in each ordering, we have either dan-nick or nick-dan
#help-36
runic fern
in each ordering, we have either dan-nick or nick-dan
yeah
marsh temple
7! isn't large enough
marsh temple
i'm not immediately sure what that means
runic fern
yeah im confused but what i meant is that i would draw cricles on every possible 2 people combination within the 8 then add that up with the 6! cuz it would be like 1x1x6x5x4...
marsh temple
that seems unnecessary
if you treat dan and nick as one person, you have 7! ways to order this new group
however, each way does not distinguish between dan-nick and nick-dan, so it under-counts
runic fern
yeah so then what percautions should i take
?
i know i learnt thesese things before but that was half a year ago in unit 2
marsh temple
if you treat dan and nick as one person, you have 7! ways to order this new grou...
for each of these orderings, there are actually 2 orderings that fulfil the requirement (dan-nick and nick-dan)
so how do we modify 7! to ensure it correctly counts every valid ordering?
final saddleBOT
@runic fern Has your question been resolved?
final saddleBOT
@runic fern Has your question been resolved?
slender vault
I wrote down that the answer was C but I don't know how I got there.
vital crag
I wrote down that the answer was C but I don't know how I got there.
Multiply both sides by sec(...)
vital crag
wait what?
Sorry, divide both sides
slender vault
like arcsec?
slender vault
ohhhhh
so multiply cos on both sides?
wait does it just cancel on the right side?
final saddleBOT
@slender vault Has your question been resolved?
slender vault
<@&286206848099549185>
vital crag
wait does it just cancel on the right side?
Yes that's the point
slender vault
but then what do you get after?
wintry cave
final saddleBOT
wintry cave
Reviewing for the exam and I completely forgot how to do this
tranquil pine
Reviewing for the exam and I completely forgot how to do this
I'm going to sleep gn
final saddleBOT
@wintry cave Has your question been resolved?
wintry cave
I'm going to sleep gn
Bra
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@wintry cave Has your question been resolved?
rose ravine
is this an adequate proof for hte following:
final saddleBOT
is this an adequate proof for hte following:
rose ravine
n=4k is the same as n=2(2k). k is an integer so 2k could be any integer in Z, proving n=4k is even, similarly, n=-4k+2 is euqal to n=2(2k+1) where 2k+1 is once again a valid integer that fits the definition of odd. thus if n is even, it is also equal to n=4k or n=4k+2 for some int k
barren hound
it looks to me like you've proven the other direction
you've shown that if n = 4k or n = 4k+2 then n is even
barren hound
you're not far off -- the idea of splitting into odd/even cases is probably useful
you just have to start with let n be an even integer, and end with "then n = 4k or n = 4k+2"
rose ravine
how should i rewrite it? could i just say if n is even, n =2k for some int k. could i then just slap the proof to follow this or would that be inadequate?
barren hound
if n is even, n =2k for some int k
this is how i would start (maybe i'd use a different letter though since k was already in use by the prompt)
rose ravine
> if n is even, n =2k for some int k
this is how i would start (maybe i'd use a ...
suppose n is an even integer st n=2j for some j in Z. If j is even, n can be rewritten as n=2(2k) for some integer k. thus, n=4k.
if j is odd, n can be rewritten as n=2(2k+1) or n=4k+2. Thus, for any integer j, n is equal to either 4k or 4k+2.
hows this?
rose ravine
dope
barren hound
you mean n=4k btw
rose ravine
mind if i run another by you in a sec?
