you find a with P
#help-28
glacial pasture
quick summit
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turbid frigate
I Did solve it but not sure if did it the right way
turbid frigate
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bold hinge
$proof that (a1+1)(a2+1)...(ak+1)=n.a1.a2...ak$
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$proof that (a1+1)(a2+1)...(ak+1)=n.a1.a2...ak$
glossy valveBOT
Lena
vestal meadow
$proof that (a1+1)(a2+1)...(ak+1)=n.a1.a2...ak$
give more context, what even is n?
bold hinge
give more context, what even is n?
n ∈ N*
urban condor
but there in no n term in the LHS
vestal meadow
n ∈ N*
that's just simply not true, e.g. a1 = 3, a2 = 7, then (a1+1)(a2+1) = 4 * 8 = 32, which is not an integer multiple of 21 = 3 * 7
urban condor
it should be A(n) I presume?
vestal meadow
!original
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urban condor
that's just simply not true, e.g. a1 = 3, a2 = 7, then (a1+1)(a2+1) = 4 * 8 = 32...
Yeah
urban condor
that's just simply not true, e.g. a1 = 3, a2 = 7, then (a1+1)(a2+1) = 4 * 8 = 32...
I think that there is an equation to A(n)
vestal meadow
idk what A(n) is, it seems that you may recognise this type of question but I don't
urban condor
idk what A(n) is, it seems that you may recognise this type of question but I do...
k
vestal meadow
@bold hinge show us the entire question pls
bold hinge
Prove that if n satisfies (a1+1)(a2+1)...(ak+1)=n.a1.a2..ak and n=p1*p2..*pi then i=k
urban condor
Prove that if n satisfies (a1+1)(a2+1)...(ak+1)=n.a1.a2..ak and n=p1*p2..*pi the...
k
one min I am helpin another guy
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heavy latch
Hello! Is a scalar field the same as a surface? If not what is the difference.
lucid flower
a scalar field is a function from a surface to the real numbers (just think: the function is the same as an assignment of a number to each point, but the notion of such an assignment is captured by a function)
heavy latch
would the function of the field be the same as a surface?
lucid flower
what do you mean by function of the field
(the point is that in order to have a scalar field you already had to have a surface to begin with)
heavy latch
ok
so lets say we have a surface f(x,y) = x^2 +y^2. I know how to find that
the surface
but how would i then go about plotting the field
i think "f(x,y) = x^2 +y^2" is called a scalar function
On a note i think i might not have gotten here yet in my multivariable class
lucid flower
oh i see what’s happening, here is a bit of pedagogical stuff that you might not know yet: f itself is not the surface. the graph of f is a surface. f is just a scalar function on the plane R^2.
so like
it depends on what you mean by “plot” but usually when people say “plot f” they mean “visualize the graph of f in R^3”
heavy latch
ok
lucid flower
so you’d draw the set of all (x,y,z) in 3d space such that z = x^2+y^2
lucid flower
yes
note that
there are generalizations of what a graph is
that you’re now set up for
just some food for thought
not that it’s important now
but graphs are everywhere!
lucid flower
not exactly sure what you mean - you need to define your own scalar field, there isn’t one given to you.
if you want one example of a scalar field on your surface, you can take the function s(x,y,z)= x+y, and then restrict the domain of s to the surface.
if you meant something else just say
heavy latch
ah I think i falsely infered that for every f and surface there was also a scalar field
lucid flower
ohh okay
i mean for every f there are in fact two things associated to f: first is a scalar field on R^2, given by the point (x,y) being assigned to f(x,y). the second is a surface, the set of all (x,y,z) such that z=f(x,y)
but you don’t get a scalar field automatically on the graph of f from just f alone
you do get one on the plane R^2
but they’re just sort of different things
heavy latch
gotcha
so if i had a R^3 function f, then it would have a surface in R^4 and a scalar field in R^3
and to get the fields i would have to assign a set of points
lucid flower
so if i had a R^3 function f, then it would have a surface in R^4 and a scalar f...
