles go and they're parallel to the axis of rotation, you use shell
If perpendicular, you use disk/washer
rough hatch
i see
spare zealot
What
It's methods for calculating the volume of objects that are defined by rotating a graph around some axis to make a 3d shape
Here's another example if you want. The region is rotated around the x axis
When you integrate dx it's always doing vertical red lines, and when you integrate dy it always does horizontal red lines (of course, if the function is given as a function of x you need to invert it to do dy, and vice versa)
In this case, the dx way is washer and the dy way is shell
devout snowBOT
@rough hatch Has your question been resolved?
rustic whale
help
rare merlin
with what
rustic whale
to solve math problem
rare merlin
what math problem
rustic whale
Basic Statistics : Types of Statistics, Different Statistical Techniques, Steps in Statistical Investigation, Uses and Limitations of statistics, Collection of Data, Sources of collecting primary and secondary data, Limitations of secondary data, Criteria of evaluating secondary data, Organization of data, Graphs of Grouped Frequency Distribution, Tabulation of Data, Parts of Table.
Measures of Central Tendency : Kinds of measures of central tendency (statistical averages or averages) :
Arithmetic Mean : Simple Arithmetic Mean, Methods of calculating simple arithmetic mean, Arithmetic Mean in case if Individual Series, Discrete series and Continuous series, Weighted Arithmetic Mean, Combined Arithmetic Mean.
Geometric Mean : Simple Geometric Mean, Methods of calculating Simple Geometric Mean, Geometric Mean in case of Individual Series, Discrete series and continuous series, Weighted Geometric Mean, Combined Geometric Mean.
Harmonic Mean : Simple Harmonic Mean, Methods of calculating Simple Harmonic Mean, Harmonic Mean in case of Individual, Discrete series and continuous series. Weighted Harmonic Mean, Combined Harmonic Mean.
Median : Methods of Calculating Median in case of Individual, Discrete series and continuous series.
Partition Value : Quartile, Quintiles, Hexiles, Septiles, Octiles, Deciles, Percentiles.
Mode : Methods of calculating Mode in case of Individual series, Discrete series and continuous series.
Range : Computation of Range, Inter Quartile Range, Computation of Inter Quartile Range, Percentile Range and Computation of Percentile Range.
Mean Deviation : Computation of Mean Deviation, Standard Deviation, Calculation of Standard Deviation, Variance, Calculation of Standard Deviation for Individual Series, Discrete Series and Continuous Series, Coefficient of Standard Deviation and coefficient of variation, Combined Standard Deviation, Correcting incorrect Standard Deviation.
Correlation Analysis : Correlation Analysis : Definition, Types of Correlation : Positive, Negative, Simple, Multiple, Partial, Total, Linear and Non-linear. Need of Correlation Analysis, Correlation and Causation, Techniques for Measuring Correlation : Scatter Diagram Method, Graphic Method, Karl Pearson’s coefficient of correlation : Correcting incorrect coefficient of correlation, calculating Karl Pearson’s coefficient of correlation in case of grouped series. Probable Error, Coefficient of Determination, Spearman’s coefficient of Correlation (Rank Correlation) : Calculation of Correct Coefficient of rank correlation. Difference between Rank Coefficient and Karl Pearson’s coefficient of coefficient, Coefficient of concurrent deviation.
Regression Analysis (Linear Regression) : Definition, Difference between Correlation and Regression, Types of Regression Analysis : Simple, Multiple, Partial, Total, Linear and Non-linear, Objectives of Regression Analysis, Methods of obtaining regression analysis : Regression Lines, Regression Equations. Methods of obtaining regression equations ; Normal Equations and Regression Coefficient, Properties of Regression Coefficient, Standard Error of Estimate, Regression Coefficient in case of Grouped Data, Uses of Regression Analysis and Limitations of Regression Analysis
@rare merlin it's my syllabus
river knot
💀
rare merlin
i am not gonna read all of that lol
river knot
just ask a specific question
rustic whale
read topic only man 😂
river knot
nobody is going to teach you your whole curriculum
steady trail
u need to memorize all of this
steady trail
the mean is the average of all the numbers
is that the type of mean or is it something else
steady trail
so ur problem is that u have an exam
rustic whale
yes
steady trail
and u have to memorize all of this for the exam
fallow forum
why don't we need to convert all the "s"'es in the answer to (s-2) or (s-6) depending on whetehr it falls under e^-2s or e^-6s?