rose ravine
sure
for this question, how is this proof:
since n is an integer, if 2 divides (n^4 - 7), then 2 has to also divide (n^4 -7 -2) or n^4 - 9. this is the same as (n^2 + 3) (n^2 -3). when n is even, (n^4-9) is NOT even -> (2t)^4 -9 = 16t^4 -9. that simplifies to 2(8t^4 -4) -1 or 2j -1. if n is odd, the expression is even: ((2t+1)^4)-9 is equal to 16t^4 -32t^3...... = 2(....). thus, (n^2 +3 ) is even. for n^2 to be odd, n has to be odd so n=2k+1 . (2k+1)^2 +3 = 4a^2 +4a +4 = 4(a^2 +a + 1). this is divisible by 4. thus, n^2 +3 is divisible by 4 if it is divisible by 2. thus n^4 -7 is divisible by 2 iff n^2 +3 is divisible by 4
its super convoluted but if it like makes sense logically im going with it 😭
not tryna have to rewrite it if i can avoid it
forgot to send the problem lol :p
rose ravine
thank god i got worried id have to rewrite it
barren hound
if 2 | n^4 - 7 then you can prove that n is odd
and then n = 2k+1
which gives you a pile of 4s
yeah seems fine
indigo plover
final saddleBOT
indigo plover
what am i looking at 😭
my first instinct just to go ahead and distribute the 9
thats all i know sadly if thats even a step this looks like too much
west berry
Are you aware of the quotient rule?
barren hound
this is why the quotient rule sucks
what i would do here i think
is start by letting $u = (9 + x)^{\sfrac13}$
soft zealotBOT
hayley!
dense coral
quotient rule can go die and burn
i think that forcing students to compute the first and second derivatives using it in order to get the critical points/points of inflection of a function's graph is just cruel and unusual punishment tbh
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@indigo plover Has your question been resolved?
odd crane
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odd crane
notice that (x+1) / (2x + 2) can be simplified
Hmmm
tiny gorge
what do you get if you factor a 2 out of 2x + 2
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@odd crane Has your question been resolved?
final saddleBOT
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fallow oriole
Can i get some help on this?
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@fallow oriole Has your question been resolved?
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@fallow oriole Has your question been resolved?
wild gust
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wild gust
I was a little confused on how to solve part c
of this question
just confused on how the piecewise function is supposed to be used to solve the integral
my initial thought was to look at the bounds of integration as the x values
rugged gate
u have to break it up
wild gust
u have to break it up
break what up
rugged gate
break the big integral
make it into smaller ones
i think
$\int_{-\frac{\pi}{2}}^0(1+\sin(x))}dx+\int_0^1{\frac{2}{1+x^2}}dx+\int_1^3{e^{-x}}dx$
soft zealotBOT
leo
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
wild gust
make it into smaller ones
ahh okay yeah that makes a lot of sense
because theres a different function defined for each set of boundaries
thank you so much
appreciate it
rugged gate
yes, but you also have to bound it accordingly if it is a definite integral
like taking note of the original -pi/2 and 3
wild gust
like taking note of the original -pi/2 and 3
what do you mean
wild gust
**leo**
Compile Error! Click the <:errors:504266556054962196> reaction for more ...
is this not valid?
rugged gate
it is valid
but for the piecewise function, it goes for all R
but in my answer, you can see it still goes in the bounds of the original integral
wild gust
mhm yeah thats true
like for example even though f(x) is defined as e^-x for like 50 or something
because its greater than 1
its still not in the bounds of the integral
got it
final saddleBOT
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Available help channel!
cosmic zephyr
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cosmic zephyr
do i just sub in a point onto the equation -3x+-0y+0z+1w
like i sub the n vector\
into the standerd form
.close
hollow hollow
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hollow hollow
Would anybody mind helping me with this IVT problem
So, it wants me to look for the roots but im not sure where to go from here after I found the values for A
Or am i only looking for the value A?
final saddleBOT
@hollow hollow Has your question been resolved?
late flicker
Or am i only looking for the value A?
I think you're just looking for the values of A
hollow hollow
I think you're just looking for the values of A
So then would this be right?
final saddleBOT
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Available help channel!
lavish flicker
can someone check these answers
final saddleBOT
can someone check these answers
@lavish flicker Has your question been resolved?
Available help channel!
gloomy roost
I’m really not sure where to go with this problem. I tried one thing, shown in the image, but am not sure if that was the right path
final saddleBOT
I’m really not sure where to go with this problem. I tried one thing, shown in t...
long copper
I’m really not sure where to go with this problem. I tried one thing, shown in t...
If you arent familiar with methods of solving such a DE, just subtitute values of y
gloomy roost
Do you mean just plug the answer choices into 4y?
gloomy roost
If you arent familiar with methods of solving such a DE, just subtitute values o...
