how do I solve the integral from 0 to pi/3 with the expression sec(x)tan(x)
#help-33
frank turtle
static quarry
do you know a function whose derivative is sec(x)tan(x) ?
marsh citrusBOT
marsh citrusBOT
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grizzled frost
im currently studying for a test and idk if this is right
marsh citrusBOT
im currently studying for a test and idk if this is right
@grizzled frost Has your question been resolved?
rancid coral
<@&286206848099549185>
Go for 3rd one
light frost
don't just tell them the answer bruhh
rancid coral
don't just tell them the answer bruhh
ok sry
rancid coral
yeah i need to understand how
Look wait
step wise step?
Let the number of ticket sold to adults be = t
Then acc. to question number of ticket sold to students was = t-15 (there were 15 less students then to adults)
Equation:
$8 to each adult, then to t adults = 8t
$5 to each student, then to (t-15) students = 5(t-15)
Now,
Total cost = $315 = 8t + 5(t-15)
better ?
marsh citrusBOT
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onyx dome
marsh citrusBOT
onyx dome
I got an answer but idk if it’s right
worn nimbus
what is your answer
onyx dome
5/72
worn nimbus
thats not quite right
onyx dome
How do I go about it then
worn nimbus
how did you go about it in the first place
onyx dome
(1/61/65/6)+(1/65/61/6)+(5/61/61/6)
Damn the asterisks didn’t go through
But I’m multiplying 3 fractions in each parentheses
worn nimbus
(1/6*1/6*5/6)+(1/6*5/6*1/6)+(5/6*1/6*1/6)
what 
worn nimbus
thats not quite right
still temple
Damn the asterisks didn’t go through
put \ before them to avoid that btw
onyx dome
put \ before them to avoid that btw
Alright
onyx dome
thats not quite right
What’s the answer and how do you find it?
mystic minnow
pretty sure that's correct for one case of getting 2 of the same number. For example, that's the probability that you roll exactly two 1's.
onyx dome
pretty sure that's correct for *one* case of getting 2 of the same number. For e...
I can’t multiply the whole thing by 6 then can I?
mystic minnow
sure
mystic minnow
work it out a different way.
there's 6^3 outcomes = 216
There's 3C2 = 3 orders for each roll with 2 of the same numbers
Then the number of ways to get 2 of the same number is found with 6 options for die one, 1 option for die two (to match the first die), and 5 options for the third die (to be different from the first two.
So there's 3 * (6* 1 * 5) = 90 desired outcomes.
So 90/216 = 30/72 = 5/12
marsh citrusBOT
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long cape
marsh citrusBOT
long cape
How would you write this to show domain restriction? It’s never ending and not just for unit circle of r=1
mystic minnow
(2k+1)pi/2, for k in the integers
long cape
(2k+1)pi/2, for k in the integers
Why the +1?
main idol
plug in a few k for yourself
mystic minnow
2kpi/2 is just kpi
main idol
(2k+1)pi/2, for k in the integers
follow this formula and evaluate it for k=-2,-1,0,1,2
mystic minnow
k is what is changing values here. everything else is constant
mystic minnow
yeah... check your math again
mystic minnow
that works too.... you should still check your math again
long cape
long cape
So you would declare domain of tangent like this?
What if they want it in set or interval notation?
long cape
Or using this symbol
mystic minnow
you could use that symbol somewhere, sure.
long cape
How would you write this to show domain restriction? It’s never ending and not j...
So going back to original question, can you show how this would look using set, interval, or element of? .. I guess “element of” is normally found in “set” notation?
sometimes I see domain written like this
x | …
mystic minnow
it can be, there's a lot of ways to write out this solution.
mystic minnow
sometimes I see domain written like this
x | …
that would work too
long cape
How would you personally write the domain restriction for tan?
marsh citrusBOT
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dim dust
Hi how can I solve this
17 Japan's worst nuclear accident.
On March 11, 2011, Japan experienced a nightmare: an earthquake with a magnitude of 9.0 on the Richter scale triggered a tsunami that caused explosions and fires in and around the nuclear reactors in Fukushima. A level 7 nuclear disaster occurred. This means that it is a nuclear disaster of the worst kind, such as the one in
Chernobyl in 1986.
Radioactive material escaped.
The radiation was so great that
about 200,000 people from an area
within a radius of 20 kilometers around the nuclear power plant were evacuated as a precautionary measure. During this nuclear disaster, a quantity of the radioactive isotope iodine 131 was released. 100 times the normal radioactive value was measured in two places. How many days should people be kept away from this area, if you know that iodine 131 loses 30% of its value every 4 days?
sullen ice
north sparrow
Hi how can I solve this
17 Japan's worst nuclear accident.
On March 11, 201...
does it say when it is a safe amount of 'radioactive value' ?
sure, after the incident it was 100 times the normal amount, but normal != tolerable
dim dust
No that's everything
north sparrow
No that's everything
not optimal, but I guess that means your goal is 1/100th of the initial value after x days
so given above`s hint, you found a fitting function yet?
north sparrow
uh
so you took 1/100 as intial value?
