Even then, I still have to get the second condition
#help-36
waxen prawn
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waxen prawn
<@&286206848099549185>
jolly cradle
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jolly cradle
Can I get someone to confirm the answers for these two. If they're wrong please let me know.
jolly cradle
second one is wrong
I thought of it like this: g'(x) has a slope of 0 at points -1 and 3
so g''(x) should pass through those points in its graph
modest birch
indeed it should
jolly cradle
So B, C, and D should eliminated
modest birch
sounds reasonable
jolly cradle
sounds reasonable
I have a question
are the slopes of certain intervals on original functions similar to the ones of the derivative?
like if from [1,3] the slope is > 0
then the slope of the derivative from [1,3] must also be > 0?
modest birch
no
the derivative is the slope of the function
if the slope is steeply upward, the derivative is large and positive
reef canyon
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reef canyon
how do u know whether to use the sin or cos to solve for the angle because they give different values
lyric summit
you need to use both
and find common value of angle
$\text{for example: }cos\varphi=-\frac{1}{2}\text{, and: }sin\varphi=\frac{\sqrt{3}}2{}$
soft zealotBOT
Joanna Angel
lyric summit
and you use tables trig ones, or you look at graphs, t find common angle
reef canyon
could you explain how to find the common angle please
shut gazelle
vital crag
,tex .unit circle
soft zealotBOT
riemann
ocean stratus
sleek pasture
is this d?
sleek pasture
em
opal plinth
No
sleek pasture
absolute maximum at 2 is -1 no?
so it should be b since abs min is higher than abs max?
opal plinth
absolute maximum at 2 is -1 no?
That's nonsense
sleek pasture
😭
opal plinth
The question is phrased a little badly but the absolute maximum of f is indeed 2, because the maximum is 2 and the minimum is -2
sleek pasture
is global and absolute the same?
opal plinth
No, global refers to the whole domain, absolute refers to the absolute value (x when x>=0 and -x when x<0)
sleek pasture
bro what
my teacher is screwing with me
she said global maximum is absolute maximum
and relative maximum is local minimum
so i was right?
or was it
c
opal plinth
Huh I guess that could be the case
sleek pasture
abs max was 2 right
opal plinth
I've never heard about "absolute" and "relative" extrema but if your teacher uses these terms that way, then sure
sleek pasture
oh ok
opal plinth
It's a really bad way to call global and local extrema because "absolute" generally refers to the absolute value (like I said)
sleek pasture
whats local then
opal plinth
A local extremum is an extremum on an infinitely small interval around a point
(-1,0) is a local minimum because it's a minimum on [-1.1,-0.9] for example, even though the function goes lower than 0 elsewhere
sleek pasture
??
they usually tell you to find minimum and maximum
relative max/min or absolute max/min*
opal plinth
Yeah local = relative according to your teacher
sleek pasture
is this d?
so this could be both b or c?
opal plinth
No?
opal plinth
The global extrema of f are 2 and -2
opal plinth
You don't really need to
sleek pasture
but one of the answers asks for concave down tho
opal plinth
Yeah, and you can directly see where the graph is concave
opal plinth
Why?
sleek pasture
cause its concaveed down?
from -4 to -3 isnt it concaved down?
u shape is concave up and n shape is concave down right
opal plinth
From -4 to -3 yeah
opal plinth
No
sleek pasture
???
opal plinth
In [3,5] it's clearly still "n shaped"
opal plinth
Yeah what are you saying
sleek pasture
i mean 1,3 is the same shape as -4,-3
opal plinth
True
sleek pasture
so they both concave down?
opal plinth
Yeah
opal plinth
No
opal plinth
Yeah
opal plinth
sleek pasture
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muted ore
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muted ore
I know the formula for covariance
I tried having heads as 1 and tails as 0
that didnt work
so I have no idea how to proceed now
viral oriole
What exactly did you try?
Can you write it down?
By the way, the say "dependent coin flips" in the question, and in the example these are independent coin flips
Is this a typo? or is there another example?
@muted ore
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muted ore
Is this a typo? or is there another example?
It’s not
Basically I set heads as “1” and tails as “0”
Then calculated variance
With a mean of 0.5
muted ore
Yea
viral oriole
Why do you think it's wrong?
muted ore
Because the answer sheet says so
viral oriole
But the covariance of independent random variables is 0
viral oriole
I think they try to refer to another example with correlated coin flips
Are you sure that there isn't any other example with dependent coin flips?
viral oriole
yes, this is Example 12.2, but I wonder if this is a typo, and there is another example later on
with dependent coin flips
Is this a book?
muted ore
muted ore
Is this a book?
