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#help-41
amber waspBOT
amber waspBOT
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sick salmon
Hi I’m having trouble making equations & inequalities with word problems think anyone could possibly help? 😔
willow furnace
can you give an example?
sick salmon
Here are some questions that idk:
- an apple has 12 calories, this is 3/14 of the calories in a banana how many calories are in the banana
Sophia’s age is 4 years less than twice beryl’s age, in two years beryl’s age will be 3/4 of Sophia’s age. How old is each of them now
Is there some way I could learn how to make equations easily when given word problems? I don’t understand how to make them but I can solve it when there is one
modern mauve
An apple has 12 calories.
Assume it to be x.
Which is 3/14 of calories in a banana.
Assume banana to be y.
y is 3/14 of x.
y=3/14*x=(3/14)*20
Sophia's age -> x
beryl' age -> y
First condition:
x = 2y-4
Second condition:
two years after,
Sophia's age is x+2
Beryl' s age is y+2
y+2=3/4(x+2)
If you seperate them into variables, it'll be easier.
sick salmon
If I want to find a variable would I just take what is being compared?
modern mauve
Yeah
For example,
If my age is three times my brother's age.
After five years, my age will be 5/2 times my brother's age.
The equation you write are..
If my age is x and my brother's age is y.
x=3y
(x+5)=5/2(y+5)
We can't find anyone's ages since no data is given.
If I add one more condition saying my age after 10 years will be 80.
I can get my brother's age. My brother's age after 10 years etc.
like,
x+10=80
x=70.
So my age is 70.
Put x in any of the equation before you can get y.
amber waspBOT
@sick salmon Has your question been resolved?
past nymph
I've done the first part of this probability question for an exam I have tomorrow - but I'm somehow getting stuck on the second page. I'm lost how to figure out the process of answering this question.
amber waspBOT
I've done the first part of this probability question for an exam I have tomorro...
@past nymph Has your question been resolved?
past nymph
<@&286206848099549185>
ionic lynx
Yes
past nymph
I've done the first part of this probability question for an exam I have tomorro...
I had a mathematics question
ionic lynx
Okk
dense moss
I had a mathematics question
okk
past nymph
And I would like some help. Please.
past nymph
The question is in the screenshot if it's visible
ionic lynx
Where
ionic lynx
How do Suzanne's household results compare to a normal distribution model with a mean of 8 minutes and a standard deviation of 2 minutes?
You should discuss at least TWO of centre, shape, and spread in your response.
past nymph
How do Suzanne's household results compare to a normal distribution model with a...
I'm aware, but it's more finding out the median, and then knowing why and how it is approximately eight and so forth.
ionic lynx
Since the area under the standard normal curve is
1
1
, the area under the given curve also represents the number of showers taken by Suzanne's family.
Since the area under the curve between
5
5
and
8
8
is
0.7745
0
.
7
7
4
5
, the number of showers taken by Suzanne's family is
0.7745
0
.
7
7
4
5
.
Solution
The number of showers taken by Suzanne's family is
0.7745
past nymph
so this is what it should look like at the end
i just don't understand it for some bizarre reason.
ionic lynx
Yes but handwriting should be neat
past nymph
Since the area under the standard normal curve is
1
1
, the area under the giv...
The format is not working lol
past nymph
Yes but handwriting should be neat
It's not my handwriting, it's a screenshot
And handwriting doesn't matter for ncea
past nymph
In this 12 page exam (4 questions per page) - this is the only question that is tripping me. at least so far
Basically, the issue is understanding the why and how with the question
ionic lynx
Yeah
past nymph
What's tripping me up is the median, which is marked as eight and the same as the mean
ionic lynx
Ok
past nymph
So that's all I need explaining
past nymph
ok
ionic lynx
Suzanne’s results are compared to a normal distribution.
Centre #1: Median of this data (approx. 8) is about the same (8) as a normal model.
Centre #2: Mean (9.16) of this data is higher than mean (8) of the normal distribution so the means are not equal.
Centre #3: In a normal distribution mean / median / mode will be all the same (8) but in this data they are not all the same.
Shape: Normal model is bell-shaped and / or symmetrical, Suzanne’s data is skewed (to the right). Could include comments about comparing peaks / mode.
Spread: Normal model s.d. is 2 suggesting range of about 2 – 14 (± 3 s.d.) while Suzanne’s data has a larger range (of 20) suggesting a larger s.d.
past nymph
Suzanne’s results are compared to a normal distribution.
Centre #1: Median of th...
yes but its the how
ionic lynx
Which how
past nymph
how do i get these answers
ionic lynx
Step 1
…
Substitute
x
7
𝑥
7
,
μ
8
𝜇
8
and
σ
2
𝜎
2
into the
z
𝑧
-score formula.
z
x
−
μ
σ
𝑧
𝑥
−
𝜇
𝜎
z
7
−
8
2
𝑧
7
−
8
2
Step 2
…
Calculate the
z
𝑧
-score.
Subtract the numbers in the numerator.
z
-1
2
𝑧
−
1
2
Convert the fraction into a decimal number.
z
-0.5
𝑧
−
0
.
5
Solution
The
z
𝑧
-score for Suzanne is
-0.5
−
0
.