I mean it works, but what is your A(t) then?
dim dust
1?
north sparrow
the formula was $current=initial \cdot (growth-factor)^{time}$
dim dust
Bc it was 100 times greater than the initial value
elfin berryBOT
Jigglyproff
north sparrow
Bc it was 100 times greater than the initial value
so what is 100
dim dust
A(t)
north sparrow
why
so you agree that the initial value is 100 times greater than what we have in the future when the radioactive material has decayed right
alas, $A_0=100$
dim dust
Bc the initial value is 1/100 but rn it is 100 times greater bc of the iodium material
elfin berryBOT
Jigglyproff
north sparrow
Bc the initial value is 1/100 but rn it is 100 times greater bc of the iodium ma...
no, the initial value is whats 100 times greater
thats the start of the decay
and you have a decay function
dim dust
Ah so it is switched
north sparrow
it is similar to every year I pay 5% of my current money, so the function for that is \
$money=initial \cdot 0.95^t$
elfin berryBOT
Jigglyproff
dim dust
So we could get
1/100 = 100*(0.7)^t
north sparrow
no what
is 100
100 times greater than 1/100?
if initial is 100, what is 1% of that?
its not 1/100
dim dust
1
elfin berryBOT
Jigglyproff
dim dust
so $1=100\cdot 0.7^t$
The right answer is supposed to be 26 but I get 13 if I solve the log
north sparrow
for some reason that is half of our answer and I don't know why
since the unit of t is in '4 days' we have to do 13*4, so we get 52, and 26 is half of that
and I don't know why
north sparrow
is there more information perhabs?
it might be that twice the normal radioactive amount is what can be called 'tolerable' to let people in again
dim dust
Maybe
The two places played a part
In two places 100 times the normal value was measured?
north sparrow
nah
its not like two places make it decay twice as fast
that would be poggers, but no
marsh citrusBOT
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hard ivy
marsh citrusBOT
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lusty sorrel
I'm not sure if I'm just doing this incorrectly or if my homework website is just being picky with how I answer this
marsh citrusBOT
I'm not sure if I'm just doing this incorrectly or if my homework website is jus...
mystic minnow
why did -3x become just -3a
lusty sorrel
the part at the top is just the parent function
OH
thank u for pointing that out omg
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marsh citrusBOT
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marsh citrusBOT
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lusty sorrel
i tried again after fixing the mistake and still got it wrong 
is there any glaring issues sticking out here?
marsh citrusBOT
@lusty sorrel Has your question been resolved?
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marsh citrusBOT
@lusty sorrel Has your question been resolved?
crimson perch
bro you still did not replace x by a+3 for this one
wary olive
Hi, I am a bit confused as to why this equals 1-x^(n+1) here and not -x^(n+1). Further context: This is part of the proof that the geometric series converges for x < 1
marsh citrusBOT
Hi, I am a bit confused as to why this equals 1-x^(n+1) here and not -x^(n+1). F...
wary olive
Perhaps I am completely blockading but if I'm not mistaken this should be (1+x+...+x^n) - (1+x+...+x^n+x^(n+1))
yes I know
x^0 = 1
nocturne fiber
the terms kind of telescope and cancel here
nocturne fiber
Perhaps I am completely blockading but if I'm not mistaken this should be (1+x+....
you made a typo here
wary olive
all good
nocturne fiber
the thing being subtracted should not start with a 1
wary olive
oh wait
Yesss omg I'm blind
its i=1
Yes ok nvm thats solved then
ty for pointing that out
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still temple
marsh citrusBOT
marsh citrusBOT
@still temple Has your question been resolved?
still temple
<@&286206848099549185>
zinc crater
ITS 3
still temple
?
marsh citrusBOT
@still temple Has your question been resolved?
still temple
<@&286206848099549185>
whats teh question
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
karmic knot
When I graph this I get this
marsh citrusBOT
When I graph this I get this
karmic knot
wouldn't it just be -8,0 thats not the solution?
the rest seem to be solutions right
karmic knot
ok
I am kinda woried cuz
This one apparently
had only one
Also this is not a test dont worry lol
this is called a mastery check
so it is just like practice assignments
u have unlimited retakes
karmic knot
Yes
worn aspen
Okay cool
Yeah so all you need to check for is which of those points would be false when applied to the inequalities
sometimes they like to mix it up with one or multiple answers for said problem
You're doing great
karmic knot
This one was the same idea idk why I got it wrong though
karmic knot
You're doing great
thanks
karmic knot
This one was the same idea idk why I got it wrong though
this must have been an error in their end I am assuming
trim quest
this must have been an error in their end I am assuming
Points on the dotted lines are not solutions to the system
karmic knot
Points on the dotted lines are not solutions to the system
oh
this all makes sense now
worn aspen
Normally I recommend plugging the points into the equation itsel
karmic knot
Normally I recommend plugging the points into the equation itsel
I see
trim quest
That's why they're dotted. Because it was > instead of ≥
karmic knot
Ohhhh
trim quest
Normally I recommend plugging the points into the equation itsel
but yes this is a better approach than using a graph, especially if the answer isn't obvious from the graph
worn aspen
Yeah sometimes graphs can cause a headache. Especially when you get further into mathematics
karmic knot
alright thank you guys so much! I will close this room now. @trim quest @worn aspen
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upbeat merlin
How'd the ans come as 3(y-5/3)+5
marsh citrusBOT
How'd the ans come as 3(y-5/3)+5
vast shoal
What is the function
marsh citrusBOT
@upbeat merlin Has your question been resolved?
upbeat merlin
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marsh citrusBOT
@upbeat merlin Has your question been resolved?