devout snowBOT
why don't we need to convert all the "s"'es in the answer to (s-2) or (s-6) depe...
fallow forum
i thought the time shift meant i had to change all the variables accordingly
devout snowBOT
@fallow forum Has your question been resolved?
urban aurora
i thought the time shift meant i had to change all the variables accordingly
You only need to shift the time, not the frequency. If it's multiplied by e^at (instead of e^as), then you apply frequency shift
fallow forum
so basically it's already shifted
this is another similar question
i think i see now
so i only need to shift for t and not s
urban aurora
👍
fallow forum
wait, it's e^-2s, not e^-2t
urban aurora
exactly
fallow forum
oh the 2 problems use different formulas?
we were given these but never taught how to use them. he just told us when, for example using laplace inverse, when we contract e^-2s to u_2(t) we just have to shift everything by 2, or in this case, slapping on a -2 on every t we get from the L^-1
i thought we needed to go the other way when we compute the laplace (non inverse)
urban aurora
i thought we needed to go the other way when we compute the laplace (non inverse...
You do still do that.
When you go backwards you find the inverse, then you shift t
Thus when you go forwards, you shift t, then find the laplace transform
urban aurora
For u_a(t) yes
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ruby parrot
what would the standard deviation of this density curve be
devout snowBOT
what would the standard deviation of this density curve be
ruby parrot
it says estimate
royal radish
its just 20
midnight echo
About 68% of the area under the curve will fall within -1 and 1 standard devation from the mean
royal radish
100+- 20
midnight echo
Ballpark would be like 20, maybe 15
royal radish
id go with 15
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unique lake
Hello, I am trying to prove that simple straight line, f(x)=ax can be approximated by infinite sum $f(x)=\frac{aL}{\pi} \sum_{n=1}^{\infty}\frac{-1^{n+1}}{n}\sin (2n\pi x/L)$. I need a little help. Thanks!
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Hello, I am trying to prove that simple straight line, f(x)=ax can be approximat...
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frozen aurora
Hello, I am trying to prove that simple straight line, f(x)=ax can be approximat...
you can only approximate a section of a straight line, but otherwise the formula for a regular sawtooth wave should work
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unique lake
Sorry, i forgot to add over a certain range, from -L/2 to L/2
unique lake
what exactly do you need help with
How do i prove that?
unique lake
Sorry, i forgot to add over a certain range, from -L/2 to L/2
I mean this is important part of the problem
I mean which technique do i use to prove that?
trail eagle
You usually get this using the Fourier series. Are you familiar with that?
humble fulcrum
What is the fastest method in solving large systems of equations
neat solstice
I think its not gauss, im gonna search real quick
unique lake
.reopen
unique lake
You usually get this using the Fourier series. Are you familiar with that?
Acutally this is some kind of intro to fourier series so i am not that familiar
neat solstice
What is the fastest method in solving large systems of equations
Gauss is O(n^3)
Gmres is an algorithm that is way faster
But afaik it is an approximation
But when n is big, computers do the calculation anyway. And afaik gauss also had bad conditioning
stone stump
exact solutions dont matter for big systems anyway
often the system ends up symmetric and positive definite so you can also use cg which is faster iirc
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humble fulcrum
But when n is big, computers do the calculation anyway. And afaik gauss also had...
Wdym gauss has bad conditioning
Is matrix method better than the standard solve for some variables until you get a number
neat solstice
With computers, you get errors. Some algorithms are more stable with handling errors. And afaik gauss is not so good at that
restive river
Let f be a real-valued continuous function on R. Prove that f is uniformly continuous on R if lim(x→-∞)f(x) = lim(y→∞)f(y) = 0.