I’ve only really done Bernoullis method and homogenous DEs, and can’t tell which one this should fall into if either
long copper
What methods for solving a homogenous DE
gloomy roost
All we’ve covered so far is for F(y/x)
gloomy roost
All we’ve covered so far is for F(y/x)
and substituting it for V
long copper
Well typically for DEs of this form, we take y=e^(rx) and solve for r
gloomy roost
If you arent familiar with methods of solving such a DE, just subtitute values o...
Okay, we haven’t done anything like that yet
What’d you mean by this
long copper
Do you mean just plug the answer choices into 4y?
Like you said here, and do the necessary derivation ofcourse
gloomy roost
So like this…?
final saddleBOT
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polar obsidian
,tex $\int \frac{1}{(1 - x)^2} dx$
final saddleBOT
,tex $\int \frac{1}{(1 - x)^2} dx$
soft zealotBOT
@polar obsidian
polar obsidian
^ thats the original problem
heres what i did:
,tex $$u = 1 - x$$
$$\frac{du}{dx} = -1$$
$$du = -dx$$
$$dx = -du$$
$$ $$
$$\int \frac{1}{(1 - x)^2} dx$$ $$=\int \frac{1}{u^2} d(-u)$$ $$\int u^{-2} d(-u)$$ $$ \frac{u^{-1}}{-1}$$ $$-\frac{1}{u}$$
but the textbook solution is positive
idk what im doing wrong
fossil geyser
-1 dx, yes
fossil geyser
no, just du = -dx
polar obsidian
ohhhh
fossil geyser
or, du = -1 * dx
polar obsidian
u = 1 - x
du/dx = -1
du = -dx
dx = -du
polar obsidian
so i multiply by -1 twice to make it positive?
fossil geyser
u = 1 - x
du/dx = -1
du = -dx
dx = -du
Look at your last line here
soft zealotBOT
@polar obsidian
fossil geyser
du literally is -dx
and dx is -du
so just replace dx with -du
I wouldn't bother with things like d(-u)
polar obsidian
I wouldn't bother with things like d(-u)
and i shoud just to -du?
fossil geyser
yes, replace dx with -du
polar obsidian
ok
fossil geyser
u = 1 - x
du/dx = -1
du = -dx
dx = -du
just like your work here says
polar obsidian
,tex $$u = 1 - x$$
$$\frac{du}{dx} = -1$$
$$du = -dx$$
$$dx = -du$$
$$ $$
$$\int \frac{1}{(1 - x)^2} dx$$
$$=\int \frac{1}{u^2} -du$$
$$=\int u^{-2} -du$$
$$=-1 \times \frac{u^{-1}}{-1}$$
$$=\frac{1}{u}$$
$$=\frac{1}{x - 1}$$
soft zealotBOT
@polar obsidian
fossil geyser
looks good. Your multiplication by -1 looks like subtraction, but other than that, the work is right
polar obsidian
looks good. Your multiplication by -1 looks like subtraction, but other than tha...
eh my teachers ok with that
thx for helping me!
fossil geyser
eh my teachers ok with that
I'd wrap the - in parentheses like (-1) just in case
but yeah, no problem 👍
polar obsidian
,tex $$\int \sqrt[2]{\tan(x)} \sec^2(x) dx$$
soft zealotBOT
@polar obsidian
fossil geyser
Do you have an idea of the substitution you want to make for this one?
fossil geyser
yes
polar obsidian
but idk exactly how to use tan in my u variable
fossil geyser
however you want
Or I mean, you can do it however you want
but what seems helpful?
if you know d/dx tan(x) = sec^2(x)
You need your du to be something you can express as du = (something) dx
and you have sec^2(x) dx in your integral
fossil geyser
you can do anything. Try it and see what happens
fossil geyser
and `int sqrt(u) du/dx dx`
but yes this seems promising
polar obsidian
,tex $\int \sqrt[2]{u} \times \frac{du}{dx}dx$
fossil geyser
yeah
soft zealotBOT
@polar obsidian
polar obsidian
and now i cancel out dx
fossil geyser
you've got it
polar obsidian
,tex $\int \sqrt[2]{u} du$
soft zealotBOT
@polar obsidian
polar obsidian
then i use power rule to integrate?