it would have a different kind of object in R^4, but yes it’s a scalar field in R^3
lucid flower
if you have ever heard the word “manifold” this is related to those
lucid flower
and to get the fields i would have to assign a set of points
if you want a scalar field, start with a set of points and make a function from those points to R
heavy latch
if you want a scalar field, start with a set of points and make a function from ...
gotcha
this makes a lot more sense
excited to learn more in my coming lectures
thank you genuinely! You are a bank of cool maths
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last locust
Is this correct?
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Is this correct?
last locust
it seems to easy a solution to be accepted like this
I see online calculators rewrite it into polar coordinates first btut the result is the same
spice orchid
Your method is only checking the limit along lines that look like y = mx, it's possible in general that while all those limits are 0, some other curve has a different limit
last locust
so we should convert into polar?
spice orchid
Yeah thats a common way
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spice orchid
Although, i forget but checking all y = mx might be enough by some theorem
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main hamlet
first you need to split that into two
vast lily
so like 4/3 - 4/(3sin^22x)
main hamlet
$ (4/3) \int{\pi /6}{\pi /3} dx - (4/3) \int{\pi /6}{\pi /3} \frac{1}{sin^2(2x)} dx$
Dunno why the bot doesn't work
vast lily
dam
craggy tapir
$ (4/3) \int{\pi /6}{\pi /3} dx - (4/3) \int{\pi /6}{\pi /3} \frac{1}{sin^2(2x)}...
remove whitespace near dollar sign
$(4/3) \int{\pi /6}{\pi /3} dx - (4/3) \int{\pi /6}{\pi /3} \frac{1}{sin^2(2x)} dx$
glossy valveBOT
فطر
vast lily
the limits are messed up
main hamlet
craggy tapir
nuh uh, thats wrong
main hamlet
???
craggy tapir
wouldnt it be 3(1-sin^22x)
tada
glossy valveBOT
فطر
main hamlet
mmm ok ok one sec
vast lily
why does it not
craggy tapir
fraction denominator is not linear
main hamlet
he is right I made a tiny rearragement mishap
vast lily
if it was multiply would it equal ?
craggy tapir
no
vast lily
dam
craggy tapir
wouldnt it be 3(1-sin^22x)
either way youre onto something
do you know whats $1-\sin^22x=?$
vast lily
either way youre onto something
for real
glossy valveBOT
فطر
main hamlet
Dear me
vast lily
it would equal 1 - (1 -cos4x/2)
craggy tapir
it would equal 1 - (1 -cos4x/2)
well, simpler than that
main hamlet
$\frac{4}{3} \int{\frac{\pi}{6}}{\frac{\pi}{3}} \frac{1}{1 - sin^2(2x)} dx$
glossy valveBOT
Mutty
vast lily
maybe like cos^2
craggy tapir
$\frac{4}{3} \int{\frac{\pi}{6}}{\frac{\pi}{3}} \frac{1}{1 - sin^2(2x)} dx$
sir this is not #latex-testing
craggy tapir
maybe like cos^2
...!
main hamlet
I was trying to make it look cleaner but this bot doesn't recognize integral limits wth
vast lily
cos^22x
main hamlet
yes
vast lily
it would equal 1 - (1 -cos4x/2)
dam so is this wrong
main hamlet
yes
vast lily
ok
craggy tapir
$\frac43\int_{\frac{\pi}6}^{\frac{\pi}3}\frac1{\cos^22x}\dd x$
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craggy tapir
now what do you see
main hamlet
The _ 🤦
vast lily
when do i know to use 1 - cos2x or cos^2x
craggy tapir
just see if which is more advantageous
craggy tapir
anyway
craggy tapir
$\int f(ax+b)\dd x= \frac1a F(ax+b) + C$
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craggy tapir
where F is the antiderivative of f
vast lily
yea
craggy tapir
thats basic?