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real arch
Guys how do I get the formula for no.14?
marsh citrusBOT
Guys how do I get the formula for no.14?
real arch
nocturne fiber
,rccw
elfin berryBOT
marsh citrusBOT
@real arch Has your question been resolved?
still temple
Help
covert herald
Oh
ivory sundial
covert herald
<#488120190538743810>
Yeah I opened my own channel
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
still temple
need help
still temple
how i do the limit of
eager basin
of?
still temple
f(x)=3x-2, si x=/=1,a = 1
runic temple
si => if in spanish?
iron meadow
so f(x) is not defined at 1 and you want the limit as x -> 1 ?
eager basin
whats the part after the comma?
still temple
si => if in spanish?
in french yes
runic temple
Do you have a picture or screenshot of your problem?
still temple
yes
runic temple
Can you show it please
still temple
iron meadow
oh hm how does that work 🤔
runic temple
Can you show the directions too please
still temple
iron meadow
,rotate
elfin berryBOT
still temple
Can you show the directions too please
Direction of what
iron meadow
are you supposed to do these with delta \ epsilon proofs?
still temple
I have to determine when limx->a- f(x), limx->a+ f(x), lima->a f(x) when f(x)=3x-2, if x=/=, a=1
marsh citrusBOT
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marsh citrusBOT
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brazen magnet
Which steps exactly are necessary to come to the result?
marsh citrusBOT
Which steps exactly are necessary to come to the result?
pure fern
so your differentiating
by chain rule
give me a moment to write it out!
@stoic saddle sorry i spotted the crosses?
stoic saddle
OP's question actually does not have to do with differentiation as such even though it may have arisen from such a context.
@brazen magnet $x^{-1/2} = \frac{1}{\sqrt{x}}$, plus other fraction-manipulation bullshit
elfin berryBOT
Ann
pure fern
many apologies!
still temple
Im trying to find mean of exponential family
For integral (partial^2/partial theta^2) f(y;theta) dy=0
We need to differentiate
(partial/ partial theta) f(y;theta)= f(y;theta) [a(y) b'(theta) + c'(theta)]
After using product rule on this the answer is
f(y;theta) [a(y) b"(theta) + c"(theta)] + [a(y) b'(theta) + c'(theta)] f(y;theta) [a(y) b'(theta) + c'(theta)]
I don't get how they got: [a(y) b'(theta) + c'(theta)] f(y;theta) [a(y) b'(theta) + c'(theta)]
hidden nacelle
still temple
Im trying to find mean of exponential family
For integral (partial^2/partial t...
Can anyone please help me?
marsh citrusBOT
@still temple Has your question been resolved?
still temple
marsh citrusBOT
still temple
what is this asking?
i converted it and i got 120 degrees
so it has to be b since 120 degrees on the circle is in quadrant 2
and x has to be negative while y positive?
is there a correct way of doing this
knotty trellis
When you sketch a circle and a point that's 120° it's pretty obvious that x will be negative and y positive
To find exact coordinates, you could just find the lengths of the sides of the triangle
lament rock
hello
lament rock
so
solving rational equations
(2/x+2) - (x/2-x) = (x^2 + 4/x^2-4)
solve for x
i ended up getting 0 as a solution, but the key says there are are no real solutions
spare sparrow
As a start have you tried simplifying this? (2/x+2) - (x/2-x) = (x^2 + 4/x^2-4)
lament rock
yes
i made the denominators constant
by making them -(x+2)(x-2)
i simplified the left side
spare sparrow
Yes, how is your numerator looking like?
lament rock
to get x^2 +4x - 4
and the right side is -x^2 - 4
sorry
-x^2-4
so0 i then got 2x^2+4x
factored out 2x
to get 2x(x+2)
spare sparrow
Are you sure you haven't missed a minus somewhere?
lament rock
-2 is apart of the domain restrictions
spare sparrow
Since I move one - from the middle to get (2/x+2) + (x/x-2) = (x^2 + 4/x^2-4)
lament rock
so i ended up with 0
spare sparrow
And that is indeed how you said x^2 +4x - 4 with the exact signs
But the right side stays like x^2 + 4
lament rock
wait what?
arent you supposed to make the right side constant too?
if you simplfy x^2-4
you get x+2 x-2
and then u need to add the -
so i got -(x^2+4)/-(x+2)(x-2)
spare sparrow
The way I am solving is that I try get the same denominator and just substract the right from the left to get a 0 in the right
spare sparrow
so i got -(x^2+4)/-(x+2)(x-2)
Here your equation basically hasn't changed since
Sec, sorry
Feel like we get one extra minus from somewhere that's why it isn't working
lament rock
oh
ok
ill try and resolve the problem
ill make a new help channel if i get the same answer
thank you for ur help!
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marsh citrusBOT
spare sparrow
Wait a sec, dw
marsh citrusBOT
✅
spare sparrow
Let's just solve it manually step by step
spare sparrow
(2/x+2) - (x/2-x) = (x^2 + 4/x^2-4)
If we put the minus on the left in the denominator we'll get +(x/x-2)
Correct?
spare sparrow
Yeah
lament rock
sorry
spare sparrow
(2/x+2) - (x/2-x) = (x^2 + 4/x^2-4)
Cause doing the right side right now would give us -x^4-4x+4
lament rock
Cause doing the right side right now would give us -x^4-4x+4
wait
i caught my mistake
i messed up on a negative for the left side
spare sparrow
Yeah
marsh citrusBOT
spare sparrow
@oak charm What's are you finding difficulty with?