fossil geyser
yes indeed
polar obsidian
then substitute u in the resulting integral with tan(x)
fossil geyser
after integrating, yes
polar obsidian
,tex $$u = \tan(x)$$ $$ $$
$$\int \sqrt[2]{\tan(x)} \sec^2(x)dx$$
$$\int \sqrt[2]{u} \frac{du}{dx} dx$$
$$\int \sqrt[2]{u} du$$
$$\int u^{\frac{1}{2}} du$$
$$\frac{2}{3} u^{\frac{3}{2}} + C$$
$$\frac{2}{3} \tan^\frac{3}{2} (x) + C$$
fossil geyser
+C
polar obsidian
oh right
fossil geyser
watch out, you flipped the exponent in the last step there
soft zealotBOT
@polar obsidian
polar obsidian
watch out, you flipped the exponent in the last step there
thx for catching that
fossil geyser
np, looks good 👍
polar obsidian
,tex $$u = 1 - x$$
$$\frac{du}{dx} = -1$$
$$du = -dx$$
$$dx = -du$$
$$ $$
$$\int \frac{1}{(1 - x)^2} dx$$
$$=\int \frac{1}{u^2} -du$$
$$=\int u^{-2} -du$$
$$=-1 \times \frac{u^{-1}}{-1} + C$$
$$=\frac{1}{u} + C$$
$$=\frac{1}{x - 1} + C$$
soft zealotBOT
@polar obsidian
fossil geyser
that looks good as well, but I'd refrain from doing things like $\int \frac{1}{u^2} - du$
soft zealotBOT
tatpoj
soft zealotBOT
tatpoj
fossil geyser
otherwise it looks like you're referring to subtraction
final saddleBOT
@polar obsidian Has your question been resolved?
pearl bane
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pearl bane
Can anyone help me with this one?
final saddleBOT
Can anyone help me with this one?
tulip coyote
Do you have an idea of how to start?
pearl bane
Partial fractions i think
tulip coyote
Those would be useful sure 
but before that, is there something you're thinking of doing first?
pearl bane
I have no idea how to start
final saddleBOT
@pearl bane Has your question been resolved?
pearl bane
<@&286206848099549185>
velvet moat
Do you know how to do polynomial division
You do that then you can do a partial fraction decomposition
For the partial fraction decomposition, think about how you can factor the denominator x^2-x, and how you can write your whole fraction as an addition or subtraction of those factors
pearl bane
Let me try that
final saddleBOT
@pearl bane Has your question been resolved?
flint iron
final saddleBOT
flint iron
this is all i need lol
modest birch
do you know what perpendicular bisector means?
flint iron
yes
modest birch
so at the very least, you can write two statements in there about CE and EF and angles CED and FED, yeah?
flint iron
true yeah
modest birch
then see what else you can conclude
writing proofs ain't about guessing what to write; it requires you to think about what you know and what you can logically conclude from it
flint iron
thats where im stuck how do i prove the congruence of the outside angles if i only have the perpendicular bisector and its given angles
modest birch
which outside ones? C and F?
flint iron
yes
modest birch
you don't have to
the idea here is to prove the two triangles are congruent, and then you can conclude that the corresponding sides are congruent, yeah?
flint iron
yes, but how would i go by doing that with only two pieces of information
modest birch
see if you can find a third piece of information
look at the two triangles that you want to prove to be congruent
and see what you can say about their corresponding parts
would you like me to walk you through that?
flint iron
yes please
modest birch
okay, let's start with CE and EF
what can you say about them from the information you're given?
flint iron
well im not sure theyre congruent but they share a similar fact that they are split by the perpendicular bisector
and theyre both perpendicular to DE
modest birch
why are you not sure that CE and EF are congruent?
can you write out the definition of perpendicular bisector?
flint iron
ohh shit
i forgot about the fact that it splits it in half lmao
thank you
makes a hell of a lot more sense knowing that
modest birch
what about CD and DF? can you say anything about them with the information you're given?
flint iron
well if the triangles are congruent by side angle side then they would be congruent aswell
modest birch
so you already know that the triangles are congruent by SAS?