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Let f be a real-valued continuous function on R. Prove that f is uniformly conti...
restive river
My plan was to choose a M,
For all positive epsilon, pick out M sao that | f(x) | < epsilon/2 for all x in R \ [-M;M]
then I use the properties of uninformly continious on [-2M;2M] but then idk wth im doing 😭
.close
wary spoke
Okay, I am unlucky af, I asked a question related to this literally a few hours ago( #help-32 message ), and I ran into the same problem In a different context(vector then, conics now)
So, I was looking at the solution for a problem, and in that problem they do the following
(x-2)/3 = y/0
y=0
Context: The above is trying to derive a straight line equation from 2 points in that line.
And surprisingly the answer is correct(I used another method that doesn't involve undefined stuff)
So my question is, did the above solution basically do the multiplication by assuming '0' to be not 0, but a value close to 0, and is this another case of practicality vs mathematical rigor.
devout snowBOT
Okay, I am unlucky af, I asked a question related to this literally a few hours ...
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
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wary spoke
Please show the original problem, **exactly as it was stated to you**, with the ...
Problem: Determine the equation of the below conic
Okay... I am dumb
.close
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shrewd kettle
Ferris wheel with Radius 30 meters spins one rotation in 3 minutes. The a person steps on the wheel at the lowest point on the ground. and then the wheel spins for 5 minutes before stopping. How high above the ground is the person?
I am cooked
shrewd kettle
aka interval is 120 degrees, and it does 600 degrees in total which is one rotation plus 240 degrees from -90degrees
do I asumme the lowest point is 0 so the amplitude would be 30 because the radius so it would be 30+30sin(150)=45m?
urban spindle
I think so. I mean, lowest point is definitely 0, and I agree the angle goes to 30 or 150 (depends in which way the wheel rotates). It looks correct.
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floral cradle
What would the answer here be?
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What would the answer here be?
old carbon
What would the answer here be?
draw a line y=x and reflect the graph across it
floral cradle
draw a line y=x and reflect the graph across it
wouldn't that be A tho? 😭.
it's being flipped over the y=x line so it goes into the other quadrant
old carbon
it's being flipped over the y=x line so it goes into the other quadrant
no?
You're thinking about flipping it over x=0. y=x is the line that is 45 degrees to the upper right corner from the origin
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stable plume
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mint stratus
which grade is this
winter patrol
did you have any issues with Q2?
winter patrol
initial set up is the same
solving comes after
first identify which parts are congruent
and that'll give you your starting equation
reef chasm
GRADE 11TH Asian maths anyone?
vernal monolith
!occupied
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stable plume
first identify which parts are congruent
and that'll give you your starting equa...
and then what😭
i’m sorry i’m a lil slow💔💔
winter patrol
are you able to determine the numerical size (measure) of angle T?
stable plume
it’s 29°
winter patrol
no
stable plume
oh
winter patrol
V is 29°, T is not V
mint stratus
triangle has 180 degrees total so just take away U and V to get T
winter patrol
i said numerical value
stable plume
i’m so slow😭😭
stable plume
triangle has 180 degrees total so just take away U and V to get T
alr
winter patrol
for this exercise, focus only on triangle TUV
stable plume
t is 61
winter patrol
math is case senstive, you should be using capital T
stable plume
AIGHT so now do i like make 3y+7 equal to 61
stable plume
math is case senstive, you should be using capital T
oh😭😭
winter patrol
by convention (with no other random stuff present) lowercase t would represent the side opposite T
stable plume
alr
mint stratus
can you use sin and cos?
winter patrol
AIGHT so now do i like make 3y+7 equal to 61
you're setting the wrong things equal
mint stratus
yeah sorry we had that earlier here
stable plume
you're setting the wrong things equal
wym
stable plume
yeah sorry we had that earlier here
oh
winter patrol
you mentioned that R is congruent to T
what is R given to be?
stable plume
8x-27
stable plume
OHHH tyty
winter patrol
and would you be able to solve that equation
stable plume
aight i got 11
slim canopy
Could you share your equation that you solved?
mint stratus
isnt just RS=VT?
stable plume
yeah i thinks
mint stratus
since all corners of triangle match
winter patrol
identify the congruent sides the same way you did in Q2,
then same idea
stable plume
so 3y+7=61??