well, have you learned derivative/integral of trigonometry functions?
vast lily
i did yea
craggy tapir
yeah
vast lily
so its tan
main hamlet
yes well done
craggy tapir
!done
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pine monolith
Hello
pine monolith
merp
just want to make sure
does the equation of any lines not only work for line, right?!
i mean in example
if we had an y=x^2 as a line
then if there and unknown dot only known for its x=2
then the y point of the dot is x^2
which is 4
then the unknown dot of x=2 is (2,4)
am i right?
ping please!!
pine monolith
point or coordinate
sturdy sparrow
r u just saying if u can plug in the value
sturdy sparrow
does the equation of any lines not only work for line, right?!
What does the sentence mean lol
pine monolith
y=x, y=x^2, and other line equations do not only works for their lines, right?
sturdy sparrow
lol r u saying
pine monolith
idk TvT
pine monolith
Eg (x-5)^2+3=y
does any value of x will make the coordinate be in the line of this??
wait
sturdy sparrow
does any value of x will make the coordinate be in the line of this??
instead of line u should say idk uh curve or equation cos it’s confusing when u get to higher degrees
sturdy sparrow
does any value of x will make the coordinate be in the line of this??
Yes
sturdy sparrow
Ok man
sturdy sparrow
oh yeah
pine monolith
instead, TenQ very much!!!!
pine monolith
Like domain and rang
and its entering function
yet TenQ very much
i will be not easily satisfied with just one answer
see you again!
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near umbra
Hi
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vital yarrow
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vital yarrow
is the first answer b and second answer A???
or wait it wouldn't be discontinuity woud it?
dull seal
Can you define discontinuity?
dull seal
Doesnt look like a good definition
dull seal
Well that is the problem
If you are not really sure about what a discontinuity is, you can’t solve the problem
You should study first, try solving problems later
Not the opposite
vital yarrow
I did study it though like I know removeable ddiscontinuity is when in a function x = a function isn't the same and in jump continuity the function ends and starts at a different point
I thought infinite discontinuity was when a function jsut had a vertical asymptote
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torn jolt
Hello
torn jolt
My questions says a triangle has side lengths of 10 units, 15 units, and 18 units. Please find its area.
would you do heron's?
tight glen
do you know heron's formula
tight glen
would you do heron's?
yes
torn jolt
so i got square root of 21.5 times 11.5 times 6.5 times 3.5
do i round that up to nearest whole number?
because it gives me square root of 5624.9375
if i round up to 5625 i got 75 as my answer
is that the area?
merry eagle
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merry eagle
what did i do wrong here
i just plugged in 4, so 1-4 which should be -3
and the floor function just gets rid of all decimals, and since there were no decimals here im not sure what i did wrong
calm ridge
what's int(1-x)?
merry eagle
how did it get -4 tho?
dull seal
-3>-4
merry eagle
dull seal
,w floor(-3.01)
glossy valveBOT
ivory cairn
how did it get -4 tho?
what integer is less than -3.1?
ivory cairn
-3 is an integer, so yes the floor of -3 is -3. but you are taking the limit of this, not just plugging in a number
merry eagle
it says here INT(1-x), you plug in 1-4=-3
ivory cairn
you don't plug in 4
that only works if your function is continuous, the floor function isn't continuous
ivory cairn
,w plot floor(1-x) on 1 < x< 6
glossy valveBOT
ivory cairn
by checking values. your limit is to 4 from the right, so check the function by plugging in 4.1, 4.01, 4.001
the limit tells you what the function is doing around an x-value, not necessarily at that x-value.
merry eagle
by checking values. your limit is to 4 from the right, so check the function by ...
i know this way, but i was just trying to see if there was a way to algebraically do it
other then plugging and checking
but thank you
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torn jolt
i dont understand
calm ridge
!status
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3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
distant panther
Hi
Need help?