5
.
past nymph
yeah ur format is broken soz
ionic lynx
Why
tulip tapir
Step 1
…
Substitute
x
=
7
𝑥
=
7
,
μ
=
8
𝜇
=
8
and
σ
=
2
𝜎
=
2
into th...
first off
!nosols
amber waspBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
tulip tapir
secondly if you copied that from somewhere i suggest you refrain from doing so
ionic lynx
No I did my self
past nymph
As a helper, please do not give out answers that could be copied as a homework s...
It's not homework! It's a practise assesment im doing in my own time so I know how to do an actual form of the test
Uhm so I don;t really know what's happening here anymore.
ionic lynx
Ok bye
past nymph
Can I request another helper
ionic lynx
Why
past nymph
Because I don't think this conversation has been too constructive, kindly.
ionic lynx
Yeah ok
past nymph
<@&286206848099549185> unsure if this is how to request another, sorry!
fathom bramble
<@&286206848099549185> unsure if this is how to request another, sorry!
Took a while but, what's the exercise?
Or the question
amber waspBOT
@past nymph Has your question been resolved?
modern mauve
Here's the question
weak zinc
Because I don't think this conversation has been too constructive, kindly.
There’s solving it, and actually being useful and explaining…
modern mauve
But she didn't get her answer.
She wants to know how to reach an answer!
Not the specific answers
past nymph
Hi, sorry, I was just getting ready for bed, it's about 1am, haha.
But yeah, I'd still really like to know how to reach the answer
This is in preparation I have for an exam in about eight hours so It's fairly important to me that I know how to achieve whatever questions I am given in the exam.
amber waspBOT
past nymph
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past nymph
<@&286206848099549185> sorry to ping ya'll again!
past nymph
so this is what it should look like at the end
But I'd like to know how to get these answers for this maths question
Thanks :))
amber waspBOT
@past nymph Has your question been resolved?
past nymph
<@&286206848099549185>
deep karma
what's the question
tulip tapir
I've done the first part of this probability question for an exam I have tomorro...
here
past nymph
what's the question
modern mauve
Here let me try even though it's not my mind subject
You calculated mean for the given histogram?
It's sum(fi*xi)/sum(fi) which comes out to be 458/50 = 9.16. which is slightly higher than mean of other new zealand people
The median of the histogram is 25th interval. Which is exactly 8.
So median is not the same as mean for this histogram.
Since mean is higher than median, the plot is right skewed.
the mode is 4 for the histogram.
According to 68-95-99.7 rule, 99.7% data lies within 3std. So the spread is
8+or-3std which yields 2 to 14.
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split kraken
feeling a bit dumb rn: if this is not true (which I feel extremely confident about), it suffices to find just one example of X where the statement doesn't hold, yes?
stuck vapor
(also known as the cocountable topology)
split kraken
indeed
stuck vapor
feeling a bit dumb rn: if this is not true (which I feel extremely confident abo...
ofc
amber waspBOT
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sand kraken
so im struggling with the last part only
amber waspBOT
so im struggling with the last part only
sand kraken
i dont understand why they dont cube the modulus (2) in this instance
oh. i actually just understood, nvm
.close
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stoic spade
I am currently learning about a theorem that ensures the existence and uniqueness of a solution of a differential equation.
It basically says that if f(x, y) is continuous in the open rectangle D = {(x, y) | a < x < b, c < y < d} and has a continuous partial derivative f_y, then for all (x_0, y_0) in D two things holds:
- There exists an open interval I that contains x_0 in which there is a solution y(x) to y' = f(x, y) that goes through (x_0, y_0).
- In that open interval I, the solution is unique.
Why is it that I'm seeing solutions to questions like:
y' = 100y^2
y(0) = y_0
Prove that this equation has a unique solution for every y_0.
The solution is to just show the theorem holds and the solution is therefore unique.
But doesn't the theorem only guarantee uniqueness in some open interval I that contains 0? Why can it be used to guarantee the solution is unique everywhere?
stoic spade
Please ping me when responding, thanks
sterile nymph
@stoic spade Because the open interval is an interval that you select. The reason why the interval is specified in these theorems is so that you can handle badly behaving functions with poles and so on. However, this function is very well behaved over the entire interval in y.
So you can specify (for instance), y in (-inf, inf) and that won't cause any problems (singularities, discontinuities, undefined values, etc) for your differential equation.
stoic spade
What do you mean an interval I select? Is it true for any open interval that contains x_0 then?
sterile nymph
in this case, yes
but if, for instance y' = 100/y^2 then your interval could not contain y = 0
stoic spade
Well of course because f(x, y) wouldn't be defined at y = 0
sterile nymph
the point of the theorem being written as being applicable on an open interval is so that it can handle cases like that where you must restrict the domain
stoic spade
But I've seen cases for which the function f(x, y) is continuous everywhere, has a partial derivative f_y that is continuous everywhere, but the solution is only defined in some part around x_0
Let me find that example, one sec
y' = 1 + y^2
y(0) = 0
Here the solution is y = tan(x) which is defined at (-pi/2, pi/2).
