okay so x^r <= x for all x in [0,1]
#help-23
obtuse jackal
Try to apply it
toxic stratus
solar hazel
HI SNOW
solar hazel
do it again
opaque sorrel
wot
solar hazel
that's my clue 🙂
solar hazel
ummm
obtuse jackal
I said apply, not apply at most once
opaque sorrel
wait this is wrong
solar hazel
that is... not right
opaque sorrel
wait wat am i doing
obtuse jackal
You ended up applying it 0 times
obtuse jackal
Did you ?
To me, it looks like
(1-x)^r = 1 - 2x + x^r
and x^r + x^r = 2x
Are the things you thought
One of which only holds for r = 2 and the other only holds for r = 1
obtuse jackal
So this is messed up
obtuse jackal
That was a good start
opaque sorrel
Hm lemme thonk
safe radishBOT
@opaque sorrel Has your question been resolved?
plucky osprey
safe radishBOT
plucky osprey
i have no idea where to start
devout shale
Do you know how to find the determinant of a 3x3 matrix?
plucky osprey
yes
devout shale
Okay, could you find the determinant of that first matrix then?
leaving it in terms of a, b, c, d, e where necessary
plucky osprey
leaving it in terms of a, b, c, d, e where necessary
(2af+3bd+ce)-(2dc+3ae+fb)
devout shale
Is there more information to go with this question?
Like what is the question asking
to solve for the values of a, b, c, d, e, f ?
plucky osprey
no more info
they just gave the determinant of the first one
and asked for the determinant of the second
devout shale
try doing the same thing for the second equation then
and seeing if something shakes out
plucky osprey
and seeing if something shakes out
i think it becomes the same
it cancels out
so i think answer is -1
.close
woeful sinew
Where did (2n)(2n-1) in the denominator come from? I understand the purpose is to cancel out the numerator but how was it obtained?
safe radishBOT
Where did (2n)(2n-1) in the denominator come from? I understand the purpose is t...
lean otter
safe radishBOT
lean otter
I'm so confused
wher I went wrong
IThe first number must be 5,6,7,9
so 4 possibilities
4 * 6 * 5 * 4 * 3
is what I got I got
Why did I go wrong
brave wolf
it should be even
lean otter
safe radishBOT
lean otter
i need help solving x
grim plover
!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
lean otter
i need help solving x
been a while since I did similarity
I think Y is 36
X is 7
how ?
lean otter
have u heard of it?
no
lean otter
bpt? whats that
grim plover
bpt? whats that
basic proporationality theorem
lean otter
basic proporationality theorem
not even that
grim plover
i see
grim plover
well u have AB || DE
lean otter
you know vsf and asf and lsf thingy
lean otter
well u have AB || DE
yup
grim plover
but what i am doing is supposely called "similarity" by my tr
yeah, BPT is basically how you prove those 2 triangles, similar
lean otter
yeah, BPT is basically how you prove those 2 triangles, similar
oh
to solve this first i divided the triangle into 2
the small one and big one
grim plover
yup
from this, can u find the equal angles? if you consider AD a transversal intersecting AB and DE
lean otter
bpt? whats that
y = 45, X = 7 I believe, might be wrong
method:
imagine a letter labelled to the top point of the triangle, label it V
DV = 25, AV = 5
therefore for each length of the triangle abv, it is 5 times smaller than a length on DVE, use that solve y and x
lean otter
from this, can u find the equal angles? if you consider AD a transversal interse...
it isnt cutting any lines
lean otter
y = 45, X = 7 I believe, might be wrong
method:
imagine a letter labelled to the...
what was your lsf
lean otter
what was your lsf
what is lsf?
grim plover
it isnt cutting any lines
well its touching, no? since its touching that is sharing a point, it counts as intersecting
lean otter
what is lsf?
linear scale factor
lean otter
well its touching, no? since its touching that is sharing a point, it counts as ...
i am not sure about it
what is see is two triangles
lean otter
the scale factor is 5:1
so y woule be 45 here?
lean otter
so y woule be 45 here?
yes
lean otter
i still dont get you how we got x
how did you get y?
lean otter
how did you get y?
the cale factor is 5
so in that case
9 x 5
ok well put that into an equation
create an equation and solve it step by step
this will give you the hint for solving for x
lean otter
ok well put that into an equation
equation?
topaz tree
OAB and ODE are similar triangles
lean otter
what is the equation
topaz tree
so,
5/25=9/y
lean otter
y = 45, X = 7 I believe, might be wrong
method:
imagine a letter labelled to the...
now i got why you keeping v at top
lean otter
equation?
Do you not agree that the equation for y is smaller side * scale factor (5) = y
lean otter
what is the equation
y = 9x5
lean otter
yeah
now create an equation for x with same variables
larger side = smaller side * scale factor
what is the larger side?
topaz tree
5/20=x/28
lean otter
now create an equation for x with same variables
the x and 28
lean otter
and what is the smaller side and scale factor?
umm the x and 5
lean otter
umm the x and 5
ok now substitute all this in the equation
larger side = smaller side * scale factor
x+28 = 5x5
no
x + 28 = 5 * X
the smaller side is x not 5
oh yeah we have an x
ok now solve
28 + x = 5 x X
x+28 = 5x
good
grim plover
y = 45, X = 7 I believe, might be wrong
method:
imagine a letter labelled to the...
ur right about X 🙂
lean otter
4x = 28
lean otter
ur right about X 🙂
what was the theorem again you said
grim plover
what was the theorem again you said
Thales Theorem
it says 5/20 = x/28 (in THIS CASE, as u havent given the one of the bigger triangles vertex a name, its difficult to state)
lean otter
Thales Theorem
will search on it
grim plover
y = 36..wait thats wrong
lean otter
i belive
lean otter
y = 36..wait thats wrong
y = 45
grim plover
yeah
lost cove
lean otter
https://www.youtube.com/watch?v=YiFwvAFk-xs
thanks too
i close the channel ?