Anything to the power of minus is 1 over the number that has the power
tribal viper
If something has a negative exponent just flip it (from numerator to denominator or denominator to numerator) and make the exponent positive
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hoary wyvern
(a)^-s = 1/(a^s)
limpid bane
help me finist this pls
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help me finist this pls
ivory cairn
looks like it's basically done...?
limpid bane
looks like it's basically done...?
then what is R and I()
ivory cairn
you have $\lim_{n\to\infty}|x| = |x|$, you need that to be less than 1\
So you have $|x| < 1$ which is the same as $-1<x<1$.
glossy valveBOT
Zybikron
ivory cairn
can you find the radius and interval from those two inequalities?
ivory cairn
yep
limpid bane
but is it closed or open
ivory cairn
test your end points, if x=1 does your series converge? what about if x=-1
limpid bane
it says incorrent to both close and open
limpid bane
test your end points, if x=1 does your series converge? what about if x=-1
why is that
ivory cairn
that's how you determine if the end points are included.
limpid bane
yeah but it says incorrect to both
ivory cairn
so you didn't actually test them, and just guessed.
limpid bane
yes
ivory cairn
the series only converges for one of the end points.
limpid bane
the series only converges for one of the end points.
what is the result of the second one
what happens when you raise a negative number to inf
ivory cairn
it alternates between -1 and 1.
limpid bane
so und
limpid bane
it alternates between -1 and 1.
[-1,1)so why is it that the interval '1' has open paranthesis when the limit converges
and when '-1' und it diverges and closed panathesis?
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minor talon
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
ok i just got to induction im kinda clueless but ik its weak induction and i use base n = 1 or wtv
stiff summit
Which part are you stuck on?
minor talon
ik how to do part b and c but not a and d
stiff summit
ik how to do part b and c but not a and d
for a, what the question is telling you to do is to prove it directly
how have you done c?
minor talon
so like substitute 2 into a
minor talon
for c i think its just i have to prove base case n = 1 is true in original formula without actually solving it yet
stiff summit
No, it’s asking you to say the statement you have to prove, not to prove that the statement is true
minor talon
okay so like in base case, (formula) must be true when n = 1
stiff summit
In this case, the answer to c is (formula)
minor talon
thats it?
oh like P(1)
into the formula
for part d after doing (k+1) why do we add (k+1)^2 to both sides?
@stiff summit
idk if im allowed to tag lol
stiff summit
idk if im allowed to tag lol
You can
stiff summit
for part d after doing (k+1) why do we add (k+1)^2 to both sides?
To prove the next case, (k+1)
minor talon
ok i did the algebra and because the left hand side and right hand side equation equals each other its proven that n = k + 1 is true as well correct?
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barren kayak
so this is my first time doing integrals with polynomials and i don't understand how my teacher did the part circled in purple
barren kayak
why is it 6A + 6B ?
steady magnet
course of A+B =-1 on the left i think
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silk island
Hi! i'm not sure how to use this channel haha, but the thing is i'm a bit desperate with some algebra. Using the expression of the photo, i want to obtain/clear K/N, but since it's not only 1 variable i'm stuck with that 😦 any help would be really welcomed
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silk island
<@&286206848099549185> any tip/help? :(((
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regal timber
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regal timber
Why does n! stay the same when finding the derivative of that series?
umbral dome
we are taking the derivative with respect to x
from the perspective of the variable x, n is essentially a constant
regal timber
we are taking the derivative with respect to x
Ah I see
Thank you for clarifying again
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regal timber
we are taking the derivative with respect to x
Would you be cool with me @ you for questions in these helps channels in the future?
umbral dome
i'm not necessarily always available, but someone who is available will help if you just post the question
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thin token
10/BC = 3/5
I have no idea what BC could be. Can I turn it around somehow and get BC alone ?
steel mural
okay so
whenever you have a fraction equals an fraction
you can do something called cross multiplication
so if 10/BC = 3/5 then 10 * 5 = BC * 3
aka 50 = 3BC
so BC = 50/3
glossy valveBOT
Oogy Boogy
thin token
so BC = 50/3
Okay
Hold up
But do I just forget about the 3/5 for now ?