Even though f(x, y) = 1 + y^2, and f_y(x, y) = 2y which is continuous everywhere
The theorem only guaranteed the existence of the solution in some interval, which in this case is (-pi/2, pi/2) or anything smaller
sterile nymph
The solution to that ODE is not tan(x) but arctan(x)
stoic spade
Oh wait really
sterile nymph
and that's not a PDE, but an ODE
stoic spade
What's a PDE?
stoic spade
Okay, just for your knowledge I'm only at ordinary differential equations
sterile nymph
tan(x + C)
stoic spade
Ah okay
sterile nymph
but just drawing your attention to the fact that it is defined for all y
not all x.
stoic spade
What is?
sterile nymph
tan(x + c)
stoic spade
Ok, what does that imply
Am I correct about the usage of the theorem in this case, with what I said above?
sterile nymph
for any x_0 you choose, you get an function that is defined for a limited set of x values, but has an x-value for which any y value is defined.
sterile nymph
Yes.
stoic spade
Okay but the theorem still only let us know there is an interval that contains 0 for which there is a unique solution there
Correct?
(My x_0 is 0. The conditions were y(0) = 0)
sterile nymph
yes.
stoic spade
So back to my original question
stoic spade
I am currently learning about a theorem that ensures the existence and uniquenes...
How, in that example, are we allowed to call the solution "unique" even though it was only guaranteed to be unique in some interval
sterile nymph
Well, you could show that there could not be another solution that contains that point outside of that interval.
which should be straightforward, because your initial condition is not contained outside of that interval.
sterile nymph
let's assume that we have an open interval
and that it's the largest open interval that the function is defined in
We have the function being unique within that interval.
So let's assume there is some function that reproduces the behavior that we are interested in (satisfies the DE, and your initial condition) but resides entirely outside of this interval
(this is required, because we have the function is unique within the interval)
Now we have a problem.
stoic spade
Wait
sterile nymph
because the initial condition, i.e. the point (0, 0) is in the interval.
so you can't have a solution outside of it.
stoic spade
So let's assume there is some function that reproduces the behavior that we are ...
How can you do that if it's defined outside of the interval with the initial condition?
sterile nymph
Exactly, you cannot.
stoic spade
What I'm saying is, that sure, the solution we have is unique inside some interval, but what if we define 2 functions: both of which are the same in that interval, but different outside of it and still satisfy the ODE.
Can't that happen?
sterile nymph
That absolutely can happen
stoic spade
So how can we even call the solution unique
sterile nymph
As long as we only apply the differential equation inside of the interval.
for instance, there's a function that satisfies the following differential equations, y'=0, y''=0, y'''=0, and so on
and with the initial condition y(0) = 0, we have the function y = 0
but that's not the only function that satisfies this differential equation
so long as you only require the function to obey the differential equation on some interval.
for instance, if you only require the interval y in (-inf, 0) to obey the DE, then you can have the following function
stoic spade
Well that example isn't really obeying the same rules but I see your point
Are you saying that I'm misunderstanding the requirement? Do they only want uniqueness in some interval? So as long as I give a solution that has unique around the initial condition, that's all they need?
sterile nymph
$$y(x) = \begin{cases} 0 \quad \text{if $x \le 0$} \ \exp(-1/x^2) \quad \text{otherwise} \end{cases}$$
grizzled pagodaBOT
OmnipotentEntity
sterile nymph
@stoic spade this is continuous and smooth and the nth derivative is equal to 0 at every point less than or equal to x = 0
so it satisfies the ODE in the open interval (-inf, 0)
but you see that once you stop enforcing the ODE, the function can do unexpected things, no matter how strictly we define the behavior.
(it also satisfies the ODE at the point x = 0)
stoic spade
In the example of y' = 1 + y^2, we found that f(x, y) = 1 + y^2 satisfies the requirements of the theorem, and that y = tan(x) is a solution in (-pi/2, pi/2).
If I find an interval, like (-pi/2, pi/2) or anything that it contains, for which my solution is defined: does the theorem guarantee it's uniqueness there?
So sure, we said I can find a solution other than tan(x) that satisfies the ODE but is different outside of (-pi/2, pi/2). But can we find a solution that is tan(x) on (-pi/4, pi/4) but different at (-pi/2, -pi/4) and (pi/4, pi/2) for example?
So can I guarantee uniqueness where my solution is defined?
(If that place is an open interval containing x_0)
sterile nymph
so long as you don't enforce the ODE in that region, yes.
stoic spade
No, I do want to enforce it
sterile nymph
then no
stoic spade
So after I found my solution, and it's defined on an open interval I containing x_0, then it's unique there?
sterile nymph
Yes
stoic spade
Okay that makes more sense.
Although I don't see how the way the theorem is worded shows that
sterile nymph
It's unique on any open interval you can define
So long as you don't run into singularities and so on
stoic spade
It just says that the interval exists, not that it's true for "every open interval I, containing x_0, where the solution is defined"
stoic spade
So long as you don't run into singularities and so on
Great
sterile nymph
So because it's unique on any open interval you can name, it's unique on every open interval you can name.
stoic spade
The theorem says "exists" though
Wait...
I think I actually wrote it down wrong. Specifically the second part
It doesn't refer to the same I defined in the first part
it says:
If y_1, y_2 are solutions, defined on an open interval I containing x_0, then y_1 = y_2 in I.