mint stratus
noo
winter patrol
why 61
stable plume
man
mint stratus
but you are looking for lengths of sides
stable plume
bear w me chat😔
winter patrol
you're setting sides equal to angles
stable plume
ohh
winter patrol
identify the congruent sides the same way you did in Q2,
which sides are congruent
stable plume
OHHHH
mint stratus
out of context a bit but can you use pythagorean theorem already?
stable plume
not yet i don’t think
mint stratus
did you get the equation to solve y?
winter patrol
note that the values given in the question are poorly chosen, (that they can't be justified with rounding issues)
that you're just supposed to take them at face value
stable plume
alr🙏
winter patrol
for a triangle with those lengths, S would actually be around 37°, nowhere close to 29°
winter patrol
!done
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stable plume
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wary ruin
Let ( X ) and ( Y ) be two independent random variables such that ( X \sim Po(\mu) ) and ( Y \sim Po(3\mu) ).
The estimator for ( \mu ) is given as:
[
\mu^*_{\text{obs}} = \frac{2x + y}{5}
]
where ( x ) and ( y ) are observations from ( X ) and ( Y ), respectively.
Determine the standard error of this estimate of ( \mu ) if the observed values are ( x = 423 ) and ( y = 1304 ).
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Let \( X \) and \( Y \) be two independent random variables such that \( X \sim ...
woven radishBOT
dghf
wary ruin
Can someone help me with this? I know that since X and Y are poisson distributed, it means the the expectation and variance is equal to the mean value. But I am not following the procedure of calculating the SOE(mu).
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vast violet
my life is a lie
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my life is a lie
vast violet
so 1 inch isnt 12 cm??
No way i thought this all my life
apparently its 2.54 CM>?!?!?!
anyway i need help
How do i get from inches to cm^3 tho
2.16 in to cm^3
I can show my attempt 1 min
acoustic leaf
inches and cm^3 are not compatible units. do you mean in^3?
acoustic leaf
2.16 in is a length
you are given a cylinder with a particular radius and height. before anything else you need to turn that into a volume
vast violet
Oh
Ok
I def did this problem a while back but i gotta review for finals
SO i use cylinder formula as well?
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scarlet patio
how do I find the slope of an angle bisector?
devout snowBOT
how do I find the slope of an angle bisector?
scarlet patio
I am trying to find the coordinates for the incenter of a triangle
urban harbor
what is known?
scarlet patio
y = -x+58.45
y = (10/13)x-30.2
y = 25x-1248
these are the equations of the 3 lines
final drift
omg this is such a horrible bash
you need to use tan addition and half angle formulas
scarlet patio
you need to use tan addition and half angle formulas
What are these?
final drift
What are these?
do you know trigonometry?
scarlet patio
do you know trigonometry?
well, only the very basics like how to find sin cos tan but nothing else
final drift
well, only the very basics like how to find sin cos tan but nothing else
i dont see how to do this without trigonometry quite honestly
(decently advanced trig)
scarlet patio
It's a project for geometry math
final drift
oh okay i got it
scarlet patio
does this work?
final drift
you dont calculate the angle bisectors directly
final drift
does this work?
nono i will explain
okay so draw the incircle of the triangle
we get something like this right?
scarlet patio
we get something like this right?
Yes
final drift
ok, so i claim that you can use this to calculate all the three points of tangency
do you understand how this would work?
scarlet patio
ok, so i claim that you can use this to calculate all the three points of tangen...
yes
scarlet patio
do you understand how this would work?
yeah
final drift
yes
ok, so if we have M_A, M_B, and M_C
the incenter of triangle ABC is the same as the circumcenter of triangle M_AM_BM_C right?
scarlet patio
Oh I get it
final drift
Oh I get it
you know how to calculate the circumcenter right?
intersection of perpendicular bisectors
scarlet patio
you know how to calculate the circumcenter right?
yeah
I understand now, thanks for helping
final drift
np
scarlet patio
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stone thorn
?