They are asking you to find the values of f(x) given the points x - the number in f(), to do so you follow your condition x = -1 or x =/= -1 and depending in which one you're in just substitute in the proper formula
spare sparrow
Ya, you start with -3, x isn't equal to -1 so you evaluate it by using the upper formula for x =/= -1
When they are asking you what's the value of f(-1) let's say you see that you have an equation where if x = -1, then f(x) = -1, so f(-1) = -1
So yeah you have to calculate f(-3) = -1/4(-3)^2 + 4 and f(3) = -1/4(3)^2 + 4 since 3 and -3 are different than -1
midnight otter
Not sure if pythagorus is too under-advanced for this server, but I am struggling to find the formulas for sin, cos and tan online, and I have a test on Friday
marsh citrusBOT
Not sure if pythagorus is too under-advanced for this server, but I am strugglin...
midnight otter
I can do the hypotenuse, adjacent and opposite stuff but I can't do the actual calculations using sohcahtoa
I believe it is year 9 / 8th grade maths
proper zodiac
do you have a particular question you're struggling with?
midnight otter
No, just all of it
proper zodiac
i suggest you look at the trigonometry section on khan academy
midnight otter
Okay, thanks
proper zodiac
if you have particular question problems, bring them to us and we can help you
sharp mortar
sin = wave(x)
graceful bolt
Why is the function convex if second derivative of the function is always greater than zero? I understand that the first derivative is used to calculate the slope and the second derivative to calculate the 'slope' of the slope. I just fail to understand how the formula above proves that the function is strictly convex
marsh citrusBOT
Why is the function convex if second derivative of the function is always greate...
leaden monolith
The slope of the slope tells you how the slope is changing
If the slope is increasing the entire time like the figure on the left
Then it’s positive
In the cubic on the right
Look at the slope as you move
It goes from decreasing at the beginning to increasing at the end
That means the sign of the slope of the slope crossed the x axis
If it crosses the x axis it’s no longer always positive
graceful bolt
Where is the inflection point in the left figure?
Is it at the very start of the domain?
Or is there no inflection point, since the second derivate is positive in the entire domain?
marsh citrusBOT
@graceful bolt Has your question been resolved?
onyx dome
marsh citrusBOT
onyx dome
Is what I have right?
There’s one more thing I need to check-off in that question
<@&286206848099549185>
marsh citrusBOT
@onyx dome Has your question been resolved?
onyx dome
Hello?
radiant geyser
Let's say i have something P(A, B | C), but whether B happens depends on A happening and whether A happens depends on C. Is it right to express then that P(A, B | C) = P(A | C) * P(B | A)
marsh citrusBOT
Let's say i have something P(A, B | C), but whether B happens depends on A happe...
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spring plank
pls help! i have found the 1st and 2nd derivatives but couldn't see the relationship.... thx
marsh citrusBOT
pls help! i have found the 1st and 2nd derivatives but couldn't see the relation...
spring plank
<@&286206848099549185>
marsh citrusBOT
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analog pier
so i know how to matrix multiply, but how do i find parts of it after the matrix is multiplied?
marsh citrusBOT
so i know how to matrix multiply, but how do i find parts of it after the matrix...
edgy jungle
Try post multiplying
With A^-1
I mean pre multiply... Whatever... Just do that
@analog pier does this makes sense
AB=X
A^-1 A B = A^-1 X
B =A^-1 X
analog pier
AB=X
A^-1 A B = A^-1 X
B =A^-1 X
actually i have an idea cant i just turn the matrix in to variables since i know its gonna be 2x3 by the multiplication rule
then multiply by those variables
analog pier
AB=X
A^-1 A B = A^-1 X
B =A^-1 X
edgy jungle
actually i have an idea cant i just turn the matrix in to variables since i know...
That's X ryt
edgy jungle
Each element made variable can be confusing
bright jay
AB=X
A^-1 A B = A^-1 X
B =A^-1 X
Follow this logic
analog pier
was that what u were suggesting?
edgy jungle
Make the entire matrix a single variable
Like x
Or y
AB=the matrix given in question=y
@analog pier ok?
analog pier
ok
edgy jungle
AB=X
A^-1 A B = A^-1 X
B =A^-1 X
A^-1 A = I
So lhs = BI=B
@analog pier does this answer ur query
analog pier
<@1064251776238366781> does this answer ur query
I used my previous method
I found it on math overflow too
edgy jungle
Ok cool
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Available help channel!
still temple
is the inverse of $f(x)=-4x-7 = f^{-1}(x)=-\frac{x}{4}-\frac{7}{4}$ or $f^{-1}=-\frac{1}{4}x-\frac{7}{4}$?
marsh citrusBOT
is the inverse of $f(x)=-4x-7 = f^{-1}(x)=-\frac{x}{4}-\frac{7}{4}$ or $f^{-1}=-...
elfin berryBOT
miky
marsh citrusBOT
@still temple Has your question been resolved?