.close
topaz tree
yeah, u cant solve for y by using Thales Theorem
u can, 5/(20+5)=9/y
safe radishBOT
u can, 5/(20+5)=9/y
grim plover
u can, 5/(20+5)=9/y
why+5?
lean otter
the chaneel reopend?
safe radishBOT
wintry pelican
One day at flight school there was a man who wanted to sit on a jet plane named O S N A I R L I N E S and when he saw the word he was confused by the seat number 1895. If the word O S N A I R L I N E S is rewritten as much as possible then the letter 1895 is??
safe radishBOT
One day at flight school there was a man who wanted to sit on a jet plane named ...
wintry pelican
Oke
brave wolf
Wait is the word "O S N A I R L I N E S" (21 letters) or "OSNAIRLINES" (11 letters)?
quasi bison
One day at flight school there was a man who wanted to sit on a jet plane named ...
is that EXACTLY how the problem was worded to you?
or did you translate?
buoyant shadow
it's the same letter if it's 21
wintry pelican
buoyant shadow
2.7 is closer to 3 than 2
wintry pelican
Wait is the word "O S N A I R L I N E S" (21 letters) or "OSNAIRLINES" (11 lette...
11,the space isn't count
buoyant shadow
you can't be certain like this
wintry pelican
or did you translate?
Idk,last night my teacher said like that
brave wolf
it's the same letter if it's 21
really?
brave wolf
I did it with python now and im getting different results, am I missinterpreting the problem? ("OSNAIRLINES"*1000)[1896]
wintry pelican
Hmmmm
buoyant shadow
[1894]
brave wolf
oh im idiot
brave wolf
You need to know the remainder after division by 11. As an example take 25th letter.
OSNAIRLINES - 11
OSNAIRLINES - 22
OSN, 25th letter is therefore N.
Notice that I wrote OSNAIRLINES twice, 2 is also the integer part of 25/11. Then there were 3 additional letters left (OSN). 3 is remainder after dividing 25 by 11. And the 25th letter is actually remainder after dividing 25 by 11 - th letter
.
So to find 1895th letter, you just need to find remainder of 1895/11
You found out that the decimal part is approximately 0.27, when you multiply that by 11 you will get the remainder
safe radishBOT
@wintry pelican Has your question been resolved?
flat frigateBOT
Pro_Hecker
topaz tree
so letter is N
scenic valley
Can someone calcúlate this for me? Cause it’s confusing.
On Tuesday, 11AM, after 3 days, what day and clock will it be after it passes 3 days from Tuesday?
obtuse plover
Try taking it 1 day at a time
What would be 1 day after Tuesday 11 am
And then do that another 2 times
safe radishBOT
@scenic valley Has your question been resolved?
scenic valley
What would be 1 day after Tuesday 11 am
1 day - Wednesday 11am
2 day - Thursday 11am
3 day - Friday 11am??
obtuse plover
Yea
safe radishBOT
@scenic valley Has your question been resolved?
raw scroll
.close
agile plank
Can someone please explain how they did this:
safe radishBOT
Can someone please explain how they did this:
agile plank
Here's the original problem (#31), use ratio test to determine whether the series converges or diverges
,w rotate
My work so far
(Ignore the 5 at the bottom)
<@&286206848099549185>
green bane
flat frigateBOT
thin bridge
they divided numerator and denominator by 2^n
agile plank
Oh okay
Hm
But what does that even do to the problem?
They got 5/2 as the answer
lofty latch
because we know that limit of 1/2^n as n goes to infinity is 0.
lofty latch
But what does that even do to the problem?
lim of 2^n as n goes to infinity isn't really nice is it? 🙂
steep pewter
when taking s definite integral are we assuming a polynomial with 0 constant as the result or I'm stupid?
safe radishBOT
when taking s definite integral are we assuming a polynomial with 0 constant as ...
unreal canyon
If I understand your question, no, you don't assume anything as the result. You define the definite integral then solve it for a result. If the function you're integrating is known that is. I guess you can also work you way backwards to an unknown function from a result
steep pewter
when we do an integral, we assume the original polynomial had a constant c; does that assumption get discarded when looking for definite integral?
unreal canyon
We don't include the constant c when calculating definite integrals.
Correct
For example
flat frigateBOT
Joachim
steep pewter
ok this is (e^x)-1
it has a constant term = -1
when this changes a rectangular area gets added or removed; im guessing summation of this constant term*dx is what we are assuming as c but doesnt that C itself change with teh value of x?
that would cause two of these C's to have different values but in class we are just blindly labeling them as C and canceling them out
unreal canyon
You add the constant term C when integrating or antiderivating to compensate for derivation deleting constant terms.
When doing definite integrals we discard the unknown added constant term C.
For your example $$e^x -1$$ the antiderivative is $$e^x -x + C$$ into which we can insert the lower and upper bounds of the integral as x and calculate the value.