yea
viral oriole
Yes, I think they were refering to this one
Try this one and see
either (1,0) or (0,1)
so you get 1/2 * ( (1-0.5) * (0 - 0.5) + (0-0.5) * (1-0.5) )
,w 1/2 * ( (1-0.5) * (0 - 0.5) + (0-0.5) * (1-0.5) )
soft zealotBOT
muted ore
this gives a cov of -0.5
nvm ur right
why do they give a different formula at a later point?
thats so strange
muted ore
viral oriole
It's been a while since I touched this, but if I recall correctly, when you estimate from a sample, dividing by n-1 gives a better estimate
But this isn't the covariance, this is an estimate
You can see that this is done for the variance too
viral oriole
yes
muted ore
yes
but how is our example representative of population
seems strange to use it like that
viral oriole
Which example?
viral oriole
Because these are known random variables
the description gives everything there is to know
You can derive all the posible outcomes and their probabilities
muted ore
Right okay
viral oriole
Yes, you are given p(x,y) for all possible (x,y)
viral oriole
I'm a CS major
viral oriole
Good luck my friend! 🙂
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jovial iris
How should I even approach such questions:
final saddleBOT
How should I even approach such questions:
jovial iris
Then test if
Like I thought of saying the following:
a, b are linear combinations of M, N, S
c, d are NOT linear combinations of M, N, S (that's why they are outside of U)
Now, if we are testing like: -3a-4b+c, these coefficients don't matter, we just have to take into consideration what we are looking at: a+b+c
(a+b) is part of U, but c is NOT part of U (not a linear combination of M, N, S))
Therefore, this whole thing is NOT inside U
Am I on the right track or?
final saddleBOT
@jovial iris Has your question been resolved?
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@jovial iris Has your question been resolved?
jovial iris
Can you send whole question
I can translate it from Serbian
It just says that M, N, S are from M_2x2 space
And that we should test what I have mentioned up there
Nothing more
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@jovial iris Has your question been resolved?
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@jovial iris Has your question been resolved?
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lapis barn
is there a trig identity for sin x + cos x = 0?
final saddleBOT
is there a trig identity for sin x + cos x = 0?
lapis barn
im trying to solve for x
cerulean igloo
sinx = -cosx,
Means thingys with π/4's but in second and fourth quadrants
If you don't know that, then just square
Getting sin2x=-1
And then it's doable
lapis barn
what
cerulean igloo
There's only the bisectors of the quadrants on which sinx and cosx are equal in magnitude
And in second and fourth quadrants they're opposite in sign
Means angles like nπ-π/4
dusk mantle
Good day, my son is in grade 4 and he has these math questions to solve and the topic is division.
I would answer logically in multiplication but not sure why they require division.
The library assistant can cover 8 books in an hour. Since there are 24 newly acquired books in the library, will the library assistant be able to finish covering the books in 4 hours? prove your answer?
final saddleBOT
Good day, my son is in grade 4 and he has these math questions to solve and the ...
dusk mantle
Hoping for help 🙂
My son and I would simply do 12x6 = 72 books and the answer would shelves not enough.. but is there a way via division?
desert mantle
well either 24/8 < 4 or 24 < 8*4
dusk mantle
thank you, kindly give me a moment to digest the divison method u just metioned.
modest birch
I guess logically, you could ask the related question "how long would the library assistant take to cover the 24 newly acquired books?" and you could figure this out by either dividing: 24 books / (8 books per hour) = 3 hours
or you could, if you don't like dividing, just start counting upward:
At the end of the first hour, the assistant has covered 8 books.
At the end of the second hour, the assistant has covered 8+8=16 books.
At the end of the third hour, the assistant has covered 8+8+8=24 books.
and since 3 hours is less than 4 hours, the assistant will be able to do the task in less than 4 hours
dusk mantle
but wouldnt it be logical to fill the shelves up with the maximum = 12 books per shelf?
modest birch
The library assistant can cover 8 books in an hour. Since there are 24 newly acquired books in the library, will the library assistant be able to finish covering the books in 4 hours? prove your answer?
I don't think your question here mentions shelves
different question maybe?
dusk mantle
96/12 instead?