lapis flower
huh
are the 2 answers not the same
anyways to solve this
take your original f(x) function
you can substitute f(x) for y
then switch x and y
so it should become
x = -4y-7
and to get the inverse
solve for y
stark field
If the variable x
increase by 1%
, then the value of the function y(x)
approximately change for Answer:
%.
stoic saddle
well you'd be better off sending an image instead of this bad copypaste
marsh citrusBOT
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cerulean meadow
marsh citrusBOT
cerulean meadow
Please help
I am very new to graphing trig functions
wait ill just use the 4 quadrants thing and ref anbgle
angle
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marsh citrusBOT
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slender cipher
Hello, I need help for this problem. I really appreciate any kind of help
elfin berryBOT
jan Niku
hazy lion
Hello, I need help for this problem. I really appreciate any kind of help
whats the magnitude of this vector?
slender cipher
i have to find it first ? , sorry for late reply
marsh citrusBOT
Available help channel!
grizzled lake
Hello, I am learning the basics of logic. If I have (P ∧ Q) ∨ P, is it correct to say that the "∨ P" part "overrides" the "(P ∧ Q)" so I can work with a "simplified" truth table instead of this one?
marsh citrusBOT
Hello, I am learning the basics of logic. If I have (P ∧ Q) ∨ P, is it correct t...
still temple
overrides?
sleek lake
yes
grizzled lake
overrides?
I mean that I can basically ignore the (P ∧ Q) part and just focus on the ∨ P
sleek lake
of course you can
we can't know if your specific phrasing is fine by someone who grades it
grizzled lake
we can't know if your specific phrasing is fine by someone who grades it
There's no one grading, I was just unsure about this 🙂 Thanks a lot!
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prisma trellis
Hi guys
prisma trellis
Can I send a photo of a paragraph, can you identify evidence?
north sparrow
Can I send a photo of a paragraph, can you identify evidence?
do it
north sparrow
just do it already burf
north sparrow
I can only identify the ‘according’ part
what do the colours mean?
north sparrow
would the part with UNICEF also serve as evidence?
marsh citrusBOT
@prisma trellis Has your question been resolved?
still temple
Suppose I have
f(y;theta)= (theta+1)y^(theta), 0<y<1 and theta>-1
I want to find mean/expectation.
How do I know which formula to use?
Since it is exponential I can use exponential family of probability distribution method to find mean
Or I can use integration method.
Both of the methods are giving me different expectations.
Please help.
marsh citrusBOT
@still temple Has your question been resolved?
still temple
Suppose I have
f(y;theta)= (theta+1)y^(theta), 0<y<1 and theta>-1
I want to f...
<@&286206848099549185>
native violet
still need help with this?
stark bronze
Hello. I am trying to understand this problem that has to do with Exponents and Polynomials.
It shows the answer at the bottom, however I can’t seem to arrive to that answer when working the problem myself?
I always seem to get 6b with an exponent of 9, not 8b with an exponent of 9. I get to my answer because when multiplying 2 by the power of 3, I get 6 — hence my answer 6b with an exponent of 9.
Could I get someone to explain how 8b9 is the answer, please? Thanks!
marsh citrusBOT
Hello. I am trying to understand this problem that has to do with Exponents and ...
@stark bronze Has your question been resolved?
trim quest
2^3 is not 2*3
stark bronze
2^3 is not 2*3
Oh ok. Would you mind explaining what the proper way to solve that problem is supposed to look like?
stark bronze
Everything there is good, except 2^3 = 8, not 6
I see. How is 2^3 broken down though? Like, how is it 8, because it seems as though (in the long form) it would be 2 x 2 x 2? Or would it be more like 2 x 2 = 4 x 2 = 8?
stark bronze
Ah, that makes sense now!
trim quest
You may have gotten used to "multiplying" with the exponents, but that's just a pattern in how exponents behave when you raise one to another
$(a^b)^c = a^{bc}$
elfin berryBOT
tatpoj
trim quest
but that 2 is just a 2, not an exponent
stark bronze
Ok. So, if this rule was applied to another problem, such as 3^3. It would look like 3 x 3 = 9 x 3 = 27. So the answer would be 27, correct?
trim quest
Yep 👍
unreal swift
proud ice
still temple
I'm getting some wierd answer
marsh citrusBOT
I'm getting some wierd answer
still temple
The answer is 1/4
But I'm getting (x+1)/2(x²+3)
I even put the equation in the calculator and I'm getting the same thing
Original equation-
It asks you to simplify it
<@&286206848099549185>
teal hearth
show your work plz
marsh citrusBOT
@still temple Has your question been resolved?
still temple
@teal hearth but is the answer 1/4 right?
No point in me doing it again if I'm right.
still temple
<@&286206848099549185>
terse wave
I tried it, but I didn't get a 1/4. Maybe I'm wrong. You can check WolframAlpha maybe.
marsh citrusBOT
@still temple Has your question been resolved?
native violet
Do you need the answer I came up with?
devout mauve
are you sure that you are supposed to simplify it? not maybe calculate maximum or something? cause the maximum of this is 1/4 (at x=1)
shy venture
I'm doing linear equations and have to do a problem in which profit is maximized shown in a graph. I have to show that if x=20 y cannot be above 0 because of the constraint 2500x+500y <= 50,000, but I don't know how to put this on the graph shown.
marsh citrusBOT
I'm doing linear equations and have to do a problem in which profit is maximized...
shy venture
also i feel that its possible im missing a line in that graph, but im not sure how, because while im trying to find the max profit for this question, it seems that the only points i can measure are the x intercept, y intercept and the intersection for line 1 and 2
marsh citrusBOT
@shy venture Has your question been resolved?
shy venture
.close
still temple
Prove that for all x, y ∈ R, if x is irrational then either x + y is irrational or x −y is irrational. i still dont get this
marsh citrusBOT
Prove that for all x, y ∈ R, if x is irrational then either x + y is irrational ...