The rectangular area you're describing im assuming is a visualization of sorts of the area under the curve and is a result of the constant term getting elevated to a first order variable, meaning it now affects the functions value proportionally with the change in x, instead of it's old constant value.
flat frigateBOT
Joachim
unreal canyon
I'm struggling a bit to understand clearly what your question is though. Do you have a specific problem you could send a picture of?
steep pewter
dont really have a question trying to believe what my matsh teacher told me
so "definite integrals we discard the unknown" means I actually am taking the area under the curve for the case the antiderivative did in fact have a constant term 0?
unreal canyon
The reason for not including it in most calculations is that it cancels out.
For the function
$$f(x) = e^x -1$$
We antiderivate and get
$$F(x) = e^x - x + C$$
So if we have the problem:
$$\int_{0}^{2} e^x -1 dx$$
We calculate the function values of the antiderivatives at the upper and lower bounds:
$$F(2) == e^2 - 2 + C = 5.389 + C$$
and
$$F(0) == e^0 - 0 + C = 1 + C$$
Which gives us
$$F(2) - F(0) = (5.389 + C) - (1+C) = 5.389 + C - 1 - C = 4.389$$
flat frigateBOT
Joachim
unreal canyon
The resulting value is the area under the curve for the given interval [0, 2]
Increasing the constant term would shift the whole graph upwards and would increase the area by (x_upper - x_lower) * C
unreal canyon
Again, struggling a bit to understand what you mean by that, but the constant term of the antiderivative of the function does cancel out, the constant terms in the original function become first order terms. The -1 from the original function became an X, whilst the + C was cancelled out
steep pewter
do u know any resource that proves ur claim
i just cant seem to get why the "deleted" part would equate on x=a and x=b
safe radishBOT
@steep pewter Has your question been resolved?
unreal canyon
You agree that calculating a definite integral works like this:
For a function $f(x)$, the antiderivative of that function is $F(x)$
When calculating the antiderivative of a function we add a term $C$ to compensate for the deletion of constant terms by derivation.
So if we want to solve the integral:
$$\int_{a}^{b} f(x) dx$$
We calculate the antiderivative of $f$ which is $F(x)$, a function with the added constant term C.
We then calculate the function value of $F$ at our upper bound $b$ and lower bound $a$:
$$F(a) = something + C$$
$$F(b) = something + C$$
We then subtract the function value at the lower bound from the function value at the higher bound:
$$F(b) - F(a) = some value$$
When we perform this last calculation, we distribute the minus symbol over the terms of F(a), which is some value, and the constant C.
Meaning the first term includes +C, and the second term includes -C. Any value added to the negative version of itself becomes 0, meaning they cancel out.
Using the example function from earlier:
For the function $$f(x) = e^x - 1$$
The integral:
$$\int_{0}^{2} e^x - 1 dx$$
Has us first calculate the antiderivative F:
$$F(x) = e^x -x + C$$
We then calculate the function values:
$$F(2) = e^2 - 2 + C == 5.389 + C$$
$$F(0) = e^0 - 0 + C = 1 + C$$
We then subtract the function value at the lower bound from the value at the upper bound:
$$F(2) - F(0)$$
A calculation that looks like this:
$$(5,389 + C) - (1 + C)$$
Following PEMDAS we want to get rid of the parenthesis, for the first parenthesis we don't have to do anything and just remove it.
$$5.389 + C - (1 + C)$$
For the second one we have to distribute the minus symbol across the values inside, which changes the + infront of the last C to a - since $+ * - = -$
$$5.389 + C -1 -C$$
We are now left with two numbers and two constant terms with opposite signs:
$$5.389 -1 + C -C$$
The numbers we can just subtract and the constants become 0, which is what we mean by cancelling out
flat frigateBOT
Joachim
steep pewter
what im trying to understand is why and how are these two "C"s have the same value
unreal canyon
They don't actually have specific any value, the variable C represents an unknown constant. They could have any value, the important part is the since they both use the same symbol C, they both have to have the same value
steep pewter
is that no the same as saying the rectangle from 0 to 1 has teh same area as the rectangle from 0 to2
unreal canyon
The x values 0, 1 and 2 have nothing to do with the constant C. Constant terms are not affected by change in the input variable X.
For a linear function $ax + b$ the $a$ tells us the gradient of the line, with the $b$ telling us where the line crosses the y-axis.
The constant term C in any definite integral can be viewed the same way as the $b$ in that example. Calculating the function value for a higher value of X does not change where the line crosses the y-axis.
flat frigateBOT
Joachim
unreal canyon
The area you are calculating it the full area under the curve, for the bounds a = 0 and b = 2 that is the full yellow area, whilst for an upper bound b = 1 it's only the green area
odd crest
what im trying to understand is why and how are these two "C"s have the same val...
Because you defined the the anti derivative as that.
Consider:
f(x)= x+k
Notice how f(1)-f(2) gets rid of the constant
steep pewter
bruh
the antiderivative gives the area
in it C is the constant term unaffected by x even tho the area the curve is affected by the variable x as clearly observed the F(x) part handles that
Thanks a ton! @odd crest @unreal canyon
.close
odd hinge
safe radishBOT
odd hinge
b) log base 5 of 9 - log base 5 of 125 = 3t -3
faint seal
why 3t
odd hinge
because logbase 5 of 3 times 3 is log base 5 of 9
flat frigateBOT
kheerii
odd hinge
i though because 3 x 3 = 9 it would apply in logs too
steep pewter
u know the answer?
odd hinge
no
steep pewter
if its 2t-3 then i might be able to help
faint seal
it is
odd hinge
but log base 5 of 125 is 3?