Okay that makes so much sense now
That's exactly what I was missing
Even though I read it multiple times I didn't notice that
sterile nymph
Yes, as long as they're defined on an open interval, and it satisfies the DE, then they must be the same.
sterile nymph
Sorry, I also read it multiple times and I didn't notice it was subtly wrong, and that you were talking about it.
my bad, I should have noticed.
amber waspBOT
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devout ledge
is 5,4 a local max why or why not?
amber waspBOT
is 5,4 a local max why or why not?
devout ledge
I know that d/dx of the function is 0 since the tangent is horizontal
torn furnace
what tests have you learned?
can you explain in plain words what it means to be a local max?
devout ledge
local min is when the derivative is 0 or undefined
devout ledge
but I think f(x) needs to be changing from increase to decrease at that point
and f(x) is continuous
torn furnace
but I think f(x) needs to be changing from increase to decrease at that point
but you can think like this too
does that seem to be true at 5,4?
devout ledge
it's increasing then increasing
torn furnace
but that doesnt always mean maxima or minima
devout ledge
so it's not a min/max point
amber waspBOT
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wooden mirage
just a small calculator issue
no clue how i've never run into this until now but on my fx991-ms if i evaluate $(-3)^{\frac{2}{3}}$ it goes MATH ERROR. I know that a fractional exponent has two representations but why does the calculator choose to do the other way
grizzled pagodaBOT
notnick
wooden mirage
$x^{a/b} = \sqrt[b]{x^a}$
grizzled pagodaBOT
notnick
wooden mirage
$x^{a/b}=\sqrt[b]{x}^a$
grizzled pagodaBOT
notnick
shadow stump
either order should not result in an error
wooden mirage
then i have absolutely no clue whats wrong with my calculator
i wrote exactly (-3)^(2/3)
shadow stump
could you show a picture of the input?
shadow stump
i'm not super familiar with casio, but you should try using the (-) button instead of the - button
some calculators need to distinguish between negative (-) and subtraction -
wooden mirage
that still runs a math error
wooden mirage
i'm not super familiar with casio, but you should try using the (-) button inste...
that is cool to know though, you just made my life a little easier with negative exponents! still have this weird issue though
night jacinth
might be some floating point crap with the 2/3, i.e. it's not treated as a fraction if I had to guess
wooden mirage
i could definitely type $\sqrt[3]{-3}^2$ but well, that definitely is a bit painful especially with messy equations
grizzled pagodaBOT
notnick
wooden mirage
oh jeez
night jacinth
unfortunately if that's the case, there's nothing you can do
night jacinth
**notnick**
except writing it in full yeah
wooden mirage
might be some floating point crap with the 2/3, i.e. it's not treated as a fract...
yeah it even occurs with 2/3 as a fraction (casio calculator fraction)
maybe it is being treated as a floating point 😭
night jacinth
rip casio
wooden mirage
this is just 🤦♂️
last thing i want is to lose some marks on a midterm because the calculator is dumb
shadow stump
i tried it out on one of my basic calculators and got a similar result. my guess is that calculators aren't very good at evaluating whether or not a fractional exponent of a negative number will be allowed or not, so to be safe they throw an error even when it should be allowed
night jacinth
calculators be dum sometimes
shadow stump
my recommendation would be to either calculate what happens to the sign manually, or do something like
((-3)^2)^(1/3) or ((-3)^(1/3))^2
wooden mirage
wish there was better programming on these calculators sometimes 😭
thanks so much!
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verbal lark
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amber waspBOT
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verbal lark
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pallid canopy
parallel lines implies slopes are equal
verbal lark
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pallid canopy
yup
verbal lark
yup
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amber waspBOT
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verbal lark
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pallid canopy
find the slope of y at any point
verbal lark
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pallid canopy
then find the equation of the tangent line at any point on the curve
verbal lark
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pallid canopy
arbitrary* not random
verbal lark
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verbal lark
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pallid canopy
yes derivative
verbal lark
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pallid canopy
yes
verbal lark
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pallid canopy
call the point P(c, ln(2c)). find the equation of the tangent line at P
verbal lark
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pallid canopy
if you've never found the equation of a tangent line, you should do that for a few points
verbal lark
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amber waspBOT
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halcyon nova
if I want to perform first transformation B and then transformation A onto vector v, would the complete transformation matrix be AB or BA?
I thought it was AB
amber waspBOT
if I want to perform first transformation B and then transformation A onto vecto...
@halcyon nova Has your question been resolved?
amber waspBOT
@halcyon nova Has your question been resolved?
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humble granite
(2^x)^2 = 32(2^4x), solve for x
amber waspBOT
(2^x)^2 = 32(2^4x), solve for x
distant herald
what happens if you try writing both sides strictly as a power of 2?
if you can get the LHS to look like 2^a and the RHS to look like 2^b, you can conclude that a = b
humble granite
oh i havent tried that, i just reduced 2^4x to (2^x)^4 so that i could sub a for 2^x but that didnt work
ill try that thank you
thank you sm i got -2.5 for x
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amber waspBOT
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split sail
how is this wrong
amber waspBOT
how is this wrong
split sail
OHH
split sail
why would it be (x,y) -> (y,-x)
the 9 was already negative so i thought it would be still -9
i get it
but it’s like a trick tho
split sail
how is it a trick
since it’s already negative i thought it would be -x on the image
but
quick ridge
🤔
split sail
that only applies when it’s positive
quick ridge
you’re welcome
split sail
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vast breach
Can someone explain how the answer isn't 88?
amber waspBOT
Can someone explain how the answer isn't 88?
vast breach
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spark iris
find the password given that 3472 2 correct 2572 2 correct 2482 2 correct 3571 2 correct password
sterile nymph
@spark iris so to confirm
3472
Has two of four digits correct, but we do not know which two, so it could be 3 and 7 or 2 and 7, etc.