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foggy otter
I'm taking AP Calc and rn we are learning about antiderivaties/indefinite integrals
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I'm taking AP Calc and rn we are learning about antiderivaties/indefinite integr...
foggy otter
I'm confused on how to rewrite the equation for numbers 11 and 12
visual hazel
I'm confused on how to rewrite the equation for numbers 11 and 12
whats the exponent for square roots
foggy otter
The exponent for square roots are 1/2 or -1/2 if it's in a fraction
visual hazel
good
now you shouldn't have any problems with 12
11 you'll need to split the fractions
foggy otter
So I would rewrite the numerator and denominator?
visual hazel
just rewrite the denominator into its exponent form
and then split the fractions then simplify exponents
(a+b)/c = a/c + b/c
foggy otter
So it would look like this?
foggy otter
Oke so simplify the fractions first and then integrate them?
visual hazel
yes
foggy otter
Oke
And when ur dividing exponents with the same bas u subtract the exponent right or no?
visual hazel
yes
foggy otter
Oke just making sure
Thank u for the help!
Wait I do have one more question tho
Do the parenthesis on number 12 change anything when trying to integrate or is it just there?
visual hazel
nope
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nova basin
How would I make it so the blue plane is a circle that is on the sphere instead of a plane
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How would I make it so the blue plane is a circle that is on the sphere instead ...
acoustic leaf
add the sphere equation as a restriction to the plane equation using {}
acoustic leaf
no you have to use {}, not []
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crimson niche
dy/dx = 1.5 + 3xy + 4y. I'm a bit rusty with derivatives, but would the second derivative of it be 3(y+(dy/dx)x)+4(dy/dx))
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dy/dx = 1.5 + 3xy + 4y. I'm a bit rusty with derivatives, but would the second d...
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restive river
need help with this last part on statistics homework
devout snowBOT
need help with this last part on statistics homework
restive river
this is what they say in an example problems answer
do you just plug in 42 in x and solve for y or
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restive river
bro came in here just to ping that, actually useless
supple knot
bro came in here just to ping that, actually useless
Follow the rules and people won't do it
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stable nacelle
Hello, would anybody be so kind to help me extract a mathematical formula akin to what this calculator utilizes?
https://www.yugioh.party/
d = Deck size
h = Hand size
a = Amount
m = Minimum
M = Maximum
(Assuming M is always equal to a)
I just know how to calculate the probability if m = M or m = 1 using binomial coefficients
devout snowBOT
Hello, would anybody be so kind to help me extract a mathematical formula akin t...
stable nacelle
I'm essentially trying to find ? and if there's a simple formula that describes all three
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viral sandal
Hypergeometric distribution?
stable nacelle
Hypergeometric distribution?
That is what I used yes
I forgot *100 on the top formula
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uneven kestrel
stable nacelle
<@&286206848099549185>
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alpine python
well, i guess you can express it as a sum
$\sum_{i=m}^{a}\frac{\binom{a}{i}\binom{d-a}{h-i}}{\binom{d}{h}}=
\frac{\sum_{i=m}^{a}\binom{a}{i}\binom{d-a}{h-i}}{\binom{d}{h}}$
woven radishBOT
Axe
alpine python
Using Vandermonde's identity, i think this can be transformed into:
$\1-\frac{\sum_{i=0}^{m-1}\binom{a}{i}\binom{d-a}{h-i}}{\binom{d}{h}}$
woven radishBOT
Axe
alpine python
i'm a little unsure since i had to assume "a choose k for k>a is 0"
but anyway this is now in terms of the CDF of the hypergeometric distribution, which i don't think has a closed form
it does simplify when m=1 to the expression you found earlier
and the other sum i wrote, before using vandermonde's identity, simplifies when m=a to the other expression you found
stable nacelle
Thank you
So you believe there's no closed form to describe the third formula @alpine python?
alpine python
yeah i mean wikipedia states the CDF in terms of the "generalized hypergeometric function" which i don't think is an elementary function https://en.wikipedia.org/wiki/Hypergeometric_distribution
stable nacelle
yeah i mean wikipedia states the CDF in terms of the "generalized hypergeometric...