faint seal
yes
odd hinge
so the problem is log base 5 of 9
faint seal
correct
faint seal
**kheerii**
use this
flat frigateBOT
kheerii
odd hinge
is it two because there's 2 threes to get to nine
odd hinge
for the second question i watched a tutorial where he made eerything fraction and then used natural log
would that be the right way to solve it or is there another technique
im stuck on the different bases
faint seal
use the base change rule
odd hinge
ok i'l try that out
could i change the base to 12 and then cancel the top ones to have log base 12 of 7 equals x
.close
safe radishBOT
safe radishBOT
Available help channel!
karmic walrus
Is there a way to do this on a ti-84? I tried 2-SampTTest but that is obviously wrong
My textbook and professor are not helpful.
safe radishBOT
Is there a way to do this on a ti-84? I tried 2-SampTTest but that is obviously ...
karmic walrus
.close
safe radishBOT
safe radishBOT
Available help channel!
crystal shale
Is my x + y = 5 line correct?
safe radishBOT
Is my x + y = 5 line correct?
crystal shale
How would you reflect B then? Cause the question said to reflect B into C with line equation x + y = 5
icy lance
your line doesn't pass through (5,0)
safe radishBOT
@crystal shale Has your question been resolved?
crystal shale
your line doesn't pass through (5,0)
Is it supposed to be a vertical line?
Idk anymore aa
<@&286206848099549185>
icy lance
if x+y=5, then when x=0, y=5 and when y=0, x=5, so two points are (0,5) which you have, and (5,0) which you missed
icy lance
what was the question you were given?
crystal shale
did*
What I do
<@&286206848099549185> sorry for the ping, I’m in a tight corner rn, I have to go very soon but I also need to finish this one question rn
Did I draw it wright?
trim swan
from each vertex of triangle B, count the number of squares you need to travel upward to the line. Then, from the line, travel that same number of squares rightward. Plot a point here and it will be a vertex of triangle C
^this works for lines with a slope of 1 or -1
crystal shale
from each vertex of triangle B, count the number of squares you need to travel u...
I did that but Idk if I can wit hthis? Uh like there isn’t nay more numbers after 10
crystal shale
^this works for lines with a slope of 1 or -1
Ah okie
So mine I s wrong
how do I fix it
trim swan
no your line is right
I didn't check all the work you did to get triangle B
But, there are numbers greater than 10. Just because they're not on the graph you drew doesn't mean you can't use them
if your triangle B is correct, then yes you're triangle C is going to be off the grid, you may need to use a smaller scale
because it will have an x-value greater than 10
crystal shale
But, there are numbers greater than 10. Just because they're not on the graph yo...
No there literally isn’t
In the original question paper
I just redrew it
trim swan
Oh, it looks like your points from A were incorrect
crystal shale
cri
trim swan
For example you graphed (9, -2) instead of (-2, 9)
and likewise with the other vertices of A
crystal shale
So it’s is what I have now
safe radishBOT
@crystal shale Has your question been resolved?
hoary crane
safe radishBOT
hoary crane
so limit x going to zero for sin(x) * x^x
so this is a question that I made up, I think it's in the form of 0^0
so I need to pull the power down
but where exactly do I put it?
is it:
x ln sin(x) * x
or sin(x) x ln x?
quasi bison
neither
if you want to work out the limit of x^x separately then work it out separately.
hoary crane
so what do I do in these kind of question?
so I separate the limits and it becomes 0 * 1?
quasi bison
yeah sure
safe radishBOT
safe radishBOT
Available help channel!
gleaming python
Can someone help me with this? Tomorrow is our deadline and im really drained and out of energy, we had a dance practice from 9am to 6pm, and its currently 9:21pm so if you're not too busy, please help me out.
safe radishBOT
Can someone help me with this? Tomorrow is our deadline and im really drained an...
frank glen
Okay
So you're given $120m to work with for both roads and bridges and other infrastructures
Then the problem tells you that 1/4 of the amount was for bridges, 1/2 of the amount was for roads, and the rest was for other infrastructures.
gleaming python
Yep
frank glen
If I understood the problem correctly, then it is referring to the $120 million
And it wants you to multiply the fraction of what was used of the $120 million and write out the amount for each part
Like bridges is $\frac 14 \times $120\text{m}$
flat frigateBOT
VulcanOne
gleaming python
ohh
frank glen
Same thing for roads and for other infrastructures
gleaming python
okay then what about the number sentence or equation?
gleaming python
?
frank glen
Something like this
"Total money = $120 million = Bridge money + roads money + other infrastructures money
Bridge money = total money divided by 4
Roads money = bridge money multiplied by 2
..."
Something like that
dusty talon
safe radishBOT
dusty talon
quotient rule yes
but im not sure how to differentiate the top
seeing kN together confuses me
Y'(N) means differentiate with respect to N right?
dusty talon
we should be differentiating (kN) right?
i need diff.. of top and bottom to set up quotient
dusty talon
differentiating kN with respect to N is k ?
remind me how to think of with respect to
quasi bison
yes the derivative of kN wrt N is k
dusty talon
and constants
quasi bison
dunno what to tell you
dusty talon
what happens when we multiply (2N) and (kN)
im not sure how to think of them because its 2 things attached
does (2N) multiply with the k and N individually?
alright im not sure why
but
dusty talon
yes the derivative of kN wrt N is k
right?
quasi bison
you realize how weird it sounds to have your "right?" (which has to do with the messages you posted just now) be a reply to an earlier message of mine which has nothing to do with them, right?
also you have some excessive parentheses
you might be throwing yourself off with them
quasi bison
but your parentheses each enclose a single term...