Similarly for the rest?
spark iris
im also a bit confused about this as the question does not give more information but im assuming it is
actually yeah i think so
should be that
sterile nymph
If so,
3472
2572
2482
3571
Note, for each column only two different digits appear. In the thousands column this is 2 or 3, in the hundreds it's 4 or 5, and so on. However, we do not know yet for a fact that a correct digit appears in every column at least once.
For each password, there are six possibilities. For instance, the first has (34)xx, (3)x(7)x, (3)xx(2), x(47)x, x(4)x(2), xx(72). And each choice invalidates possibilities in other rows. For instance, (34)xx implies that the 10s and 1s columns cannot be 7 and 2, meaning that xx(72) is not a valid choice for the second row 2572. However, that causes a contradiction. Because that would require (25)xx but if (34)xx is correct then (25)xx cannot be
My guess is you simply have to work through the cases, and manually weed out impossible situations.
sterile nymph
My best guess is the more restrictive form
It feels like there would be too many possibilities otherwise to get a unique solution.
There are programs that will do this logic for you, they're called SAT solvers. https://github.com/Z3Prover/z3
spark iris
wait but if they contradict then that means 3 cant start
sterile nymph
I only proved that (34) can't start
It's not proven that only 3 or only 4 doesn't work
For instance, (3)x(7)x might work. This opens the possibility of x(57)x for the second row
Then you need to check the rest to see if it's valid or not.
sterile nymph
I haven't put that much effort into actually proving anything yet. Does it work for all 4 columns?
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fathom ruin
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fathom ruin
these are the answers and i am confused by this part of the solution:
when i try one arrangement around the table, there isnt always 1 way for f2, f3 and f4 to be arranged
compact yarrow
can you show this arrangement?
fathom ruin
can you show this arrangement?
ok so for example,
here there would be 2 ways to place F4
then for F2
there are another two places it can go
in between M3 and M4 or between M1 and M4
compact yarrow
my initial thought is that one of those would lead to an impossible setup
though i'm trying to see it in my head which is a little tricky, hang on
ah yes, if F2 goes between M1 and M4, where does F3 go?
fathom ruin
ah yes, if F2 goes between M1 and M4, where does F3 go?
ohhhhh
so there really is only just one place it can go
compact yarrow
F3 can only go in that slot, and once it's there, F2 also only has one slot
fathom ruin
ahhh
do you have any idea how you would figure something like just under exam conditions?
compact yarrow
when under such conditions, pattern recognition reigns supreme
so doing problems like this
compact yarrow
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marsh coyote
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marsh coyote
how to draw the diagram
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clear finch
I wanna help and I remember this specific problem but the way to solve it escapes me, sry
marsh coyote
I wanna help and I remember this specific problem but the way to solve it escape...
Ok
potent sapphire
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potent sapphire
,calc
y e^{xy} + y^2 + (x e^{xy} + 2xy + 8y) y{\prime} = 0
grizzled pagodaBOT
The following error occured while calculating:
Error: Colon : expected after object key (char 8)
potent sapphire
,calc y * exp(x * y) + y^2 + (x * exp(x * y) + 2 * x * y + 8 * y) * y' = 0
grizzled pagodaBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 66)
potent sapphire
😭
potent sapphire
Differential equations
Yes
Its the class which i suffering the most in this semester
pliant copper
,calc y * exp(x * y) + y^2 + (x * exp(x * y) + 2 * x * y + 8 * y) * y' = 0
use ,w surely
potent sapphire
,w y * exp(x * y) + y^2 + (x * exp(x * y) + 2 * x * y + 8 * y) * y' = 0
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dire hemlock
chat gpt tells me to solve it numerically lol
potent sapphire
i feel like laplace?
Im thinking about exact test
dire hemlock
no clue what that is x.x
hopefully someone else in chat can help u out here <@&286206848099549185>
potent sapphire
I hope so
dire hemlock
i wish u luck o7
potent sapphire
Thank you 🙂
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final matrix
I was thinking move the third part of the LHS in brackets with y' to the RHS and then divide to isolate y'
Then you would have a gnarly but hopefully doable solution
final matrix
what if you flip the diff equation to dx/dy = (flipped fraction)
is it in the form f'(x)/f(x)?
tepid tendon
what is the issue bro
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potent sapphire
what if you flip the diff equation to dx/dy = (flipped fraction)
Good idea
Shall i look for suitable substitution now?
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potent sapphire
Ok thank u ll try
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karmic cobalt
This looks a lot like an occasion for implicit functions!
For function f(x,y), by the chain rule we have df/dx = ∂f/∂x + ∂f/∂y * dy/dx. If we can find a function f(x,y) such that its partial derivatives coincide with the corresponding parts in the given equation, we will have df/dx = 0, or f(x,y) = C for some constant C.
This gives an implicit function solution, which for this case doesn’t seem to have a nice explicit form.