ah wait ur correct my bad
copy pasted the wrong question 😦 im sor sorry
- There are 96 new books in the library. And there are 6 available bookshelves that can hold 12 books each shelf. Are the shelves enough to hold the new books? explain your answer
this is the one. im very sorry
desert mantle
each shelf would need to hold 96/6 books
but yeah multiplication is much more natural to use here
dusk mantle
yes im just confused why the teacher requires multiplication instead. 96 / 6 = 16 books per shelf
but the question is are the shelves enough to hold the new books
bit confusing
modest birch
generally, in mathematics, there are many ways to approach problems and many ways to reason about things
you could suppose that there are 6 shelves, and this won't change, and then logically reason that each shelf would have to hold 16 books for all of the books to be held by a shelf
and since each shelf can only hold 12, you can conclude that the books won't fit
or you could suppose that each shelf holds 12 books, and then you could conclude that there would have to be 8 shelves, but you only have six, so the books won't fit
or you could suppose that you have 6 shelves, each of which holds 12 books, and then you could conclude that the shelves can hold a maximum of 72 books, which is less than 96
dusk mantle
thank you very much for clarifying. I will save this conversation and digest it as you are right that there are many ways to solve it
May I also kindly as for this one, as u mention there are multiple ways. But i dont see the divison in this question:
In the library, there are 12 tables with 6 chairs. If 96 pupils were all allowed by the librarian to do their research work, will there be enough chairs for the pupils? Explain your answer
as for me i can see only multiplication as a solution
modest birch
Suppose someone had to distribute 96 pupils among 12 tables. Then, by computing 96/12, one could figure out how many pupils would be seated at each table. This comes out to 8. Therefore, since each table only has 6 chairs, there are not enough chairs for the pupils.
Or suppose that we wish to distribute 96 pupils into tables of 6 chairs. Then, by computing 96/6, we could figure out how many tables are required. This comes out to 16.
It turns out that all of these are just different ways of stating the same inequality
warm axle
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warm axle
,rotate
soft zealotBOT
warm axle
What am i doing wrong?, why am i not getting all of the answes?
final saddleBOT
@warm axle Has your question been resolved?
warm axle
<@&286206848099549185>
random forge
,w cos(3x) = cos(6x)
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modern wraith
If I take the ring given by the unit circle, and $x^2+y^2=2$ and transform the plane with the relation of $(\cos(x), \sin(x)) \sim \cos(x+\pi), \sin(x+\pi)$ Will this give the moebius strip? Why yes or why not?
final saddleBOT
If I take the ring given by the unit circle, and $x^2+y^2=2$ and transform the p...
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bigpufik
modern wraith
Intutievly Id Say yes, taking a point we basically twist the whole circle, and with that the plane 180 degrees and then stick them toegther?
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modern wraith
<@&286206848099549185>
mellow verge
Intutievly Id Say yes, taking a point we basically twist the whole circle, and w...
Yes, your intuition is correct. The transformation you described, where ((\cos(x), \sin(x))) is mapped to (\cos(x+\pi), \sin(x+\pi)), effectively flips each point on the unit circle by 180 degrees. When you apply this transformation to the unit circle defined by (x^2+y^2=2), it results in a Möbius strip.
soft zealotBOT
⩩ 𓍢 ׅ 🎀⃞ꭑֹ𝗮̈𝗱ꫀ𝗹𝗂n͟𝗲̄ ♡゙ ˖ ݁ ˓ :
modern wraith
Yes, your intuition is correct. The transformation you described, where \((\cos(...
wdym the unit circle described by x^2+y^2=2?
modern wraith
Yeah so the ring effectively becomes a mobius strip?
mellow verge
If I take the ring given by the unit circle, and $x^2+y^2=2$ and transform the p...
To prove mathematically that the transformation you described turns the unit circle ((x^2 + y^2 = 1)) into a Möbius strip, you can use parametric equations.
Let (r(\theta) = (\cos(\theta), \sin(\theta))) represent the unit circle. The transformation you mentioned is (T(\theta) = (\cos(\theta + \pi), \sin(\theta + \pi))).
Now, apply (T) to (r(\theta)):
[T(r(\theta)) = T(\cos(\theta), \sin(\theta)) = (\cos(\theta + \pi), \sin(\theta + \pi))]
Expanding this using angle sum identities, you get:
[T(r(\theta)) = (-\cos(\theta), -\sin(\theta))]
This parametric equation represents a Möbius strip. To prove it rigorously, you'd want to show that the resulting curve is non-orientable and has the topological properties of a Möbius strip. The key is in understanding how the transformation affects the orientation and connectivity of the points on the unit circle.
soft zealotBOT
i_loves_bonbons
modern wraith
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crimson sparrow
I saw a proof about switching the boundaries of an integral, which makes the area negative. So I got a question about the first step where they do:
$\int_{a}^{b} f(x) , dx + \int_{b}^{a} f(x) , dx = \int_{a}^{a} f(x) , dx = 0$
soft zealotBOT
Bennxy
crimson sparrow
Is it possible to say $\int_{a}^{b} f(x) , dx + \int_{b}^{a} f(x) , dx = \int_{b}^{b} f(x) , dx = 0$ instead? I don't think we could, because b > a right? But if b < a, we can right?
soft zealotBOT
Bennxy
crimson sparrow
Because, if we think about two vectors a={3,0} and b={5,0} for the interval [3,5] we do b-a which is 2, and we call this vector c. But if we did a-b we get -2, which is a negative vector of c. So we end up again at vector a terminal point.