I understand, thanks once again for your time
alpine python
um
let me explain
if there was a closed form for the third formula, call it function f
then 1-CDF/(d choose h) = f
and so
CDF = (1-f) * (d choose h)
and we've found a closed form for CDF, which is something no-one else seems to have been able to do, or at least they haven't put it on wikipedia
so it's unlikely that i can find a closed form for f
stable nacelle
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spring oasis
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spring oasis
Find $k \in \mathbb{R}, k \neq 0$, such that $P$ has a multiple root. Then, for the value of $k$ found, determine all roots of $P$ and their multiplicities.
[
P = 12x^4 - 64x^3 + 96x^2 + k
]
woven radishBOT
938c2cc0dcc05f2b68c4287040cfcf71
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spring oasis
how would u do it
spring oasis
Raphael
spring oasis
first i factored out (x-r)^2 from P
r?
alpine python
consider the case when P has a root r of degree 2
then (x-r)^2 will factor out of P cleanly
spring oasis
okay so?
alpine python
expand: x^2-2rx+r^2
spring oasis
ok let's do it
alpine python
that's why it's tedious...
spring oasis
its doable, is okay
bleak tide
**938c2cc0dcc05f2b68c4287040cfcf71**
there is a quick way to do this with calculus
alpine python
$P(x)=(x^2-2rx+r^2)(12x^2+(24r-64)x+(48r^2-128r+84))$
woven radishBOT
Axe
alpine python
there is a quick way to do this with calculus
yes please
bleak tide
You know that if there is a multiple root of any polynomial q at some x, that the derivative of q at x is 0
In this case, you need to pick k so there is a point x such that P(x) = 0 and P'(x) = 0
you can see that's equivalent right?
bleak tide
So conveniently, solving P'(x) = 0 doesn't depend on k at all, because it's a constant
so find an x that satisfies that, then pick k such that the other condition is satisfied
alpine python
it will end up quadratic, that's good
the derivative
because we can divide out x
spring oasis
In this case, you need to pick k so there is a point x such that P(x) = 0 and P'...
?
doing P'(x)=0 why does it imply same x will make P(x)=0
spring oasis
lets go step by step
alpine python
you're looking for a multiple root x
because it's a root P(x)=0
because it's multiple, P'(x)=0
spring oasis
,, P' = 48x^3 -192x^2+192x \ P' = x(48x^2-192x+192)
alpine python
looks good
spring oasis
you're looking for a multiple root x
because it's a root P(x)=0
because it's mul...
hmm
woven radishBOT
938c2cc0dcc05f2b68c4287040cfcf71
spring oasis
,w 48x^2 -192x +192 = 0
woven radishBOT
alpine python
the problem statement says the multiple root is not at 0
wait..
i'm wrong
sorry
it says k is not 0
that's different
bleak tide
Well so you know now that if P has a root at 2, it will have a multiple root at 2.
spring oasis
wdym?
spring oasis
Well so you know now that if P has a root at 2, it will have a *multiple* root a...
ok so?
bleak tide
Well, now you need to make P have a root at 2
spring oasis
problem is i don't get why the multiple root at 2
spring oasis
like I agree but idk
spring oasis
what is your definition of a multiple root
P' has a root at 2
what does that have to do with P?
spring oasis
what is your definition of a multiple root
two repeated roots for example x = 2 twice is factored as (x-2)^2
bleak tide
right
spring oasis
bleak tide
I mean yeah, that's a correct definition
for a polynomial q, you can say it has a multiple root at a iff it factors as q(x) = (x - a)^n * something
where n >= 2
spring oasis
yeah
I mean I agree with differentiating the polynomial
but that only works because we know has a repeated root right
alpine python
for a polynomial q, you can say it has a multiple root at a iff it factors as q(...
now i see why the derivative must be 0
bleak tide
yeah you use the product rule, and (x - a)^{n-1} ends up as a factor of q'
bleak tide
but that only works because we know has a repeated root right
Well if it doesn't
you have a factorization as (x-a)*something
where the something is nonzero at a
a single root
spring oasis
yeah
bleak tide
take the derivative of this, use product rule, and you get the derivative is nonzero at a
alpine python
but that only works because we know has a repeated root right
what is it you're worried about?