final saddleBOT
@flint iron Has your question been resolved?
leaden sparrow
I just have a quick question, does these two mean the same? I'm new to summations so I am not sure
final saddleBOT
I just have a quick question, does these two mean the same? I'm new to summation...
soft zealotBOT
dr. matlab plot
final saddleBOT
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Available help channel!
idle terrace
help
idle terrace
simplifying
where do i go from here
or i guess what is a good method to simplify these types of problems?
formal trail
try to factor out any common quantities, and apply the pythagorean identities as much as possible
idle terrace
i went to here
idle terrace
try to factor out any common quantities, and apply the pythagorean identities as...
yeah okay
idle terrace
any ideas on where to go from here though? @formal trail
formal trail
you have a common factor in 2/3 terms
formal trail
yes
idle terrace
i can't read this respectfully 😭
formal trail
try to see what you can do to simplify inside the parentheses
tranquil pine
😦
idle terrace
try to see what you can do to simplify inside the parentheses
i mean i can make it tan^2
but that doesn't really help
i don't think
formal trail
tranquil pine
this -1 will cancel the +1
idle terrace
that's really interesting
formal trail
(you can get the second two by dividing the first one by cos^2(t) and sin^2(t) respectively)
idle terrace
idle terrace
yes or no? @formal trail
formal trail
yes. but you can go further than that even
formal trail
i would focus on the definition of sec^2(t)
tranquil pine
nahh leave it ig i am wrong
formal trail
yes
idle terrace
this really helps, but what is a good way to remember all of these identities?
like a good way to do all of this algebraically without memorizing them
formal trail
if you know the first one, the second one you get by dividing both sides by cos^2(theta) and the third one you get by dividing both sides by sin^2(theta)
idle terrace
if you know the first one, the second one you get by dividing both sides by cos^...
the first what?
idle terrace
if you know the first one, the second one you get by dividing both sides by cos^...
oh so memorize the first identity?
then just divide the 2?
so much memorization in trig.. man
formal trail
,, \sin^2\theta + \cos^2\theta = 1 \
\frac{\sin^2\theta}{\cos^2\theta} + \frac{\cos^2\theta}{\cos^2\theta} = \frac{1}{\cos^2\theta} \
\tan^2\theta + 1 = \sec^2\theta
soft zealotBOT
cloud
formal trail
very similar process for the other one
idle terrace
@formal trail you still there?
rq
why can't I square the sides of those identities?
like are these not equal?
formal trail
because
$$(1 + \tan\theta)^2 \ne 1^2 + \tan^2\theta$$
soft zealotBOT
cloud
idle terrace
wait
so it would turn into
because you can't break up 1 and tan?
like this is not possible
because you can break up square roots right?
formal trail
in general $\sqrt{x^2} = \abs{x}$
soft zealotBOT
cloud
formal trail
you need the absolute value bars for the equality to hold true for all θ
formal trail
because you can break up square roots right?
you can't break up square roots like that, no.
idle terrace
also is there a better program to use than word for math
it's so annoying with trig functions 😭
idle terrace
you can't break up square roots like that, no.
okay that's what i was missing
i was thinking that $sqrt(a+b)=sqrt(a)+sqrt(b)$
soft zealotBOT
ScriptedEli
i was thinking that $sqrt(a+b)=sqrt(a)+sqrt(b)$
idle terrace
$sqr(a+b)=sqr(a)+sqr(b)$
soft zealotBOT
ScriptedEli
idle terrace
how do you do sqrt lol
idle terrace
**ScriptedEli**
```latex
i was thinking that $sqrt(a+b)=sqrt(a)+sqrt(b)$
```
which i forgot this is not true
$√(a+b)≠√a+√b$
soft zealotBOT
ScriptedEli
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
formal trail
all you need to type is something like "sin \theta" and it should take care of the rest
,,\sqrt{a+b} \ne \sqrt{a} + \sqrt{b}
soft zealotBOT
cloud
formal trail
,,\sqrt{\cos^2\theta} = \abs{\cos\theta}
soft zealotBOT
cloud
idle terrace
**cloud**
i'm confused
i'm trying to rewrite cos in the form of sin
like only using terms that have sin in them
formal trail
if $\cos\theta$ is negative, then $\sqrt{\cos^2\theta} \ne \cos\theta$ (square root is always positive)
soft zealotBOT
cloud
formal trail
the absolute value is needed whenever you take the square root of a quantity squared (unless you can be sure it's always positive)
idle terrace
man this sucks LOL
it's getting really tough ugh
here's the question
not sure if i'm on the right track or not
formal trail
try to rewrite the two fractions on the left with a common denominator so you can add them
idle terrace
try to rewrite the two fractions on the left with a common denominator so you ca...