So if we wanted to be strict, saying $\int_{a}^{b} f(x) , dx + \int_{b}^{a} f(x) , dx = \int_{b}^{b} f(x) , dx$ is not correct right?
soft zealotBOT
Bennxy
wraith crater
it is correct since LHS = RHS = 0
crimson sparrow
Hmm so $\int_{a}^{a} f(x) , dx = \int_{b}^{b} f(x) , dx$?
soft zealotBOT
Bennxy
wraith crater
they are both zero for any f(x) (as long is f is integrable)
the area between a point and itself is zero
crimson sparrow
Yea that's what I thought at first too
crimson sparrow
Because, if we think about two vectors a={3,0} and b={5,0} for the interval [3,5...
But then I came up with this
I dunno if this is correct though
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crimson sparrow
My question is above
final saddleBOT
My question is above
wraith crater
im not sure what youre trying to say
stone wagon
Because, if we think about two vectors a={3,0} and b={5,0} for the interval [3,5...
how are you then putting a vector as a boundary?
stone wagon
im not sure what youre trying to say
same here
crimson sparrow
how are you then putting a vector as a boundary?
Ehh, yea I think I'm over thinking this
Anyway, thanks for the help
.close
coral bluff
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west berry
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@coral bluff Has your question been resolved?
regal drift
Have you learned that D= b²-4ac ?
If so then I have a more efficient way of solving it
Also why do both examples use inequalties when there isn't a inequality in the question?
final saddleBOT
@coral bluff Has your question been resolved?
coral bluff
Have you learned that D= b²-4ac ?
Yes please
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wide folio
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muted prairie
They wanted r≤0
wide folio
i got that part
but for the angle
I thought the angle would have to be pi/4 because the range of arctan is (-pi/2,pi/2)
muted prairie
that is the range of arctan, it does not imply the angle has to be in it
Do you know why their answer and your answer correspond to the same point
muted prairie
?
wide folio
They should bothw work because sqrt(2)/2 divided by sqrt(2)/2 = 1
and -sqrt(2)/2 divided by -sqrt(2)/2 = 1
muted prairie
oh, quadrants?
wide folio
yeah thats why I believe 5pi/4 would also work
muted prairie
Anyways, their answer corresponds to the same point but has r,θ inside the desired range, so it is correct
Your answer is correct, aside from the r,θ values not being in the range they asked for
muted prairie
Np
wide folio
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unique dagger
How should Integrate this?
final saddleBOT
How should Integrate this?
unique dagger
I would separate the nominator into separate integrals
But how do you calculate t³/(t+1)?
green ibex
,rccw
soft zealotBOT
green ibex
But how do you calculate t³/(t+1)?
you mean integrate it? you can use a u-sub :)
@unique dagger
unique dagger
Wait
Ah ok
So I sub the denominator so that I would get (a+b)³ and then separate into elementary integrals
Ok thx man
.close
tranquil pine
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tranquil pine
i know the capital E (epsilon)? is mathematical shorthand for "the summation of" eg, the sum of all expressions evaluated at i from i to L / delta s - 1. what is the other large letter and what is it shorthand for, i am guessing the products of all expressions to its right evaluated at that each value of j?
craggy plume
capital pi, your guess is correct, similar to "capital e" which is Sigma
use it in the same way as sigma but multiply instead of sum
craggy plume
type ".close"
tranquil pine
great, thanks again.
tranquil pine
type ".close"
hey sorry, i actually have one more question
when evaluating this expression, does it become the evaluated sigma expression times the evaluated pi expression?
craggy plume
when evaluating this expression, does it become the evaluated sigma expression t...
looks like it to me, yeah
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misty umbra
Can someone help with part c)? The coordinates are O(0,0) , A(1,0) , N(4/5,16/125) . I know that the area of a triangle is 1/2xbxh
final saddleBOT
Can someone help with part c)? The coordinates are O(0,0) , A(1,0) , N(4/5,16/12...
@misty umbra Has your question been resolved?
misty umbra
<@&286206848099549185>
terse dagger
what's the base
wait
lets think of the base and height from a very convenient perspective
namely the xy plane
where one is the x direction and the other the y direction
very convenient
especially when one of the sides of the triangle is in the x direction
misty umbra
especially when one of the sides of the triangle is in the x direction
Do we consider y as the height
and x as the base?
terse dagger
yes
terse dagger
well the base is at y = 0
and so the height is the third point's height - the base height
misty umbra
well the base is at y = 0
wdym
terse dagger
when we pick directions for base and height
in this case we picked x as the direction the base is in
and y as the direction the height is in
the base is just a side of the triangle
misty umbra
Yes
terse dagger
and the height is the distance from that side to the third point
this distance has to be perpendicular
to the side that we chose as our base
but because x and y are perpendicular
we don't have to worry here
all we need to find is the y values for the third point
and the base
since the base goes from the point 0,0 to 1,0
the y value is 0
misty umbra
and the height from 1,0 to 4/5,16/125?
misty umbra
what's the y value of the third point?