spring oasis
we know P has a root at x = 2
alpine python
do we?
bleak tide
We don't actually know where any of P s roots are
we get to pick that
by picking k
I argued above that we want P to have a root at 2
alpine python
oh... we know P has a multiple root, and the only place this root can be is at x=2
so yes P does have a root at 2
sorry took me a second to catch up
alpine python
I argued above that we *want* P to have a root at 2
or i guess this is more correct
spring oasis
we need a root at x = 2 because at x = 0, k is zero
idk if we want P to have a root at 2, is like the only choice
spring oasis
take the derivative of this, use product rule, and you get the derivative is non...
I didnt understood
,calc 12(2)^4 -64(2)^3+96(2)^2
woven radishBOT
Result:
64
k = -64
spring oasis
,w expand (x-2)^2
woven radishBOT
spring oasis
$\polylongdiv{12x^4-64x^3+96x^2-64}{x^2-4x+4}$
woven radishBOT
938c2cc0dcc05f2b68c4287040cfcf71
woven radishBOT
spring oasis
x=2 is triple root
alpine python
yeah
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stark shale
hey, in this exercise, i understand z=0, but i don't get why they set it only on one part of the formula
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hey, in this exercise, i understand z=0, but i don't get why they set it only on...
stark shale
i get that dz part is discarded in the final answer because we're looking only for dw/dx and that part doesnt contribute to it. But they drag it along anyway without substituting z=0
I also think there is a mistake, there should be a negative when they solve for dy
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compact parrot
\begin{align*}
\frac{dw}{dx} &= \frac{\partial w}{\partial x} + \frac{\partial w}{\partial y} \frac{dy}{dx} + \frac{\partial w}{\partial z} \frac{dz}{dx} \
&= \frac{\partial w}{\partial x} + \frac{\partial w}{\partial y} \left( -\frac{2xy + y^2}{x^2 + 2xy} \right) \
&= \frac{\partial w}{\partial x} - \frac{(2xy + y^2)}{x^2 + 2xy} \frac{\partial w}{\partial y}
\end{align*}
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stark shale
reopen
tall stirrup
What is w, post the full problem
stark shale
stark shale
What is w, post the full problem
this is w
for the constraint function if i use chain rule i get
(x^2 +2xy)dy/dx + 2xy + y^2 = 0
dy/dx = -(2xy + y^2) / (x^2 +2xy)
so
dy= ( -(2xy + y^2) / (x^2 +2xy) )dx
and i see z = 0 in the constraint
devout snowBOT
@stark shale Has your question been resolved?
stark shale
it seems that they likely intended to hold
z constant at 0 temporarily but did not propagate that simplification fully to the other terms.
devout snowBOT
@stark shale Has your question been resolved?
devout snowBOT
@stark shale Has your question been resolved?
devout snowBOT
stark shale
.reopen
devout snowBOT
✅
devout snowBOT
@stark shale Has your question been resolved?
devout snowBOT
@stark shale Has your question been resolved?
daring bobcat
given a 4th order polynomial with possibly complex coefficients, $A x^4 + B x^3 + C x^2 + D x + E$, does anyone know some necessary conditions in order for the polynomial to have ALL PURELY imaginary roots?
devout snowBOT
given a 4th order polynomial with possibly complex coefficients, $A x^4 + B x^3 ...
woven radishBOT
Ginger
daring bobcat
(i am considering the requirement $B = D = 0$, but not sure if it applies when $A$, $C$, and $E$ can be complex)
woven radishBOT
Ginger
daring bobcat
i believe the polynomial $(x-i)(x-2i)(x-3i)(x-4i)$ is a counterexample to the claim that $B = D = 0$ is required. is there anything useful we can say at all?
woven radishBOT
Ginger
lusty sapphire
i believe the polynomial $(x-i)(x-2i)(x-3i)(x-4i)$ is a counterexample to the cl...