omg i did it
formal trail
yes
formal trail
Feels like a little bit of luck tbh
to be fair the question was set up to simplify nicely that way
trig class is one of those classes where it looks very easy once you know how to do it but until then you just try different things until you get a sense for what works
lean dawn
final saddleBOT
lean dawn
I did this correct right?
whole halo
yea thats clean
you can also consider the shaded as a sideways triangle
(with base 2 and height 4)
lean dawn
Sideways triangle ?
whole halo
a triangle with the base on the left and the height being horizontal
lean dawn
Oh yea
And also it its from two corners so it cross through the middle
Therefore the top left triangle fits into the blue one
Ok ok ty
whole halo
np
lean dawn
.close
final saddleBOT
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Available help channel!
fallow oriole
Can some one please help me with this
final saddleBOT
Can some one please help me with this
@fallow oriole Has your question been resolved?
final saddleBOT
@fallow oriole Has your question been resolved?
fallow oriole
<@&286206848099549185> 🥺
urban tundra
Can some one please help me with this
whats the question
final saddleBOT
@fallow oriole Has your question been resolved?
final saddleBOT
@fallow oriole Has your question been resolved?
verbal steppe
Given two vectors in R^5, u = (2, 1, −1, 1, 3)^T and v = (1, −1, 2, 1, 1)^T. Divide the vector u into two mutually orthogonal components, u = u′ + u′′, where u′ is parallel to v and u′′ ⊥ v (check your answer!).
final saddleBOT
Given two vectors in R^5, u = (2, 1, −1, 1, 3)^T and v = (1, −1, 2, 1, 1)^T. Div...
verbal steppe
When i get a question like this, how should i think?
I know that a vector is orthogonal when the dot product between them = 0
So i can potentially make
$(2,1,-1,1,3) \cdot (x,y,z,a,b) = 0$
soft zealotBOT
Merineth
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Available help channel!
lunar gazelle
Are there any graphical calculators that allow you to, for example, set the x axis to x^2?
final saddleBOT
Are there any graphical calculators that allow you to, for example, set the x ax...
robust mulch
i dont think so, but you should be able to input f(sqrt(x)) if you want to something like setting the x axis to x²
lunar gazelle
.close
potent idol
Hello I have one question regarding multiplying permutations.
Is it possible to multiply more than 2 permutations? Let's say
a = (1, 3, 5, 2)
b = (1, 6, 3, 4)
c = (1, 5, 2, 3)
abc = (1, 3, 5, 2)(1, 6, 3, 4)(1, 5, 2, 3) ?????????
what would be output of this????
final saddleBOT
Hello I have one question regarding multiplying permutations.
Is it possible to...
potent idol
i cannot find any info about this on the internet
stone wagon
Hello I have one question regarding multiplying permutations.
Is it possible to...
yes, moreover it's associative
potent idol
hm alright. so what would be the output of it?
also thank you for a reply
oh i think i made a mistake with c permutation
so i would be something like:
stone wagon
can you evaluate just (1, 3, 5, 2)(1, 6, 3, 4)?
final saddleBOT
@potent idol Has your question been resolved?
potent idol
can you evaluate just (1, 3, 5, 2)(1, 6, 3, 4)?