dusty talon
it just helps me visually
quasi bison
anyway, certainly kN^2 - 2kN^2 is equal to -1 kN^2 but then you put a minus sign before that
don't
quasi bison
if you know "it" becomes a plus, then why didn't you make "it" a plus?
anyway, your work appears correct, aside from the excess of parentheses.
dusty talon
so when i look back ill see there was a negative that turned positive
so now i set it equal to 0
but should i expand the denominator (36 + N^2)^2
quasi bison
???
dusty talon
quasi bison
so when i look back ill see there was a negative that turned positive
you'll see incorrect notation and you'll make conclusions from said incorrect notation, which can only be correct by coincidence or by an elaborate network of workarounds.
quasi bison
and now you've made a sign error. and also a typo (lowercase n should be uppercase N)
dusty talon
where is the sign error?
dusty talon
ok so numerator says 36k + kN^2 - 2kN^2. the kN^2 - the 2kN^2 gives me -1kN^2
quasi bison
yes
quasi bison
no
dusty talon
it being a fraction and having things "attached" to the N is making this hard to think about
i cant multiply the denominator and 0
quasi bison
define "can't"?
does God Himself appear before you and bellow "THOU SHALT NOT DO THIS, SMARTY PANTS TWENTY ELEVEN"
dusty talon
idk but it feels like that just "kills" the denominator and isnt right
quasi bison
so you consider it dodgy to go from (36k - kN^2)/(36+N^2)^2 = 0 to 36k - kN^2 = 0?
dusty talon
i guess not if its ok to have that happen
quasi bison
well... anything times zero is zero after all.
quasi bison
you fucked up with writing down Y'(N) so everything went to shit.
an extra N appeared out of nowhere.
slow fern
Watch organic chemistry tutor's videos on derivatives
dusty talon
point out where i messed up
dusty talon
Watch organic chemistry tutor's videos on derivatives
is there a video where the problem is set up exactly like this?
it has to be the exact same or it will be confusing
slow fern
dusty talon
the numerator stays 36k - kN^2 because adding a negative is just subtracting
quasi bison
point out where i messed up
ive been doing that for the last however many minutes
it's just that your fuckups keep on coming in larger and larger amounts and none of them are calculus-y in nature
dusty talon
so how is my derivative bad?
quasi bison
and its kind of exhausting
numerator's wrong, should be 36k - kN^2 instead of the 36kN - kN^2 that it is rn
quasi bison
that is just a silly little mistake
ALL of your mistakes could be described as such
dusty talon
now i put in a number to the left and right of 6 into my original function
im just a little guy, just a little stinker pal
quasi bison
im just a little guy, just a little stinker pal
not sure what reaction that was meant to elicit.
dusty talon
one sec
quasi bison
you should know that when doing math, and in particular algebra, precision is required.
dusty talon
yes
i feel like the 2 answers should look like something else
but i am going in the right direction right?
so the derivative is = to 0 at x= 6
i need to plug in numbers on either side of 6 to find out if its a maximum or minimum
<@&286206848099549185>
hello?
.close
fiery socket
Does predictors in statistics refer to the number of independent variables? So given a quadratic equation f(x) = ax^2 + bx+ c, it will only have one predictor?
safe radishBOT
Does predictors in statistics refer to the number of independent variables? So g...
fiery socket
or 2?
granite idol
that's not a linear equation in the context of regression
assuming x is the unknown
fiery socket
sorry quadratic
fiery socket
that's not a linear equation in the context of regression
yes x is the unkown
granite idol
is there some context you can provide for this question?
fiery socket
I'm just confused whether predictors refer to the number of independent variables (the number of different variables) or the number of coefficients/terms with an independent variable
granite idol
"predictors" are independent variables, yes
and in linear regression that would sometimes include the intercept
fiery socket
Like I found a quadratic regression model
Would this still be one predictor?
Or 2?
granite idol
what is the context for that?
fiery socket
x is the number of orders a restaurant solds and g(x) is the monthly profit
granite idol
well that's not a linear model but I would say 1 predictor
fiery socket
ok so any polynomial regression containing only a "x" variable is 1 predictor?
granite idol
that'd be my guess. I'm more familiar w/ linear regression and the form $Y = X\beta + \epsilon$, where the $\beta$ are the (unknown) parameters
flat frigateBOT
cwatson
fiery socket
so that has 1 predictor
this sounds to be like they treat different coefficient as different predictors
granite idol
ah, then I would say there is 1 independent variable (X) and multiple predictors.
fiery socket
wait sorry so how should I describe predictors?
This is for a school paper I'm writing
I originally defined it as the number of independent variables
granite idol
well it seems like there is one independent variable, whatever "X" represents. but you "create" more predictors by X^2, X^3, etc.
fiery socket
well it seems like there is one independent variable, whatever "X" represents. b...
Can I say the number of terms containing an independent variable?
granite idol
I suppose. I would ask your professor/teacher, without knowing the context I don't know if it matters much TBH
granite idol
why are you defining it to begin with?
fiery socket
Because I'm modeling a function and I'm trying to say that using higher predictors/more coefficient terms result in overfitting the data
granite idol
I would personally say the number of predictors equals the number of parameters (beta values), including the intercept
but since you're making a general statement I don't think it matters so much. it's generally going to be true
safe radishBOT
@fiery socket Has your question been resolved?
fiery socket
I would personally say the number of predictors equals the number of parameters ...
Thank you!
safe radishBOT
safe radishBOT
Available help channel!
vale hollow
Linear algebra question
safe radishBOT
Linear algebra question
vale hollow
If a question says a parallelogram with an area of 3 units squared is mapped to a new parallelogram using a matrix called T.