Keep it general
$(x-\alpha i)(x-\beta i)(x-\gamma i)(x-\delta i)$
woven radishBOT
SWR
arctic field
f(x) has purely imaginary roots iff f(ix) has purely real roots
daring bobcat
Keep it general
(i was trying to specifically show a counterexample with the particular form i chose)
but this is a nice form, makes sense!
daring bobcat
f(x) has purely imaginary roots iff f(ix) has purely real roots
this also makes sense. i'm fine with either approach
lusty sapphire
snow always with the 300 
🇶 plays
arctic field
you then end up with the question of which real polynomials are reducible over R
daring bobcat
Keep it general
ok i get your point. this is just the general form for polynomials with purely imaginary roots, with the greek letters real
lusty sapphire
Yeah. But's Blake's got the better play
daring bobcat
you then end up with the question of which real polynomials are reducible over R
my next move is 1. e5
i'll just say i'm a physics person, not a mathematician, so haven't worked with the idea of (ir)reducible polynomials before
i think i see what you're saying, but i don't know what the requirements are for (any? why only real?) polynomials to be reducible over R
(well i technically do from SWR's answer, but still)
arctic field
a polynomial with only real roots certainly can be represented as a complex multiple of a real polynomial
so it suffices to consider real polynomials only
then one can always factor a quartic real polynomial as the product of two real quadratics
it then remains to impose that both these quadratics have non-negative discriminant
daring bobcat
a polynomial with only real roots certainly can be represented as a complex mult...
(ah true i left off the complex multiple before)
but i don't know how to conclude this without SSR's answer
arctic field
well that is essentially the answer
the coefficients of a polynomial are the elementary symmetric polynomials in the roots
so roots being real implies the coefficients are real modulo a constant factor
daring bobcat
i think i'm getting lost about whether there are 2 separate approaches here
or just basically a single one
arctic field
sometimes in life, you take what you can get rather than trying to put artificial boxes around everything
who cares whether one thing is "an approach"
daring bobcat
i am really trying to get a mental map of all the different parts
and how they connect
i don't have to draw boxes around them
but there are a lot of parts i'm not familiar with
daring bobcat
ok
i have enough to think over myself so i don't have to keep you here
but it seems to me like there is the fact that any polynomial has 4 roots, $\alpha$, $\beta$, $\gamma$, and $\delta$ and thus can always be written as a complex multiple of $(x - \alpha)(x - \beta)(x - \gamma)(x - \delta)$
woven radishBOT
Ginger
daring bobcat
then, when the roots are real, this clearly implies the coefficients are real (up to the complex multiple)
arctic field
without loss, just assume it's monic
daring bobcat
sure
daring bobcat
a polynomial with only real roots certainly can be represented as a complex mult...
if we start from this approach, it seems like we needed to do this (take the above as just an intuitively true fact)
arctic field
what?
arctic field
yes it does
daring bobcat
a polynomial with only real roots certainly can be represented as a complex mult...
is this meant to prove: if real coefficients, then real roots?
daring bobcat
ok
right
but then it does seem we're starting with the knowledge that the polynomial can have all real coefficients
arctic field
i'm not sure what you mean
daring bobcat
**Ginger**
how can we know that without doing something like this?
arctic field
the assumption is that the polynomial has all real roots
daring bobcat
i guess i'm asking about this part:
a polynomial with only real roots certainly can be represented as a complex multiple of a real polynomial
so it suffices to consider real polynomials only
arctic field
yeah, so one starts with a polynomial which is known to have all real roots
and then one concludes that up to a complex multiple, the polynomial is real
daring bobcat
but it seems to me like there is the fact that any polynomial has 4 roots, $\alp...
how can we do that without doing what i said here?
daring bobcat
ok, np, that's what i was asking
ok i think i roughly get it
i might've been misunderstanding that there was some more general condition for whether polynomials are reducible or not that would spit out the answer
arctic field
well perhaps you could use calculus to help
the criterion is not straightforward at a glance
i suppose in this case it really comes down to the quartic formula
daring bobcat
i don't see how to use calculus here, that's interesting
arctic field
there's a good breakdown of what happens on wikipedia
daring bobcat
daring bobcat
it definitely does look interesting, thanks