I'll try but i started learning this today
So it'll be something like
1 2 3 4 5 6
6 2 4 1 5 3
6 1 4 3 2 5
???
aaaaaa
so in other form it'll be
1 2 3 4 5 6
6 2 4 1 5 3
6 1 4 3 2 5
1 -> 6
6 -> 5
5 -> 2
2 -> 1 so we close it
then
3 -> 4
4 -> 3
so in summary it'll be (1, 6, 5, 2)(3, 4)??
how do i now multiply it with c?
so abc is
1 2 3 4 5 6
5 3 1 4 2 6
5 4 6 1 2 3
2 4 6 3 1 6
am i right??? it looks wrong with those two 6
idk if it's even possible as i came up with this c permutation by myself, the other two are from some pdf
@stone wagon what you think
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past bronze
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past bronze
i do not understand this
final saddleBOT
i do not understand this
past bronze
first of all how did he do the table?
i did my table like this : -pi | 0 | pi | 3pi
and then pick a random value between these 2 intervals , ex ( -pi and 0 )
i also do not understand how 2pi is an inflection point
it should be pi
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olive turtle
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olive turtle
can someone explain the steps to answer this question?
i'm having trouble with counting the elements of X
(if unclear P(X) is the powerset of X)
viscid fossil
P(X) has 2^|X| elements
olive turtle
P(X) has 2^|X| elements
yes that's fine
but when counting the elements of X
is it 4, or is it 3?
viscid fossil
4
olive turtle
so it'll be 2^4 U the 4 elements of X?
viscid fossil
Remember that the 2^4 already contains the elements of X as sets individually
olive turtle
Remember that the 2^4 already contains the elements of X as sets individually
yes so their union would be 2^(|X|) + 1
for the empty set?
viscid fossil
Minus 1
olive turtle
uhh
viscid fossil
Because you don't want to double count the empty set
olive turtle
but the answer that is given is 17
olive turtle
Because you don't want to double count the empty set
yeah i get that
i'm confused, shouldn't it be 16?
<@&286206848099549185>
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wary atlas
please help me with question c). Im having trouble proving that the left hand side is equal to the right. I don't know what to do next because I'm stuck here.
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please help me with question c). Im having trouble proving that the left hand si...
wary atlas
sorry i mean question b
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fair coral
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fair coral
Any ideas
fair coral
I keep going in circles
soft zealotBOT
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tired plume
Okay basically you want to involve the Geometric mean
Use the log rule: log(A)+log(B)=log(AB) to simplify the sum!
fair coral
That’s the next part
Of the question
Can’t use it here
I have to involve log(t)<t-1 somehow
tired plume
Nope?
tired plume
I believe you're trying to show that inequality right?
tired plume
Ah yes my bad, too tired haha
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tired plume
Im thinking you need more than this inequality but this question looks well written
Have you tried with just 2 variables?
limber isle
help!!
limber isle
i dont understand how to do this
inland kettle
it's just standard form
final tangle
"standard" is vague
what it describes depends on where your from
odd garnet
Third option is the correct ans
final tangle
general would be a better description
elfin oak
Standard doesn't matter
As 3 options are not even the same equation
final tangle
as "standard" is also used to refer to vertex form
limber isle
can someone give me like a step by step list
final tangle
based on context, rearrange equation so that one side is 0
odd garnet
A step by step list of?
final tangle
and combine the like terms /simplify
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autumn geode
simple proof but idk how to do it $n\binom{2n-1}{n-1}=\sum _{k=1}^n\left(k\right)\binom{n}{k}^2$
final saddleBOT
simple proof but idk how to do it $n\binom{2n-1}{n-1}=\sum _{k=1}^n\left(k\right...
soft zealotBOT
nosqldb
autumn geode
ig the hint is differentiate binomial thm
autumn geode
Almost everything comes from binomial
mhm
rustic wedge
hi hope you are doing well
I am wbu
rustic wedge
rustic wedge
I mean think abt it how do u get the binomial coefficient squared
rustic wedge
n * 2^n-1 = \sum from k = 0 to n of k (n chooose k)
Yeah that's the easy part
autumn geode
Yeah that's the easy part
but how do I go from here
autumn geode
I mean think abt it how do u get the binomial coefficient squared
I mean ig like
(2n choose n)
or sm like that is equal to the sum of the squared
autumn geode
This can explain better than md
Yeah but my prof was like differentiate binomial
And the answers don’t
<@&286206848099549185>
rustic wedge
Yeah but my prof was like differentiate binomial
There is one in thread iirc
autumn geode
There is one in thread iirc
Wait where
Nahhh you’re capping
Nah nvm
It’s there
Thank you
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sacred lynx
i got a 60 degree angle in that angle there is a point thats distanced from the side by sqrt7 and 2aqrt7 i need to find the distance from that point to the corner
final saddleBOT
i got a 60 degree angle in that angle there is a point thats distanced from the ...