And says what is the area of the new parallelogram?
What does the word mapped refer to here?
I found the area of the parallelogram using matrix T
Do I now just add 3 to that new area?
near surge
I'd Imagine it's asking you to use the determinant of the transformation to see how much the area of any region of space gets changed (including the parrallelogram). The determinant scales the original area so you'd have to multiply it to 3 units^2.
vale hollow
I'll show u the entire question
This is the entire question
The first part would just be the standard matrix which is [1 1
1 -1
0 2]
The second part will just be multiplying A by the standard matrix above
So now if we have just that matrix
How would the last part be done?
near surge
I'd find the determinant of T_2 and do: |T_2|*3
vale hollow
Yeah ok that makes sense
cuz the determinant will give us the area of that parallelogram
ok cool
thanks bro
near surge
the determinant tells you how much volumes (here areas) change after a linear transformation
vale hollow
yeah
near surge
so if the determinant is, say, 2 that means that the area of the parallelogram has doubled
near surge
no problem!
vale hollow
.close
tender vine
safe radishBOT
grand basin
Do you know any formulas related to triangle sides/angles that can help?
tender vine
Do you know any formulas related to triangle sides/angles that can help?
area
of equalitareal triangle
@grand basin
ugh dang it
tender vine
ummm
grand basin
Do you know law of cosines? Also known as Al-Kashi law
timber latch
You Can construct the center of the square it might give you simple ideas to solve this
safe radishBOT
@tender vine Has your question been resolved?
floral osprey
do you know the height of an equilateral triangle
then you can use 2*that + 2 to find the height of this diamond
and then yeah
safe radishBOT
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Available help channel!
tardy frigate
24 divided by x-3 is a positive integer smaller than 5. How many possible values of x are there?
safe radishBOT
24 divided by x-3 is a positive integer smaller than 5. How many possible values...
river wharf
@tardy frigate your question?
tardy frigate
Yes
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
4
river wharf
you want a direct answer?
tardy frigate
Yes
river wharf
help doesn't work like that here
you don't understand a concept and you can ask to learn it
river wharf
how did you come up with the answer
river wharf
have you tried anything to solve it
do you process the information given so that you have a clue what to start with?
tardy frigate
24 = 1 * 24 = 2 * 12 = 3 * 8 = 4 * 6
Adding 3 to each, we get:
x = 4, 6, 7, 9
So there are four possible values of x that satisfy the equation.
The reason why the answer is between 2 and 5 is because (x-3) cannot be negative, since we cannot divide by negative numbers. Therefore, the smallest possible value of x is 3+1=4. Also, since we are looking for a positive integer smaller than 5, the largest possible value of x is 3+5=8. So the possible values of x are limited to the interval [4, 8], which contains four integers: 4, 5, 6, and 7.
x such that 24/(x-3) is a positive integer smaller than 5. Let's call this integer n, so we have:
0 < n < 5
and
24/(x-3) = n
Multiplying both sides by x-3, we get:
24 = n(x-3)
Dividing both sides by n, we get:
x-3 = 24/n
Adding 3 to both sides, we get:
x = 24/n + 3
We need to find the values of n such that x is a positive integer. For x to be a positive integer, 24/n + 3 must be an integer, which means that 24/n must be an integer that is greater than or equal to 2 (since we want x to be greater than 3). Therefore, n can only be one of the divisors of 24 that are greater than or equal to 2. These divisors are 2, 3, 4, 6, 8, 12, and 24.
For each of these divisors of 24, we can calculate the corresponding value of x using the equation x = 24/n + 3. We get:
n = 2: x = 15
n = 3: x = 11
n = 4: x = 9
n = 6: x = 7
n = 8: x = 6
n = 12: x = 5
n = 24: x = 4
Therefore, there are 7 possible values of x: 4, 5, 6, 7, 9, 11, and 15.
I don't know.
tardy frigate
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
All
serene ledge
holyy u type fast mister chatgpt
tardy frigate
Do you have problem with your brain?
river wharf
holyy u type fast mister chatgpt
ye chatgpters have grown big lately
bro said "we" and "let's" as if he is teaching us
topaz palm
@tardy frigate you can also start by guessing... so the answer has to equal less than 5. So try 24 ÷ 2 suppose.... that gives you 12.... that's greater than 5. let's try 24 ÷ 3... that gives you 8, still not less than 5 but getting closer.... so as you divide by a greater number, the answer gets smaller. Let's divide by 4... 24 ÷ 4 is 6 still not yet. 24 ÷ 5 doesn't give you an integer. 24 ÷ 6 gives you 4 which is lower than 5. That's one value which gives you lower than 5..... 24 ÷ 8 gives you 3... that's second value which gives lower than 5.... 24 ÷ 12 gives you 2, another value less than 5..... finally 24 ÷ 24 gives you 1, which is the final integer which gives you less than 5. So in total that's 4 values.
river wharf
tl it's much simpler, dont do math with chatgpt cause it sucks at it
tardy frigate
It's not that simple. I think.
topaz palm
It's not that simple. I think.
read the explanation I wrote above... the answer is 4.
tardy frigate
How to solve it using system of equations or calculus?
tardy frigate
I graphed it in desmos. Still no help.
topaz palm
theoretically x can be infinite number of values but it is asking for the values which give an integer value out
tardy frigate
Who's gonna use floor function for integer.