16/125
misty umbra
So 16/125-0 which is 16/125?
misty umbra
1-0?
terse dagger
yes
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fossil shuttle
final saddleBOT
fossil shuttle
both arent
lofty crescent
you can factor a term out of b
fossil shuttle
you can factor a term out of b
how
lofty crescent
what variable is in both 17ca and 8cd
fossil shuttle
c
lofty crescent
exactly
lofty crescent
no you take it out from both sides
c(17a) - c(8d)
like that
and then thats equal to c(17a-8d)
lofty crescent
you cant factor that
fossil shuttle
so if it isnt divisible and it doesnt have 2 of the same terms it isnt factor?
lofty crescent
well you can factor but it would be decimal
but you probably shouldnt do that
if they are different variables it isnt factorable
lofty crescent
hi
lofty crescent
one sec
this is the question
idk how to rotate it
but
for this part
i just wanted to know if the way i was doing it is right
so i plugged in y into the formula before i took the derivative
torpid meteor
I don't think you did it right
lofty crescent
how am i supposed to do it
torpid meteor
R is constant right?
torpid meteor
Then dR/dt is
lofty crescent
oh wait
lofty crescent
r = sqrt(50y-y^2)
radius r is the radius of the waters surface apparently
i couldnt see the letter through the papers ink
one sec
torpid meteor
(25-y)²+r²=25²
lofty crescent
yeah
torpid meteor
Yeah
lofty crescent
i simplified that
torpid meteor
Correct
uneven light
final saddleBOT
uneven light
not sure where to start
found c’(x) and tried to find critical points using quadratic formula
came out undefined
so idk
uneven light
why over x
ohh
@random forge i dont think theres been any progress
i will still get 3x^2 - 44x + 20000
random forge
,w minimize x^2-22x+20000
soft zealotBOT
random forge
looks like it should work fine? I don't understand your work
I don't know why you still have a cubic anywhere, much less in your derivative
@uneven light
random forge
find derivative of c(x)/x
try simplifying c(x)/x first
although that other method should end up working, just a lot harder
uneven light
uhh
random forge
every term in c(x) has an x in it...
uneven light
ye but wouldnt you need to find the derivative of that
in order to get critical pts
random forge
you want to find the minimum of $\frac{c^x}{x}$
soft zealotBOT
random forge
c^x/x is just a nice little quadratic that's easy to find the min
you don't even need calculus for this problem
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fierce blade
Hello! I'm stuck in the last part of this algebra problem. I don't know how to find one side of the shaded square that will help me find its area
final saddleBOT
Hello! I'm stuck in the last part of this algebra problem. I don't know how to f...
fierce blade
viral oriole
Hi
@fierce blade you can focus on the mid square, if you can find its area, you can derive the area of the innermost square in the same manner
Can you?
I mean the square DC__
Can you find its area?
and I think you can, you wrote there DC = 8 sqrt(2)
and DE = 4 sqrt(2)
So you can find in the same way the side of the shaded square
The same way you found DC
fossil shuttle
what did I do wrong
final saddleBOT
what did I do wrong
rotund citrus
you can't pull out x^2 from 16xy^3
dense storm
what did I do wrong
you factored out the 2x^2y but then didnt divide the rest by it
rotund citrus
i mean, you technically could, but you would be introducing a fraction
find the largest common factor between each term.
your line of thinking should be something like "what is the largest factor that goes into 14 and 16?" "what is the largest factor between x^2 and x?" and "what is the largest factor between y and y^3?"
combining all those factors gives you the lcf between both terms.
fossil shuttle
i mean, you technically could, but you would be introducing a fraction
i dont think its supposed to be fraction
was the 2x^2y correct
rotund citrus
i dont think its supposed to be fraction
exactly, so your factor was too large.
rotund citrus
yes it is not correct.
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@fossil shuttle Has your question been resolved?
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@fossil shuttle Has your question been resolved?
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timid tulip
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grizzled tusk
since you wanna plot them why are you not just using geogebra 3d or whatever other app ?
timid tulip
i can plot parametrics in geogebra?
grizzled tusk
see here https://www.geogebra.org/m/pm9q9sem for example
candid hull
grizzled tusk
also, you could share your eq so that we check in general, it's not very long
final saddleBOT
@timid tulip Has your question been resolved?
timid tulip
ok thanks but hers's the thing
i did find places to plot parametric equations but not together with cartesian ones
i want to compare them together
also i have absolutely 0 coding knowledge and am strictly dealing with lines
no curves or surfaces
grizzled tusk
a line is a particular kind of curve
you could look for desmos if you prefer its interface over geogebra's
timid tulip
im not rlly concerned with interface
i wanna see those two kinds of equations plotted on the same space
timid tulip
a line is a particular kind of curve
yea thanks
final saddleBOT
@timid tulip Has your question been resolved?