Ohhh wait
Tysm
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strange summit
Probability theory. The lifetime (in hours) of a certain type of electrical components can be considered as a stochastic variable with the density function f(x) = 0.001e^(-0.001x)x ∈ ℝ^+1. Two such components are interconnected to form a system. Calculate the probability that the lifetime of the system exceeds 100 hours, if a) the components are connected in series.
strange summit
Is this correct?
The right answer is e^-0.2. But do I go through it in the right way?
Don't really have a teacher to ask 🥲
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strange summit
<@&286206848099549185>
Follow up question.
b) the components are connected in parallel.
Is this correct?
If I don't subtract answer for a) I get 1.8
The right answer is 0.99
strange summit
<@&286206848099549185> Anyone? 🙃
somber remnant
<@&286206848099549185> Anyone? 🙃
mind's going brrrrrrrrrrrr
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blissful hill
How do I solve this?
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How do I solve this?
blissful hill
I am not even sure on where to start
I figured I could just try joining BR and RC but that's going to give me 12, which isn't even in the list of options 😭
willow sedge
tangents drawn to a circle from a point are equal in length
fossil river
How do I solve this?
what are some theorems related to circle geometry and tangents?
willow sedge
what are some theorems related to circle geometry and tangents?
guess you're late to ask that question
blissful hill
Holdup, what if I just draw a line from R to Q, and thus, subtract 4 from 15 which gives me 11 and then add 8 to it which gives me 19, which is also the right answer?
I am not so certain on how this works, but when I was told to draw a line from R to A, I figured why not do R to Q and start from there
fossil river
Holdup, what if I just draw a line from R to Q, and thus, subtract 4 from 15 whi...
We know that BR = BQ. This is from the theorem B-eard mention. Applying this again but on QA and PA we get PA=11. Once again we apply the theorem (I will leave the details to you). https://math.libretexts.org/Bookshelves/Geometry/Elementary_College_Geometry_(Africk)/07%3A_Regular_Polygons_and_Circles/7.03%3A_Tangents_to_the_Circle
tough hazel
think you about this pic
torn jolt
think you about this pic
@blissful hill
tough hazel
blissful hill
Oh!
Lemme check.ig out!
OoO, it sure is extensive but I do sorta get an idea!
In any case, @willow sedge, @torn jolt, @tough hazel, and @fossil river - thank you so much for helping out!
While initally it was a bit hard to understand, I actually do understand it now on a better light!
Thank you so much!
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zenith haven
Hello
zenith haven
Please I need urgent help
How to solve these kind of questions what is the procedure
<@&286206848099549185>
somber remnant
<@&286206848099549185>
rapid rain
<@&286206848099549185>
please wait 15 min before pinging helpers
rapid rain
Hello
also, there is a link between partial sums and general term of a series, given by $a_N = ...$
glossy valveBOT
rafilou2003
rapid rain
(hint : it's a difference of two partial sums)
slate violet
The partial sum is just the sum of the first n terms
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wide tulip
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wide tulip
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wide tulip
Yeah
wide tulip
And you get x from this
wide tulip
X-x is zero bruv
wide tulip
Xd
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merry olive
Hi
merry olive
neat aspen
did you have a particular question about this problem
merry olive
Do I use riemann sum
torn jolt
u dont need to
neat aspen
you can but the question's asking you to compute it geometrically
merry olive
Sorry I was googling how to spell that word lol
merry olive
Thank you guys. I got it. It’s just a right triangle right?
torn jolt
yes
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pure nymph
how do you solve this problem?