24/(x-3)<5, 24/(x-3)∈Z+
How to solve an system of equations like this?
topaz palm
wait are you asking how to solve it?
tardy frigate
∈ means belongs to
topaz palm
oh wait I figured how to do it by equations. So the equation to use it is: 0 < 24 ÷ (x-3) < 5 because the equation has to be positive so greater than 0 and less than 5
And here's how to solve: 0 < 24 ÷ (x-3) < 5
lean otter
So I've done task 1 and 2. Task 2 n+1 = 4 and r[n+1] = r[4] = 0 and r[n] = r[3] = 2. What is Task 3 asking me to do? Do i take the final loops values of r[n] and r[n+1] or what?
safe radishBOT
So I've done task 1 and 2. Task 2 n+1 = 4 and r[n+1] = r[4] = 0 and r[n] = r[3] ...
@lean otter Has your question been resolved?
queen violet
So I've done task 1 and 2. Task 2 n+1 = 4 and r[n+1] = r[4] = 0 and r[n] = r[3] ...
it's asking you to actually 'do' the euclidean algorithm
lean otter
So from the very beginning? I was confused cause I basically did it in Task 2
safe radishBOT
queen violet
ask your professor or something if you arent sure
lean otter
he doesn't respond on weekend 🙃 but i think your right anyway
safe radishBOT
Available help channel!
plush zodiac
Hello
plush zodiac
$\int{\dfrac{\sin\left(\sqrt{x}\right)}{\sqrt{x}}}$
flat frigateBOT
noel
flat frigateBOT
noel
sonic geyser
That's correct
flat frigateBOT
noel
plush zodiac
@sonic geyser Is it okay to not replace the bottom root(x) ?
plush zodiac
Because if it's u = root(x), shouldnt it then be sin(u) / u
plush zodiac
But then it would not cancel
Oh okay
so I can choose what to replace and what to not
sonic geyser
Or sin(√x)/u
sonic geyser
so I can choose what to replace and what to not
Yes
plush zodiac
Alright, well, thanks
sonic geyser
👍
safe radishBOT
safe radishBOT
Available help channel!
cyan acorn
Let A and B be positive definite matrices, and let Q be a unitary matrix. Prove that if A = BQ then A = B.
I'm pretty sure I should use the facts that the magnitude of the eigenvalues of Q is 1 and that the eigenvalues of A and B are positive. I can easily prove that the determinants of A and B are equal and the determinant of Q is 1 but I can't see how that helps me.
safe radishBOT
Let A and B be positive definite matrices, and let Q be a unitary matrix. Prove ...
@cyan acorn Has your question been resolved?
safe radishBOT
@cyan acorn Has your question been resolved?
cyan acorn
<@&286206848099549185>
safe radishBOT
Available help channel!
wooden oyster
safe radishBOT
wooden oyster
I dont understand how i've gone from 1st to the 2nd
I get the 2=root of 4, but how does the -1+ +/- come into play
brave wolf
In the first part, there should be +/- too
fluid token
root gives you a positive and a negative
wooden oyster
i dont know the rule for that is all
fluid token
-2^2 = ?
wooden oyster
what
wooden oyster
i am saying how does the -1 appear
brave wolf
the -1 is -2/2
fluid token
the -1 is -2/2
i think they just isolated -1, as it’s the same as (-1)/(1)
brave wolf
2=root(4)
wooden oyster
in my mind is just says -2+ root of 12 divided by root of 4
after this is somehow gets turned into -1
which i dont doubt is correct, but how
to put it a bit prettier:
pliant pendant
They used the fact that
$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$
flat frigateBOT
jafar/جعفر
pliant pendant
So:
$\frac{-2+√12}{2} = \frac{-2}{2} + \frac{√12}{2}$
flat frigateBOT
jafar/جعفر
pliant pendant
- should be ± but idk how to latex that but anyway you get the idea
pliant pendant
yup
lean otter
safe radishBOT
https://cdn.discordapp.com/attachments/1094687801154486393/1094691547217416403/I...
drowsy moss
flat frigateBOT
late crescent
Hello i need help understanding this solution for Sequences (About it being strictly monotonic decreasing.
Now this is in German but it roughly translates to this:
- Show that a_n > 1/5 for all n ∈ N
- Show that the Sequence (a_n)_n is strictly monotonic decreasing.
Number 3 is not important for now.
The part where it says Lösung in Bold is the Answer.
At 1. they simply showed via full induction that a_n > 1/5 for all n ∈ N and i understood that part.
But when it comes to 2. i get a little confused.
It says we should do a_n+1 - a_n which is to see if it is strictly monotonic decreasing.
safe radishBOT
Hello i need help understanding this solution for Sequences (About it being stri...
late crescent
i dont understand this part on the right
how do they get to 3-15a_n from 3 + 5 a_n?
brave edge
$-a_n = \frac{-20a_n}{20}$
flat frigateBOT
Epsilia aka Mellow
brave edge
And $5-20 = -15$
flat frigateBOT
Epsilia aka Mellow
late crescent
is it really that simple?
fluid token
yes
brave edge
Yeah just making it in the same denominator in order to get it into a single fraction
Because it's easier to compare a quotient with 0
Than two real terms added together
late crescent
okay and because it is < 0 that means its strictly monotonic decreasing?
brave edge
They wrote a "1." above the < sign
Which means they've used the result of the 1st question
Do you see how they could have used that info ?
late crescent
is it because a_n is always < 1/5
brave edge
Yup
late crescent
oh yea my bad
brave edge
Here's how you use it, but if you don't want the solution and search it out by yourself, you don't have to click on it
safe radishBOT
Available help channel!