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
surreal vale
still temple
Hard to directly prove that something is irrational don't you think
smoky plover
Let $x=a\sqrt{b}+c$. For $x$ to be rational, $y= \pm a\sqrt{b} + d$.
Does something like this work?
iron meadow
if (x + y ) and (x - y) were both rational, then (x + y ) + (x -y) would also be rational, but wait that's = 2x, so 2x/2 would also be rational but wait you started with the assumption that x is irrational 💥 contradiction 💥
glass silo
Let $x=a\sqrt{b}+c$. For $x$ to be rational, $y= \pm a\sqrt{b} + d$.
Assumes that irrationals are all of that form, no?
smoky plover
Assumes that irrationals are all of that form, no?
oh yeah whoops
still temple
uh
can we start from the beginning
how shold i start this
like what proof method
okay proof by contradiction
iron meadow
so to setup the beginning: assume that the statement that you are trying to prove is false. Then there must exist some irrational x and real number y such that x + y and x - y are both rational
iron meadow
if (x + y ) and (x - y) were both rational, then (x + y ) + (x -y) would also be...
then this ^
still temple
tysm im going to refer to this and try to make a proof
abstract oyster
Just for fun, it is in fact sometimes possible to do a constructive proof that a number x is irrational: you prove that given any rational q, you can construct a nonzero lower bound of how far x is from q. https://en.m.wikipedia.org/wiki/Square_root_of_2#Constructive_proof . A fun exercise is to try to come up with a similar proof for e.
abstract oyster
Hard to directly prove that something is irrational don't you think
(oh, the above was supposed to be a reply to @still temple )
still temple
Ah interesting
Haven't heard of that method
Will give it a look thank you
uh im not rlly that good at math tbh
abstract oyster
To be sure I offer that as a fun aside, you don't need it for this problem :). That said, don't sell yourself short! You'll get there!
iron meadow
that's interesting
marsh citrusBOT
@still temple Has your question been resolved?
still temple
if (x + y ) and (x - y) were both rational, then (x + y ) + (x -y) would also be...
how did you get the 2x
oh wait the ys cancel out
still temple
so to setup the beginning: assume that the statement that you are trying to prov...
howd you get the 2x/2
the /2
iron meadow
well the goal for ending up with the contradiction is to get that x is a rational number
and you got to the point that 2x is a rational number right?
iron meadow
well the product of two rational numbers is also rational so multiply 2x and 1/2 together and that leads to x also being rational
still temple
why are we taking the product
iron meadow
to get x
still temple
like we just want to isolate x?
iron meadow
the proof is based on the contradiction between the initial assumption "there exists some irrational number x" and "these assumptions lead to ... and ... and we get that "x is a rational number"
so you want to get to the point that x is a rational number to create the contradiction
does that make sense?
still temple
yes tysm
bright elk
i need help checking my answers
main idol
closed your other channel
marsh citrusBOT
@bright elk Has your question been resolved?
bright elk
.close
latent acorn
Hi there! Can someone teach me how I can solve these derivative problems?
iron meadow
well you would find y' and y'' and plug them into the equations where they come up and check whether the equality holds
(hopefully you're comfortable with y' and dy/dx being the same thing, too lazy to type the long versions)
latent acorn
i understand the plug in thingy, but I just don't know how to solve for the derivatives of y in the first place T-T
iron meadow
so you dont know how to do derivatives at all?
i would assume you would have learned that if you have this kind of problem to solve
latent acorn
i only know the basicss,, i'm not too familiar w/ implicit though since it was just given to us right now as a module for the first timee
elfin berryBOT
Sooshon
iron meadow
ok lemme give you a simple quick example so you get the gist
say y = x^3, then we have y' = 3x^2 and y'' = 6x right?
and say i wanna check that the same equality that you have in problem 8 holds
$3y'' - 2y y' = 0$
elfin berryBOT
Sooshon
iron meadow
with me so far?
latent acorn
yep!
iron meadow
so all im gonna do is plug in x^3 for y, 3x^2 for y' and 6x for y'' and then check whether the equality holds or it doesn't
$3(6x)-2(x^3)(3x^2) = 0$
elfin berryBOT
Sooshon
iron meadow
blah blah and we can see that isn't true for all x because i just picked some random function
that
that's all it is, just compute the first and second derivatives and plug them into the functions they want you to plug them into and check whether the equality holds or not, probably some things will cancel nicely for at least one of them because they would usually give you at least a problem where it works you would think
latent acorn
so i really just solve for the derivatives of y? then plug them in?