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neat wind
potent sapphire
Thank u i solved it by looking on that
viscid cobalt
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viscid cobalt
can someone give me some tips on how they factorised this?
horrible expression 😭
Im lost
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fiery igloo
is b^la^n Type 3
a^nb^2nc^n Type 1?
a^nb^m Type 1?
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is b^la^n Type 3
a^nb^2nc^n Type 1?
a^nb^m Type 1?
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deft vine
is this right?
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is this right?
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deft vine
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deft vine
The 3
blissful blade
oh
deft vine
yes
blissful blade
Alright… umm… wecan take out the constant outside the differentiation right?
take it out first…
and then do you know chain rule?
deft vine
Yup
deft vine
take it out first…
so it's zero?
blissful blade
alright… apply it step by step..
blissful blade
so it's zero?
no no!
so listen, if you want to derive a function and its multiplied by a constant n
then you derive the function and multiply its derivative with the constant
the derivative n f(x) is n f’(x)
Clear or is there anything i can get you more clear on?
deft vine
what am I gonna do with the denominator 3?
it's gonna remain there?
while I solve the others?
blissful blade
yes…
deft vine
Ohhhh
blissful blade
you can just cancel a pair of 3’s and youll remain with one 3 on the denominator
simplify it into the needed answer
also, the third term in the power, you forgot to write -3/4
deft vine
Ok I'll rewrite it, and have it checked.
blissful blade
alright! See ya
blissful blade
umm
whats with the third term?
Its a -3/4 in the power right?
also, why did you multiply the second and third terms with a 2 in the 4 th step?
deft vine
idk how to explain it
can I send you a picture instead?
I did it like this
Help?
<@&286206848099549185>
tidal meteor
another thing
chain rule
u must mutliply with the differenciation of 3x for the middle term
and differenciation of (1+4x) for the thrid term
@deft vine
tidal meteor
sure
deft vine
🙏🏼
tidal meteor
go ahead
tidal meteor
yes
you could simplify it a bit further by cancelling out the 3 and four
numberator and denominator
tidal meteor
its the same
deft vine
but it brings down the numerator to make the power positive
tidal meteor
when there is a negative sign in the power then that means it needs to be in the denominator
so basically 2^-3 is the same as 1/2^3
they are the same thing
deft vine
but the first problem has negative power
tidal meteor
yes you could bring it to the denominator if you would like
deft vine
can I write it and show it to you?
tidal meteor
sure
tidal meteor
also small mistake in this one
tidal meteor
or else it is like you are writting 5x+4
deft vine
I need to answer first
tidal meteor
answer what?
tidal meteor
anyways if you have any free questions feel free to ask me and i have no problem explaining it in voice chats so you can friend me. Anyways if you have any free questions feel free to ask me and i have no problem explaining it in voice chats so you can friend me
if u want i can help with the other problem too
deft vine
U over v?
tidal meteor
yes
deft vine
Oh no
deft vine
1st year in college ✋🏻🥹
tidal meteor
so like uhhh 11th ish?
tidal meteor
kinda
deft vine
I'm in college
deft vine
O
tidal meteor
issok do you know the basics?
deft vine
Yes
tidal meteor
e^x^2 is your u here
which is the numberator
and v is the expression in the denominator
why dont you find du/dx and dv/dx first
wise verge
With this?
deft vine
You need to use quotient rule, you know what that is, right?
Yes
But I'm having problems with differentiation
deft vine
Is this correct?
wise verge
No
wise verge
how do I do it? 🥹
Alright so for differentiating V, you almost got it but (4e^x)((e^2x) + e) was supposed to be (4e^2x)((e^2x) + e) and U is completely wrong but I’ll start with V first
To get this, you tried doing chain rule which is correct, but since you didn’t show your working, I’m not quite so sure where you messed up, can you tell me the steps you’ve taken to reach your answer?
deft vine
Alright so for differentiating V, you almost got it but (4e^x)((e^2x) + e) was s...
hereeee
@wise verge
wise verge
You messed up when differentiating e^2x, you correctly brought down the 2 to the front to get 2e but you seemingly forgot a rule about differentiation of exponential functions as the power always stays the same
Since the power of e^2x was 2x, then what should the power after differentiation be?
2e^(?)
deft vine
2?
wise verge
2?
No, the power stays the same before and after differentiation, right?
The power was 2x, so now it should be?
deft vine
The power was 2x, so now it should be?
2x
wise verge
Yes, you got your u correct
deft vine
So then it would be (4e^**2x**)((e^2x) + e), correct?
Why 4e^2x?
wise verge
No, your chain rule is incorrect
First you did power rule to get 2(e^2x + e), this is right, but you need to differentiation the inner function
wise verge
Ohhh
Do you understand now why it’s this? #help-41 message
When you differentiate the inner function, you should get that answer
Which was what you tried to do earlier
The only thing you missed out was the 2x in 4e^2x
deft vine
So it's like this?
wise verge
No no, we were just finding the values of u’ and v’ since that’s where you left off with the other guy
But now that we have the values of u’ and v’, we can easily apply it into quotient rule, right?
deft vine
Yes
deft vine
Can you do this and tell me what you get?
Ok, gimme a second
I can cancel out, right?
Or no?
@wise verge
wise verge
I can cancel out, right?