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Available help channel!
obsidian geode
Hi, I would like to get help with this problem about centre of mass and why the answer is different depending on whether I choose to work with volume or area
final saddleBOT
Hi, I would like to get help with this problem about centre of mass and why the ...
obsidian geode
here's the question
here's what I tried
and here's what my book says
talking about finding z bar
even though I wrote x bar in my working out
why's the answer different or have I misinterpreted the question?
shouldn't like both methods be equally valid?
obsidian geode
$$M_{\text{solid}} x = m_{\text{big cube}}x_{\text{com of big cube}} - m_{\text{small cube}}x_{\text{com of small cube}}$$
soft zealotBOT
Eisenhower
obsidian geode
<@&286206848099549185> 🥺
final saddleBOT
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.close
main eagle
final saddleBOT
main eagle
is chat gpt correct about this ?
i ofc know chatgpt is infamous at being bad at maths
severe hawk
sonic crystal
!nogpt
final saddleBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
final saddleBOT
severe hawk
.your chatgpt response is literally saying 2=3
main eagle
.reopen
final saddleBOT
✅
final saddleBOT
final saddleBOT
Available help channel!
atomic kite
final saddleBOT
atomic kite
Need help on the third question
final saddleBOT
@atomic kite Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
lusty maple
Im trying to design a new statistics test for homework. My question is, what letter, greek, english etc should i use to represent its result. I literally dont care im just too tired to think
final saddleBOT
Im trying to design a new statistics test for homework. My question is, what let...
@lusty maple Has your question been resolved?
lusty maple
somone name a letter lol please
sturdy cypress
$\zeta$
soft zealotBOT
frownyfrog
soft zealotBOT
frownyfrog
soft zealotBOT
frownyfrog
lusty maple
thank u
final saddleBOT
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final saddleBOT
final saddleBOT
Available help channel!
foggy granite
-3/4(5y-2) = 1/2(y+3)
Is this correct
-3/4x5y =- 3,75y
-3/4x-2 = 1.5
1/2xy=0.5y
1/2x3=1,5
1,5-3,75y = 0,5y + 1,5
-3,75y=0,5y+3
-3,25y=3
Y = 3,25Y/3
final saddleBOT
-3/4(5y-2) = 1/2(y+3)
Is this correct
-3/4x5y =- 3,75y
-3/4x-2 = 1.5
1/2xy=0.5y...
foggy granite
Well to finish it y = 1,0833
final tangle
is incorrect
the structure of the work is suboptimal, but valid up until
1,5-3,75y = 0,5y + 1,5
try again from there
vestal sentinel
Subtract
foggy granite
To remove variables
final tangle
adding 1.5 to the left would result in having 3 on the left
foggy granite
Subtract
One other thing
Can g(x)=((a (a+1) (b+3))/(x b+3 x))-((a^(2) x^(2))/(x^(3)))+(((3 c-3) (3 c+3))/(9 c^(2)-9))-1
Be simplified to:
G(x) = (A^2b+3a^2+ab+3a)/(xb+3x) - (a^2)/x + (9c^2-9)/9c^2-9) -1
final tangle
do you have a pic, its a bit painful to read that
foggy granite
This is the original one
Lemme draw mine brb
@final tangle
Wait its error in that one part
9c^2-9 is under the bracket
final saddleBOT
@foggy granite Has your question been resolved?
final saddleBOT
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Available help channel!
flint marsh
need help with figuring out the convergence of $\sum_{n=1}^{\infty} \ln(1 + \frac{1}{2^{n}})$
final saddleBOT
need help with figuring out the convergence of $\sum_{n=1}^{\infty} \ln(1 + \fra...
soft zealotBOT
texaspb
flint marsh
The exercise is asking to use the comparison test
but idk what series to compare this to
final saddleBOT
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flint marsh
.close
nova basin
By any chance could I get some help on this one?
final saddleBOT
By any chance could I get some help on this one?
nova basin
,rotate
soft zealotBOT
nova basin
Feel like I’ve missed a step
final saddleBOT
@nova basin Has your question been resolved?
nova basin
<@&286206848099549185> sorry
unkempt moon
So you put it in the right form
But then after x gets removed from both of the variables inside
nova basin
Oh yea, I forgot to remove x
unkempt moon
Also also
Don’t forget that when u square the second variable it’s the whole thing squared
So it’s best to use brackets
nova basin
Alright
unkempt moon
👌👌👌
unkempt moon
Yh
nova basin
Alright, thank you 👍👍
unkempt moon
Don’t forget to square the stuff aswell
unkempt moon
👍👍👍
nova basin
Got it
unkempt moon
Lmk what u get at the end
nova basin
I’m eating my dinner now, I’ll lyk
tranquil pine
An earthquake of magnitude 9.0 (Moment Magnitude Scale) happened in March 2011 near Honshu, Japan. Another earthquake happened in April with a magnitude of 7.1. How much more powerful (in terms of earth movement) was the first earthquake? Use the formula $M=\frac{2}{3}\log(\frac{E}{E_0})$, where $E_0$ is the baseline measure.