tardy frigate
Solve for any value of x:
\frac{-x}{-x}=-1
safe radishBOT
Solve for any value of x:
\frac{-x}{-x}=-1
compact ferry
$\frac{-x}{-x}=-1$
flat frigateBOT
heavy
tardy frigate
Nononono
obtuse jackal
Does not exist
1 is solution in F2
tardy frigate
$\frac{d}{dx} \frac{-x}{-x} = \frac{d}{dx} 1 = 0$
flat frigateBOT
tl
tardy frigate
$\lim_{x\to a} \frac{-x}{-x} = \lim_{x\to a} \frac{x}{x} = 1$
flat frigateBOT
tl
tardy frigate
I think 0 is a solution.
misty coral
I think 0 is a solution.
inner tapir
I think 0 is a solution.
an extraneous one 🙂
tardy frigate
\begin{align*}
\lim_{x\to0}\frac{-x}{-x} &= \lim_{x\to0}\frac{\lim_{x\to0}-x}{\lim_{x\to0}-x}
&= \frac{\lim_{x\to0}-x}{\lim_{x\to0}-x}
&= \frac{0}{0} \quad \text{(by direct substitution)}
\end{align*}
flat frigateBOT
tl
tardy frigate
\begin{align*}
\lim_{x\to0}\frac{-x}{-x} &= \lim_{x\to0}\frac{\cancel{-x}}{\cancelto{-1}{-x}}
&= \lim_{x\to0}\frac{1}{1}
&= 1
\end{align*}
flat frigateBOT
tl
misty coral
tardy frigate
\begin{align*}
\lim_{x\to0}\frac{-x}{-x} &= \lim_{x\to0}-1
1 &= -1
\end{align*}
flat frigateBOT
tl
inner tapir
also not sure if limits are necessary here?
-x / -x = -1
-x = x
only 0 solves that and it's extraneous
tardy frigate
$\frac{-x}{-x} = \frac{1}{\frac{-x}{-x}}$
$\frac{1}{\frac{-x}{-x}} = \frac{1}{1 + \sum_{n=1}^\infty\frac{1}{(-x)^n}}$
$\frac{1}{1 + \sum_{n=1}^\infty\frac{1}{(-x)^n}} = \frac{1}{1 + \frac{1}{-x} + \frac{1}{(-x)^2} + \frac{1}{(-x)^3} + \cdots}$
$\frac{1}{1 + \frac{1}{-x} + \frac{1}{(-x)^2} + \frac{1}{(-x)^3} + \cdots} = \frac{-x}{-x + 1}$
$\frac{-x}{-x} = \frac{1}{\frac{-x}{-x}} = \frac{1}{\frac{-x}{-x + 1}} = \frac{-x + 1}{-x}$
$-1 = \frac{-x + 1}{-x}$
$x = x - 1$
flat frigateBOT
tl
inner tapir
lol
tardy frigate
not a true statement for any value of x, including 0.
Let's make a imaginary number which gives -1 if divided by itself.
.close
safe radishBOT
safe radishBOT
Available help channel!
deep arch
@whole acorn @meager igloo , Can someone please help me with this. Thank You
safe radishBOT
<@483962566977126401> <@823462958079803432> , Can someone please help me with th...
@deep arch Has your question been resolved?
woven barn
safe radishBOT
floral osprey
yeah 1 to n + 1 looks right
floral osprey
ohh
floral osprey
make sure the divided by 2 is inside the parens
woven barn
make sure the divided by 2 is inside the parens
im a btu confused tho
so
should it be that
woven barn
or this
woven barn
it’s (x_k+1 + x_k)/2
my teacher wrote x_k-1 + x_k/2
woven barn
it would be a + kdelta + a + (k + 1)delta
yes so that is x_k-1 + x_k
floral osprey
all over 2 ye
woven barn
then why do u keep saying its x_k+1 + x_k
floral osprey
minus?
floral osprey
x_k+1 + x_k
that’s what it is if you start k = 0
woven barn
u said this is correct but then also said x_k-1 + x_k is correct
so this is for k = 1?
floral osprey
mhn
floral osprey
the minus 1 is hidden in the definition of x_i
x_i = a + (i - 1)*delta
which is quite unnatural imo
floral osprey
anyway none of this is helping you fix the issue in this
you need (a + (i - 1)delta + a + (i)delta)/2
woven barn
anyway none of this is helping you fix the issue in this
ok i see so that stupid shit just confused me
floral osprey
apologies
woven barn
woven barn
no don’t cancel out the 5 with the divided by 5
so like this
woven barn
delta x
floral osprey
delta x is inside the function and multiplied by the k values
you already got that
floral osprey
oh yeah dumb me
woven barn
so that is correct?
floral osprey
also why k(k+1)
floral osprey
looks right to me
woven barn
u sure?
floral osprey
this is like (5 + oddnum/10)
which will be 5.1, 5.3, … 14.7, 14.9 which there should be 50 of from 5 to 15
so ye
floral osprey
it’s the same actually
10/2 is 5
and (2k - 1)/2 is (k - 1/2)
they just distributed in the 1/2
floral osprey
floral osprey
you can
woven barn
@floral osprey also the number of rectangles estimating is n right?
floral osprey
yee
safe radishBOT
@woven barn Has your question been resolved?
lean otter
hello
lean otter
im confused
😫
one of that digist in every case to make a real expresion
one in one case
and then other in one case
and like that
i think it dont exist because of the zero
every digit in every case need to be different
<@&286206848099549185>
floral osprey
it exists I just figured it out
lean otter
how