I wouldn’t suggest cancelling out because you have other things to factorise out as well and you should do it as one group
So whatever you see that is common on both sides of the numerator, pull it out
deft vine
Yes, and what else is also common?
e?
wise verge
e?
No, but you see that there’s a 2 on the left side and a 4 on the right side, correct?
And do you also see that the left side has (e^(2x) + e)^2 while the right side has (e^(2x) + e)?
So what else do you factor out now knowing this?
deft vine
So the commons are ex(e^2x+e)?
wise verge
So the commons are ex(e^2x+e)?
No, you already said here that one of the commons is e^2x
You’re correct in saying (e^(2x) + e) is also a common though I’m not sure where you got the ex from so that part is wrong
But you have one more common left
What do 2 and 4 have in common? (What is their highest common factor?)
wise verge
2
Yes, so you can factorise out 2, e^(x^2), and (e^(2x) + e)
Can you do this and work out what happens to the rest of the terms when this happens?
deft vine
Yes, so you can factorise out 2, e^(x^2), and (e^(2x) + e)
Can you do this and w...
Like this?
@wise verge 
tidal meteor
u guys got it?
tidal meteor
idk im gonna have to check
deft vine
okk
tidal meteor
cuz this is wrong
deft vine
cuz this is wrong
why?
wise verge
No, sorry, where did your denominator go? And where exactly did you pull out 2e^(x^2)(e^(2x) + e)?
tidal meteor
4e^2x (e^2x+e)
right
deft vine
what is v^2?
I forgot the denominator
tidal meteor
but then in the next step you cancelled something out?
deft vine
but then in the next step you cancelled something out?
Yes
tidal meteor
im kinda confused what that was
deft vine
No, sorry, where did your denominator go? And where exactly did you pull out 2e^...
It's not gonna stay there?
wise verge
It's not gonna stay there?
Take abc - abde for example, when you factorise out ab, it turns into ab(c - de) right? Nothing disappears from this, because when you multiply back in what you factorised out, you’ll get the exact same thing as before
wise verge
So remember your numerator over here? I need you to factorise out 2e^(x^2)(e^(2x) + e), because we established that both sides have those terms in common
Don’t forget to write the denominator but we won’t touch it for now until you can get the factorisation of the numerator correct or else it’ll end up wrong
deft vine
Okkk
glossy plover
ez
wise verge
Well um it’s wrong, but hold on I’m trying to figure out what you were doing
You cancelled out a few things you weren’t supposed to
deft vine
You cancelled out a few things you weren’t supposed to
Where? 🥹
@tidal meteor can you check too? 🥹
So it's like this?
wise verge
Where? 🥹
Instead of focusing on where, why not we just start again with something more simple since I think the method you’re doing may be a bit confusing as it’s all over the place
deft vine
a new problem?
wise verge
a new problem?
No, we’re using the same one but we’re just factorising normally instead of that broken down method you’ve used
deft vine
No, we’re using the same one but we’re just factorising normally instead of that...
how do I do it?
wise verge
Right so we have $((2xe^(x^2))(e^(2x) + e)^2) - 4e^(2x + x^2)(e^(2x) + e)$
Bruh
One sec
deft vine
okk
deft vine
There's no +x^2 on 4e
wise verge
There's no +x^2 on 4e
There is when multiplied with e^(x^2)
deft vine
Oh that's why it disappeared
wise verge
Yes, it doesn't have to if it makes it more confusing for you, so we can rewrite it later if needed
wise verge
There's no ex^2, you wrote it wrongly here which was why I suggested restarting completely
Some of your powers randomly became numbers multiplied with others
wise verge
Just next time when you're differentiating, make sure you write the powers properly or else you'll misread and mistake it for something else
deft vine
ok, noted. ☺️
wise verge
Alright so this is the numerator, correct? We already established earlier that we're taking everything that is common on both sides out: 2, e^(x^2), and (e^(2x) + e)
deft vine
yes
wise verge
So first we need to write that on the outside like this (2(e^(x^2))(e^(2x) + e))(?)
wise verge
Alright so this is the numerator, correct? We already established earlier that w...
The entire thing we took out multiplied by the ? will get us back to this
wise verge
ex^2?
That doesn't exist, but hold on we'll go step by step so you don't accidentally go off track
I'll write it out on paper for better visualisation
deft vine
That doesn't exist, but hold on we'll go step by step so you don't accidentally ...
Okkk
wise verge
So the question mark over here is what we're trying to figure out
You need to keep in mind that ? × all that we pulled out will get us back to the first line, this enables you to figure out what to write in the question mark box
So when we look at the first line right, we need to check the left side first
I want you to just look at the picture and cross out everything we have factorised out that you see in the left side in your head
So if we factorised out abc for example and you're looking at abcde, you'll mentally cross out abc and you're left with de
Apply the same concept here and tell me what we're left with for the left side (you don't need to work it out on paper)
deft vine
e^2x + e - 4e^2x??
wise verge
e^2x + e - 4e^2x??
No no, okay look we won't touch the right side first, we'll do one at a time
So look at this, this is the left side
deft vine
No no, okay look we won't touch the right side first, we'll do one at a time
Yes
so it's gonna be e^2x + e
cuz it's squared
wise verge
so it's gonna be e^2x + e
Yes but you left out one more term
Here? I wrote a number one to show that one entire (e^(2x) + e) was crossed out from two of them, so we're left with one more of it which is what you did right
There's an x still left
deft vine
the 1?
deft vine
the number 1?
wise verge
That's okay, so now we'll look at the right side and do the same thing
amber waspBOT
@deft vine Has your question been resolved?
wise verge
the denominator?