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how do you solve this problem?
pure nymph
i've tried factoring equation 1 and divide but it doesn't quite work
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forest jackal
is there any trigonometric indetity that helps me deal with this?
stiff musk
what's your goal with it, is it part of a larger problem you have to solve?
forest jackal
well yes it is,
I try to solve this using lhoptials
but end up with cos(theta/k) = k+2
(sorry dunno how to use latex)
So was wondering if there is a trigonometric idenetity for this
stiff musk
the derivative of sin(theta/k) is not just cos(theta/k)
lofty vine
divide top and bottom by k
forest jackal
ahh that forms a quadratic
lofty vine
L'hopitals rule is overused . teachers should show students how to manipulate limits normally
lofty vine
ahh that forms a quadratic
yes
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L'hopitals rule is overused . teachers should show students how to manipulate li...
especially when calculating the sin(x)/x limit, it's circular reasoning to use l'hopital
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atomic hare
how is this constructed? OD = DA?
warm turret
hi
weak shell
hello
weak shell
weak shell
there is no numbers
weak shell
11
weak shell
no its Plane geometry
warm turret
i mean theres E which is 90° u js need to find B angle to do 180-90- B angle number = A angle number
warm turret
no its Plane geometry
okay
weak shell
i mean theres E which is 90° u js need to find B angle to do 180-90- B angle num...
and because of that i came here
I cant find B
warm turret
yea theres like no number
💀
if there was any type of number of angle u coudl find
i would help u
but since there isnt its quite difficult
and im the same gr lvl as u aswell
<@&286206848099549185>
weak shell
ok ty
warm turret
this might be solvable i remembered this in gr 10 my math teacher
basically it might have to involve trig
and i dont rmemeber exactly but bascially since its o a
thats toa
tan of sumthing = opposit/adj
naive wasp
is there anything that goes with this
warm turret
and i rmemeber u could do something with this with a calculator
weak shell
weak shell
BEAC = BE baptizes AC
warm turret
is there anything that goes with this
bro im kinda positive on this answer do u think so too
naive wasp
idk
warm turret
im kinda proud
naive wasp
lots of assumptions
warm turret
look
no
cus were trynna find A
and since were finding that angle
we put the opposit angle as opp
then the 90° and angle we need to find is adj
and since opp and adj = toa
i may think tan^-1=45 means 45°
so if thats true and right triangle on google says other sides should be 45 each other side along with 90°
naive wasp
@weak shell where did you find this q
weak shell
<@763318386138152980> where did you find this q
its from our math book
naive wasp
then it must have an answer
warm turret
cus i gave a reasonable answer
weak shell
then it must have an answer
no it doesnt have i just checked right know
warm turret
what
it doesnt have answer sheet?
what textbook r u using do u kno the name of it
what chapter and page and question
weak shell
yeah just give a sec
warm turret
https://tenor.com/view/waah-waa-sad-wah-waaah-gif-25875771
im so confident at this one
ik its
partially right
warm turret
wait
naive wasp
🖌️
warm turret
isossclese
no like perfect triangle
naive wasp
ik what you mean
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@weak shell Has your question been resolved?
oblique skiff
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oblique skiff
how do i find the interval
like what is my goal
as t gets smaller y gets smaller and x gets smaller right and vice versa
but i dont understand what "correct" interval means
i mean im getting an answer
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@oblique skiff Has your question been resolved?
oblique skiff
<@&286206848099549185>
vital thorn
Your answer has $x$ as a function of $y$, so what's the domain of $y^3$, i.e., for which values of $y$ is $y^3$ defined?
glossy valveBOT
bondalton
oblique skiff
so the interval is communicating that y cant be less than 0
?
wait so y just gets infinitely smaller but never past zero
is that it? @vital thorn
vital thorn
Yep, it's just that $y$ is never negative or zero because $e^t$ is never negative or zero.