final saddleBOT
An earthquake of magnitude 9.0 (Moment Magnitude Scale) happened in March 2011 n...
soft zealotBOT
Matt
tranquil pine
Mostly confused about what they mean baseline measure. My original plan was to just plug both of the data in but idk what to plug in for E0
final saddleBOT
@tranquil pine Has your question been resolved?
slim magnet
final saddleBOT
slim magnet
question c
s=d
u(Q)= 5u/4
u(P)=u/2
so surely t=4d/(5u)
so distance of P is 2d/5
not 3d/5
You can use the answers it gives you to find U(Q) and U(P) instead of doing the whole question'
final saddleBOT
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@slim magnet Has your question been resolved?
final saddleBOT
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Available help channel!
sand solstice
sand solstice
No
final saddleBOT
@sand solstice Has your question been resolved?
quaint hull
?
tranquil pine
$\tan\frac{5\pi}{12}$
final saddleBOT
$\tan\frac{5\pi}{12}$
soft zealotBOT
mj
tranquil pine
I'm not getting the right answer, being asked to give an exact answer using trig ratios
I firstly converted to degrees and found it was 225
which simplifies to 45 RA
then through that I have tan(90-45), which rationalized is tan(pi/2 - pi/4)
subbing it in to my trig ratio for tan I get:
soft zealotBOT
mj
tranquil pine
which = -1, and that's incorrect so I'm confused
final saddleBOT
@tranquil pine Has your question been resolved?
rustic acorn
final saddleBOT
rustic acorn
after I get the volume formula, what do i do
wait is the 30*45 even in the volume formula?
blissful meadow
You have to find an expression for the sidelengths of the base of the box.
blissful meadow
It`s almost there.
rustic acorn
oh would it be 2s^2
blissful meadow
Notice that once you flip the sides sticking out after the corners are removed, the base won`t be 30 by 45 anymore.
rustic acorn
yeah
blissful meadow
So let's just look at the top bit. The tin sheet has width 30 cm
What's left in width after you remove the corners?
rustic acorn
30 - w
blissful meadow
Say, in terms of x.
blissful meadow
Well in that case 2x is rather small compared to 30 isn't it?
So you'd have 30-2x.
rustic acorn
oh yeah yeah
blissful meadow
Good
rustic acorn
30 - 2x
blissful meadow
So what about the other side?
rustic acorn
45 - 2y
blissful meadow
Well it's squares you're removing, so it's still in terms of x right?
45 - 2x
Makes sense?
rustic acorn
oh yea thats right
blissful meadow
Good, now once you flip the sides up, what is the height of the box?
By height, I mean how deep it is.
blissful meadow
Exactly, so x
Good, so now your box has one side (30-2x), one side (45-2x) and the other x.
So what is its volume?
rustic acorn
(30 - 2x)(45 - 2x)(x)
blissful meadow
Spot on.
rustic acorn
ohhh and now I differentiate it
rustic acorn
wait, question
so I got v' = 12x^2 - 300x + 1350
and when I set it equal to zero, I'm expecting a radical answer
is that right
blissful meadow
Yes you will likely find some x that contains roots and stuff.
rustic acorn
but don't I have to find the maximum dimensions?
so like would I set it equal to 0, find its answers, and then also compare it with smtg
?
like if I'm solving for optimization with area, Id compare it to the highest possible length with 0 width, highest possible width with 0 length and see how it goes
idk my teacher taught us to do l * 0w and w * 0l even though itll yield to zero
and use that to compare
blissful meadow
Sorry I was doing something.
Once you find x such that the volume is maximal, you immediately have the dimensions since it's the only thing missing in the sidelengths of your box.
So you will have one side 30 - 2x = 30 - 2(value of x that maximizes volume), ...
Obviously, you want to make sure that the lengths respect some boundaries, so that none of them are negative.
rustic acorn
yeah so I got l = 30 - (25 + 5 root 7) || w = 45 - (25 + 5 root 7) || h = (25 + 5 root 7 )/ 2
idk why theres a black box over the w part
but it disappears if I click on it so ig you could try that if you cant see it
blissful meadow
It's a spoiler tag || . Here is a ||spoiler||.
rustic acorn
ohk
blissful meadow
hmm, it seems to me like you didn't divide by 2 in the answers.
rustic acorn
i did
blissful meadow
Moreover, remember you have 2 roots given by your quadratic equation.