iron meadow
indeed, it's just going to be mostly algebra and checking how things can cancel out that is the hard part
latent acorn
dang i made it seem so much harder in my head dnwajbdha HAHA
iron meadow
d^2x dy^2 looks intimidating
so thats why i prefer y'' 😛
easier to remember oh yeah this is just some function
that happens to be the derivative of another function
which also happens to be the derivative of another
latent acorn
easier to remember oh yeah this is just some function
that's smart dnjadahbaw never thought about it like that xD
iron meadow
just be careful with the algebra here anyway good luck
marsh citrusBOT
marsh citrusBOT
Available help channel!
jaunty mountain
hi
jaunty mountain
i need help on the 2nd part
of this question
i tried finding the intital speed
but couldnt
marsh citrusBOT
@jaunty mountain Has your question been resolved?
marsh citrusBOT
@jaunty mountain Has your question been resolved?
jaunty mountain
not yet
marsh citrusBOT
@jaunty mountain Has your question been resolved?
wary bluff
marsh citrusBOT
wary bluff
Im stuck
I dont knowhow to approach thios question
also this isnt an assignment
or test
its a practice test
I am alrdy given the solution but I dont want to look at it yet
so can I get a hint on like
how to approach this
do they want me to use Riemann sum
to calculate
this
where $\Delta x = \frac{3}{n}$ and $x_i = \frac{3i}{n}$ and we have 3 rectangles?
elfin berryBOT
Worth
wary bluff
.close
still temple
Hello
still temple
An exponential function passes through the points (-1, -0.2) and (4, 2499)
How do I write the expression in y = ab ^x + k form?
I know you need to do system of equations
But I donno how to solve le system
-0.2 = (ab^-1) - 1
.8 = ab^-1
Never I figured it out
.close
elfin scroll
For the RHS of a combinatorial proof, $2(n - 2) + \binom{n - 2}{2}$ can be written as:
\begin{align*}
&2(n - 2) + \binom{n - 2 - 1}{2 - 1} + \binom{n - 2 - 1}{2}\
&=2(n - 2) + \binom{n - 3}{1} + \binom{n - 3}{2}\
&=2(n - 2) + (n - 3) + \binom{n - 3}{2}\
&=(n - 2) + \binom{n - 1}{2}\
\end{align*}
elfin berryBOT
phamous
elfin scroll
Can someone explain how we are able to get rid of the coefficient 2 for 2(n - 2) and (n - 3)?
and how we turned (n - 3 \choose 2) to (n - 1 \choose 2)?
marsh citrusBOT
Available help channel!
elfin scroll
<@&286206848099549185>
marsh citrusBOT
<@&286206848099549185>
marsh citrusBOT
@elfin scroll Has your question been resolved?
elfin scroll
Can someone explain how we are able to get rid of the coefficient 2 for 2(n - 2) and (n - 3)?
and how we turned (n - 3 \choose 2) to (n - 1 \choose 2)?????
light frost
You're not making any sense
stoic saddle
**phamous**
this looks dodgy
do you have the original problem statement and/or worked solution
elfin scroll
yeah
Give a combinatorial proof of $$ \binom{n}{2} - 1 = 2(n-2) +\binom{n-2}{2} $$ where $n\geq2$.
Solution:\
For our counting question: John is at the pet store to buy $k$ pets for his home and wants to keep a 1:1 ratio of dogs and cats with a minimum purchase of 2 pets. The store has $n - 2$ dogs and 2 cats. In how many ways can John buy $k$ pets from the store while keeping a 1:1 ratio?\
From the lecture notes in Module 4.2 on Pascal's Identity, it has been proven that $$\binom{n}{k} = \binom{n - 1}{k - 1} + \binom{n - 1}{k}$$
For the LHS, $\binom{n}{2} - 1$ can be written as:
\begin{align*}
&\binom{n - 1}{2 - 1} + \binom{n - 1}{2} - 1\\
&= \binom{n - 1}{1} + \binom{n - 1}{2} - 1\\
&= (n - 1) + \binom{n - 1}{2} - 1\\
&= (n - 2) + \binom{n - 1}{2}
\end{align*}
For the RHS, $2(n - 2) + \binom{n - 2}{2}$ can be written as:
\begin{align*}
&2(n - 2) + \binom{n - 2 - 1}{2 - 1} + \binom{n - 2 - 1}{2}\\
&=2(n - 2) + \binom{n - 3}{1} + \binom{n - 3}{2}\\
&=2(n - 2) + (n - 3) + \binom{n - 3}{2}\\
&=(n - 2) + \binom{n - 1}{2}
\end{align*}
Thus, $(n - 2) + \binom{n - 1}{2} = (n - 2) + \binom{n - 1}{2}$. Therefore, we conclude that the RHS and LHS are equal.
phamous
elfin scroll
You're not making any sense
My question is how did we simplify in the RHS. Going from the 2nd to last step to the last step.
Or is it even possible at all?
.close
obsidian night
Hey 🙂 I'm taking a course on mathematical analysis, but for some personal reasons, I couldn't really attend to many lectures, but I would really like to give my exam anyway. I don't have many problems in solving exercises, my main issue lies on theorems and their proofs. Do any of you have any recommendations for that, I tried using my textbook, but it seems that I just can't figure out their explanation.
marsh citrusBOT
Hey 🙂 I'm taking a course on mathematical analysis, but for some personal reaso...
rose wolf
Hey 🙂 I'm taking a course on mathematical analysis, but for some personal reaso...
what textbook are u using?
still temple
Hey 🙂 I'm taking a course on mathematical analysis, but for some personal reaso...