glossy valveBOT
bondalton
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wraith river
'\
umbral dome
that, or use the product rule
umbral dome
is $0.6te^{-\frac{1}{20}t}$ $y$ or $\odv{y}{x}$?
glossy valveBOT
pnoןɔ
wraith river
im not sure
umbral dome
could you post the question this came from?
wraith river
could you post the question this came from?
umbral dome
ok i would recommend you follow the product rule here
wraith river
oh ok
wicked forum
a
wraith river
.close
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icy raft
This is what I'm looking at and struggling with; It is a transportation problem start I do not know how they filled in the BVs and NBVs here. I can try to give additional context, but this is what the example problem has that's relevent.
I am very, very far behind in this class and struggling to catch up. You may need to explain this in baby terms to me; I don't really understand what any of this means, but I am trying very hard.
This does not have an assignment tied to it for at least a few days (and I completed part of it that I was able to figure out), so i have time. If anyone has resources that are good to learn from, I would also appreciate those!
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This is what I'm looking at and struggling with; It is a transportation problem ...
@icy raft Has your question been resolved?
wraith river
how to differentiate?
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how to differentiate?
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obtuse harness
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obtuse harness
what is this question asking
fair oracle
It’s asking which all options are equivalent way to ask
obtuse harness
huh
silver pasture
3 of the four statements mean the same thing
or the way .doc put it, are equivalent
so u need to find the odd one out
fair oracle
find the one which is same for all 3, then find the remaining
silver pasture
ohh
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night lion
why does the F and T disappear?
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why does the F and T disappear?
night lion
and how exactly do u determine if after u distribute the V or Λ, do I write Λ or V next like shown on the circled area
is it cuz I distribute the negation of x and V together and Λ already existed there before the distribution so I just keep it as it is
frigid path
why does the F and T disappear?
its an axiom look at the sheet, but if u think abt it right, X OR F is just X because the F doesnt change the outcome, only X does (if that makes sense) same thing for X AND T, the T doesnt affect the result, its completely dependant on X so you can get rid of the AND T
night lion
its an axiom look at the sheet, but if u think abt it right, X OR F is just X be...
😭 what u doing here
frigid path
im helping ???
night lion
thanks
night lion
its an axiom look at the sheet, but if u think abt it right, X OR F is just X be...
ohh I see
so no matter the sign whenever F or T is involved I just disregard it
frigid path
and how exactly do u determine if after u distribute the V or Λ, do I write Λ or...
idk how to explain this to u icl 🤣
but that circled one stays the same
frigid path
so no matter the sign whenever F or T is involved I just disregard it
that is NOT ❌ true
night lion
😭 but isnt that what u said
frigid path
NO\
night lion
u said like x and T or x and F I should remove the T or F
frigid path
no i didnt
night lion
hm
frigid path
look at the axiom sheet
night lion
then when exactly do I remove it
night lion
look at the axiom sheet
I looked I didnt find anything that was -x V F
frigid path
pretend not x is x for the axioms
night lion
ohh
frigid path
i cannot believe i have to tell you this
frigid path
yup
night lion
ok ok
frigid path
we'll see
frigid path
once grades come back
night lion
any other things I need to nkow for boolean
night lion
once grades come back
chill, remember what happened last time with u
frigid path
chill, remember what happened last time with u
nono that was just unlucky
anyways
u need
to know
night lion
nono that was just unlucky
nah not unlucky u made that happen
frigid path
consistency and contraposition
night lion
oh the axioms?
night lion
I dont see it anywhere
frigid path
u need it for a lot of boolean question
night lion
contraposition isnt a axiom just know it
oh what does it do
oh wait
its a method to solve
nvm
yeah Ik whats contraposition
frigid path
wdym
night lion
like u know how u have to do the opposite of what the question says for contradiction and contraposition?
so like lets say questions tells u to prove x<a or something and then u use either then do the opposite so it would be a<x or something u know
so how do u do that for boolean algebra
neat aspen
for boolean whenever u have to do negation of P or Q
!(P or Q) = !P and !Q, is that what you're asking?