Have you checked both?
rustic acorn
yeah but the other one is negative
blissful meadow
Ok that's good then.
rustic acorn
but if it was positive, I'd choose the one that yields a higher value right
blissful meadow
Well here I would actually check.
Like either plug them into a calculator or try and look at the function, seeif maybe one is a max and the other a min.
rustic acorn
hmm
blissful meadow
but if it was positive, I'd choose the one that yields a higher value right
Because this isn't necessarily true.
rustic acorn
so like their exact decimal values, even if one is higher, wouldnt necessarily have to be the one
blissful meadow
Well look at the expression for the volume. (30-2x)(45-2x)x
rustic acorn
mhm
blissful meadow
If x is higher, then your last factor is larger which is good.
But the two others are smaller aren't they?
rustic acorn
mhm
blissful meadow
Give me one sec. Also what I said earlier about you forgetting to divide by 2 was wrong, apologies.
rustic acorn
no worries
blissful meadow
Indeed, this is what I thought.
So let's go back to the volume right?
This is where the boundaries come in.
We want the sides to be positive right?
I'd have trouble imagining a box with negative sides.
So in particular, you must have 30-2x >= 0, 45-2x >= 0 and x >= 0.
Unfortunately, with the solution you chose, x is too large :
,w 30-(25+5sqrt(7))
soft zealotBOT
blissful meadow
The other solution, even though it involves a minus sign, isn't negative.
rustic acorn
so it would be (30 - (25 - 5 root 7))(45 - (25 - 5 root 7))((25 - 5 root 7)/2)
rustic acorn
The other solution, even though it involves a minus sign, isn't negative.
Yeah I rechecked my work, I had an extra negative sign
its 25 - 5 root 7 )/2
blissful meadow
Yes that is the other root. You'll notice that it's the only one that makes sense in your problem, considering we want every sideto be positive.
boreal willow
hello i am trying to solve this equation, could anybody help me?
final saddleBOT
hello i am trying to solve this equation, could anybody help me?
boreal willow
i got x^3 * 2y^2 * 1/z^4, but this isn't right according to my consultation with chat gpt >.>
regal hamlet
in my experience, IAs tend to fail in most mathematics areas
fringe steeple
hello i am trying to solve this equation, could anybody help me?
you mean simplify the expression?
regal hamlet
im just saying, not telling you to not use them, since they got some use
boreal willow
yes
regal hamlet
i got x^3 * 2y^2 * 1/z^4, but this isn't right according to my consultation with...
what did you do to arrive to this expression?
fringe steeple
i got x^3 * 2y^2 * 1/z^4, but this isn't right according to my consultation with...
you are right
trail hearth
yeah your answer is just correct
unless i missed something
dont ask chatgpt for math
fringe steeple
ye. if the question was to simplify the given expression, you're right
boreal willow
i completed the division first
boreal willow
created tha sequence
n added it all together
we've learned a valuable lesson
don't ask chat gpt for math help
.close
violet crow
How is g(x) ≥ alpha/2 in (c, d)?
final saddleBOT
How is g(x) ≥ alpha/2 in (c, d)?
trail hearth
If $g$ is not identically zero, then there is some $z \in [a,b]$ such that $g(z) > 0$. Then setting $\epsilon = g(z)/2$ in the definition of continuity, we can find a $\delta > 0$ such that $g(y) \in (g(z) - \epsilon, g(z) + \epsilon)$ whenever $y \in (z-\delta,z + \delta)$. This gives an interval $I = (z-\delta,z+\delta)$ such that $g(x) > g(z) - \epsilon = g(z)/2$ for all $x \in I$.
soft zealotBOT
aldo booze
trail hearth
The interval $I$ is the needed interval $(c,d)$, and $g(z)$ corresponds to $\alpha$
soft zealotBOT
aldo booze
final saddleBOT
@violet crow Has your question been resolved?
violet crow
If $g$ is not identically zero, then there is some $z \in [a,b]$ such that $g(z)...
I see. Thanks a lot for the elaborate explanation!! 🙏
. close
.close
grizzled crescent
This problem has been unanswered for a while I just don't really understand the prompt that's given because the wording is always kinda confusing haha
final saddleBOT
This problem has been unanswered for a while I just don't really understand the ...
grizzled crescent
I just need like a definition and if I don't rlly understand then idk
I can just ask
sweet summit
do you mean the definition of a ratio?
grizzled crescent
ehm no
i should specify haha
uhh 6.5.7
the problem
i dont know what its asking me it's so vague
you uhh... do you understand what it wansts 😭
ok uh.....
<@&286206848099549185>
severe dagger
what do u need help with
grizzled crescent
i dont rlly understand what 6.5.7 means
grizzled crescent
ok