I'd like to reference you to #book-recommendations
obsidian night
what textbook are u using?
Our professor suggested it, Mathematical Analysis I, by C. Canuto and Anita Tabacco
late geode
dont they give you course notes?
obsidian night
Sadly nope
rose wolf
the three books our professor recommended are Basic Analysis: Introduction to Real Analysis, Elementary Analysis - The Theory of Calculus and Fundamentals of Mathematical Analysis. I haven't personally checked any of em yet but you may want to see if they do proofs better than ur book
obsidian night
ok, I'll check them out, thanks!
vague crag
how to put cosec in (first part)
marsh citrusBOT
how to put cosec in (first part)
sour relic
Wdym
marsh citrusBOT
@vague crag Has your question been resolved?
vague crag
what's same/different/similar about them
cot2x different
late geode
be more specific
marsh citrusBOT
vague crag
.reopen
marsh citrusBOT
✅
vague crag
be more specific
change of theta to 2x and cot to cot2
late geode
its simply just
change of theta to 2x
that already includes the change of the theta in cot(theta)
to cot(2x)
and applying that,
what would the bottom one be equal to
marsh citrusBOT
@vague crag Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
marsh citrusBOT
still temple
T is not onto, but S is
what gets mapped to (1,1)?
np
R^2 means everything (x,y)
yup
woeful glade
marsh citrusBOT
woeful lantern
A string is wound symmetrically around a cylinder. The string is twisted exactly 4 times around the cylinder. The cylinder is 12 cm long and has a circumference of 4 cm
marsh citrusBOT
A string is wound symmetrically around a cylinder. The string is twisted exactly...
sleek lake
i can solve it but only in a weird way with like, speed
woeful lantern
oh okay
sleek lake
like if it takes t seconds to move along the string, that means a speed of 12/t along the cylinder and 16/t "across"
so they add up to sqrt(400/t²)=20/t, so the string is 20 long
woeful lantern
thank you
woeful lantern
Ladder collector John has a 10-metre ladder, which he only places in one way:
it must always be set so that it stands twice as high up the wall as it stands out from the wall.
How high does John put the ladder up the wall to meet that requirement?
(The answer must be given in meters and to 4 decimal places, as John is quite precise)
marsh citrusBOT
Ladder collector John has a 10-metre ladder, which he only places in one way:
it...
woeful lantern
sleek lake
this is so much easier
woeful lantern
lmao
sleek lake
there's no way the previous one is supposed to be of this level
woeful lantern
its some quiz my teacher gave me some questions are insanely hard and some are uh 2+2
woeful lantern
this is so much easier
anyway if its easier can you help`?
woeful lantern
100?
sleek lake
yeah 100 =
traingles
square of longest side is sqaure of the other side plus the square of the other other side
woeful lantern
im lost 💀
woeful lantern
square of longest side is sqaure of the other side plus the square of the other...
so what would it be with this
<@&286206848099549185>
mighty dew
you know the pythagorean theorem?
woeful lantern
no
merry terrace
Find the value of x
mighty dew
how
mighty dew
you shouldnt be able to solve it then
mighty dew
golden sparrow
i just told it
mighty dew
you should know this
merry terrace
10 = 4x^ + x^2 right
10x=5x²
x²=2 yeah but don't give direct answer
woeful lantern
You don't know about Pythagorean theorem
i dont know all the advanced names
mighty dew
to solve
golden sparrow
my bad
merry terrace
i dont know all the advanced names
You should know it is a really basic and really famous name
(hypotenuse)²=(perpendicular)²+(base)²
Pythagorean
Use it
woeful lantern
tbh i dont know any of the names for stuff
merry terrace
Ok so
merry terrace
Here hypotenuse is the length of the ladder
Cause it is the longest side
And let's just say 2x is the perpendicular and x is the base
You can also say that x is perpendicular or 2x is base but it doesn't really matter you are gonna end up with same result
So here
The length of the ladder is 10metre
And perpendicular is 2x
Base is x
merry terrace
(hypotenuse)²=(perpendicular)²+(base)²
Putting all the things to this formula
We get
(ladder)²=x²+(2x)²
Length of the Ladder is 10m
So I am plotting it
10²=x²+4x²
Now solve it
woeful lantern
okay lemme try
merry terrace
Yeah
merry terrace
10 = 4x^ + x^2 right
I realised that it would be 100 not 10
golden sparrow
yea
woeful lantern
im just really bad at this part of math
merry terrace
im just really bad at this part of math
Bad at algebra
Use laws of exponents
100=5x²
x²=100/5=20
x²=20
x=√20
That's it
Now you find the value of 2x cause you have to find that jhon put his ladder how much high with respect to ground and wall basically the height of the wall
Find the value of 2√20
You got you answer
Adjust it into decimal places
golden sparrow
u dont need to find the value of 2root20
woeful lantern
8.944?
golden sparrow
we got the value of x
and we have the value of the ladder
and the question says that the ladder is placed at double the height of the wall
woeful lantern
yeah sorry im understanding nearly nothing
merry terrace
u dont need to find the value of 2root20
You need to find the decimal approximation
As mentioned in the question
golden sparrow
alr then find the value ig
merry terrace
alr then find the value ig
Yupp you could leave it if it was not mentioned
golden sparrow
true