Yes, so now we can put it into form like this (blue is LHS, red is RHS) and then put it over the denominator to cancel out (e^(2x) + e)
deft vine
Ohhh
wise verge
However if you're asked to simplify or expected to, then you're still not done with the numerator because it looks very ugly as of now
deft vine
oh ok
Thank you so muchhh 
🫶🏻
you're so good at teaching ✋🏻🥹 (but I'm just slow)
.close
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sweet silo
I have difficulty with this problem:
Jimmy has scoop of ice cream every day and he chooses either chocolate vanilla or strawberry. If today he chooses to have chocolate, then the next day has a 50% chance of choosing vanilla, a 40% chance of strawberry tomorrow, and a 10% chance of chocolate. If, however, today he chooses vanilla, he has a 50% chance of choosing chocolate, a 20% chance of choosing vanilla, and a 30% chance of choosing strawberry. If he chooses strawberry, then 30% chance of choosing chocolate, a 10% chance of choosing vanilla, and a 60% chance of choosing strawberry. What are the probabilities after the 5th day?
How would you solve it?
hollow salmon
I have difficulty with this problem:
Jimmy has scoop of ice cream every day and...
Do you know how to do Markov Chains?
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@sweet silo Has your question been resolved?
sweet silo
Do you know how to do Markov Chains?
I heard about it but no. Is it the way to solve it?
snow blade
yeah you'd have to make a matrix with probabilities of each and then multiply the initial state by the transition P^5 because 5 days
hollow salmon
I heard about it but no. Is it the way to solve it?
We're you taught Markov Chains? If not, then make a probability tree. If yes, then use a Markov Chain.
sweet silo
We're you taught Markov Chains? If not, then make a probability tree. If yes, ...
How do I do a probability tree?
sweet silo
https://www.youtube.com/watch?v=w4wKXVwtGac&t=2s
Thank you
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main flame
Can someone help me answer this question please?
amber waspBOT
Can someone help me answer this question please?
@main flame Has your question been resolved?
split sail
Can someone help me answer this question please?
try drawing it out
with widths and lengths labelled
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candid estuary
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candid estuary
what is the domain and range of this
honest dagger
The graph does not present as a function of x, so the question is kind of 
strong nacelle
what is the domain and range of this
Domain is x lesser than 2 range is all real numbers but it's not even a function
honest dagger
However, I suppose if you are dealing simply with relations, then the graph need not represent a function
strong nacelle
Or maybe it's a function in y
honest dagger
In the context of relations, the domain is the set of all inputs and the range is the set of all outputs. Simple as that
candid estuary
.close
junior vale
amber waspBOT
junior vale
how to solve this
strong nacelle
how to solve this
Like number of solutions or exact solutions
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spring badger
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spring badger
could someone help explain what I am meant to do here?
ivory river
could someone help explain what I am meant to do here?
You should divide the volume that is not occupied by the tins by the volume of the box itself.
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tired granite
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tired granite
did i bound this correctly?
it turns into an integral that might end up becoming zero so i feel like i goofed
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tired granite
<@&286206848099549185>
patent raptor
I feel like this resembles a half sphere's volume
patent raptor
The set up is fine and all but that substition, where you divide by sine, seems to mess up with stuff real bad
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tired granite
That bottom integral is really frustrating, yea
It's gonna be hard to pick a better u tho
patent raptor
It's gonna be hard to pick a better u tho
yeah I am thinking about it currently
,w integrate -9(cos^3(x)-1)/sin^2(x)
grizzled pagodaBOT
patent raptor
,w Limit[9(sin(x)-cot(x)+csc(x)),x->2pi]
ok strangely the limit points that it's 0 actually
which could somehow make sense? but i calculated the integral in cartesian which yields 72 (actually 144 if you consider the bottom part too)
grizzled pagodaBOT
tired granite
Yea zero is what I kept getting
Which makes me think that my double integral is wrong, probably in the setup of bounds
patent raptor
it's difficult the substitution because it makes the other bounds invalid basically
Maybe
change order of integration
grizzled pagodaBOT
bacc (unhelpful)
grizzled pagodaBOT
patent raptor
ok nvm
tired granite
On an attempt I got 18pi(sqrt 2 - 1)
With these new bounds
Not certain it's correct, but keeping note if it comes up again
grizzled pagodaBOT
patent raptor
@tired granite
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patent raptor
On an attempt I got 18pi(sqrt 2 - 1)
What did you attempt?
tired granite
im pretty certain it was wrong, i'm contacting a buddy of mine whos really good at this sort of thing
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patent raptor
,, \int_0^{2\pi} \int_0^3 \left ( r \sqrt{9-r^2\sin^2\theta} \right ) : \dd r \dd \theta
grizzled pagodaBOT
bacc (unhelpful)
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patent raptor
.close
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cold mango
rose sorrel
try finding a right angle with the line connecting the 25 degree angle and the 75 degree angle
cold mango
I got 100 for x is that right
rose sorrel
howd u get that
rose sorrel
looks right
cold mango
180-80=100