night lion
!(P or Q) = !P and !Q, is that what you're asking?
yes
oh wait no
so like lets say I solved this question using contradiction
so over here x A y = F is P and -x V y= -x is Q
frigid path
!(if P then Q) is just P and !Q
night lion
yeah so how would it look like for this question
like does the "and" or "or" symbol change?
or does -x become x?
and y become -y?
frigid path
x A y = F and -x V y != -x
night lion
ohh ok
frigid path
yeah so it becomes not equals
frigid path
implies
night lion
is that like a relation?
frigid path
yes
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cursive grotto
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cursive grotto
Could I please get a hand with this
neat aspen
!status
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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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@cursive grotto Has your question been resolved?
strong agate
I can't seem to know where to begin with #33, I think I'm stuck midway but I don't even know if I'm doing this correctly 😅
strong agate
I've been looking on this online, apparently I need to make it so that it turns into an inverse tan, but I just can't seem to reach it
lament wagon
are you familiar with u-substitution?
strong agate
Yes, I've been trying that for the past few attempts
I just suck at it 😭
I'm inserting the (2x) into the root by squaring it right now but it's probably gonna be my many failed attempts
lament wagon
set u = sqrt 4x^2 -1
strong agate
Ok
lament wagon
the arctan is going to be from using identities
strong agate
This is what I've got so far
lament wagon
okay i’m just gonna write this out because i don’t feel like doing latex LOL
what exactly did you get for du?
lament wagon
derivative of u
lament wagon
not quite
you can just use power rule for this and rewrite sqrt (4x^2-1) as
(4x^2-1) ^ 1/2
oh wait you just didn’t move the -1/2 power as a fraction
you’re good
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@strong agate Has your question been resolved?
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sturdy mango
I'm confused
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I'm confused
sturdy mango
hm?
opal isle
are u familiar with double integrals?
sturdy mango
yes we just learned about them
so should the bounds for x be 0 to cuberoot 1/27 aka 1/3?
and y is 1/27 to x^3?
@opal isle
opal isle
for A or B
sturdy mango
both?
opal isle
no
sturdy mango
for a i guess
opal isle
mmm
you cannot get the definite integral as a constant if the bounds for the last integral to evaluate don't have constant bounds
sturdy mango
i'm not following
sturdy mango
okay hold on
opal isle
what did u get
sturdy mango
x^3/3 - 1/81
opal isle
yep and that's not an area
opal isle
u need the outer integral (dy) have constant bounds
the bounds cannot be functions
so that part is the easiest to do
sturdy mango
how do i do that?
opal isle
what is the least value y can take
and the max value it can take
look at the curves
isn't it 0<=y<=1/27
sturdy mango
yes
opal isle
ok imma give you a way to remember this
ok just watch a video prob is the easiest way than looking at static pictures
anyways
remember the last integral should have constant bounds
like if it doesn't, what would be the point of having a definite integral which evaluates to a function and not a number?
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@sturdy mango Has your question been resolved?
molten island
how do i do this? I dont get what theyre doing in the answers either
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hoary aspen
suppose we have the function
y = x^2 + sin x
is it possible to find dx/dy?
regal shuttle
suppose we have the function
y = x^2 + sin x
is it possible to find dx/dy?
yeah it is
split the derivative
hoary aspen
how do we do that?
regal shuttle
oh
hoary aspen
dx/dy, not dy/dx
regal shuttle
dx/dy = 1/(dy/dx)
torn jolt
^
hoary aspen
oh shi
i was thinking of that
but i thought calculus has its own weird ass rules
so i thought it wouldnt apply
anyway, thankyou then
🫶
tough nest
''X in the equation''
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''X in the equation''
tough nest
I have no idea how to solve this thing
ancient folio
Use log
tough nest
uhhh