reef sparrow
do you have drawing?
final saddleBOT
@sacred lynx Has your question been resolved?
reef sparrow
can you also give names to all the points on the drawing?
so it would be easy to explain
reef sparrow
so, we have to find length of AM
first of all, you need to notice that points A, B, M, C lie on the same circle
sacred lynx
wym circle?
reef sparrow
ABMC is cyclic quadrilateral, do you see why?
sacred lynx
nope
reef sparrow
<ABM + < ACM = 180
reef sparrow
ABMC is cyclic quadrilateral, do you see why?
AM is the diameter of this circle
so all you have to do is to find radius
it's easy to find with triangle BMC
sacred lynx
BMC how?
ik 2 sides
how do i find BC
@reef sparrow
idk what to do how do i find it?
@reef sparrow
reef sparrow
cosines law gives you BC
sacred lynx
cos60?
reef sparrow
cos(120)
reef sparrow
use law of sines to find radius
sacred lynx
wym how?
reef sparrow
https://en.wikipedia.org/wiki/Law_of_sines here is the law of sines
and you can find radius directly using this
sacred lynx
would it be 2sqrt7/2sin120 degrees
reef sparrow
yes, but you have mistake in calculations
reef sparrow
yes
sacred lynx
so i put in 7 in the sin law?
reef sparrow
yes
reef sparrow
yes
sacred lynx
can you explain every step we did so i get the problem better
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sacred lynx
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rich linden
I need help with this problem
final saddleBOT
I need help with this problem
rich linden
I need to know where to place the diging parts and the added parts on this problom and on witch number line
.close
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tranquil pine
it is correct that the norm of x= sqrt (x*x)
final saddleBOT
it is correct that the norm of x= sqrt (x*x)
tranquil pine
it is to do with triangle inequalities
magic sparrow
Okay then normally the norm of x is sqrt(x*x) yes
unique aspen
||x|| is the norm usually
tranquil pine
it says that in the book
magic sparrow
now when you do the norm and compute it
unique aspen
and it's just a fact that ||x|| = sqrt(x dot x)
magic sparrow
you will see why it equals that
unique aspen
like that's how it's defined
magic sparrow
like that's how it's defined
for the 2-norm
tranquil pine
oh my bad i should've mentioned
if x,y are orthogonal then
= norm of x^2 + norm of why^2
the proof is then that
is equal to (x+y)*(x+y)
@magic sparrow
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slate quest
I’m calculating this wrong in my calculator I keep getting negative
final saddleBOT
I’m calculating this wrong in my calculator I keep getting negative
unique aspen
I’m calculating this wrong in my calculator I keep getting negative
make sure you're using degrees, not radians
normal hill
What r u putting into your calculator
eager stirrup
how would i find the constant and do this
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how would i find the constant and do this
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unreal timber
why does the symbol change?
final saddleBOT
why does the symbol change?
vivid apex
tiny gorge
if you have a positive number less than 1 and you take it to higher and higher powers, what happens?
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unreal timber
if you have a positive number less than 1 and you take it to higher and higher p...
OHHH
thank u sm bro
jovial crag
hii
unreal timber
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scarlet plank
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spice zinc
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spice zinc
k is a constant
how did they integrate the right side and get Tsubs e^kt
like how does the k dissapear when the inegral happens
wait i got it
thank you
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tranquil pine
NEED HELP PLEASE
final saddleBOT
NEED HELP PLEASE
tranquil pine
caps
tranquil pine
alright which one do you need help with
is a the quotient rule it is yea
hello?
tranquil pine
is a the quotient rule it is yea
yes
so u = e^x^2 yea
v = x^2 + 1
whats the asnwer help me out
keen prism
u still need help?
soft zealotBOT
riemann
tranquil pine
I need help, how is the answer is not KM, KL, LM
final saddleBOT
I need help, how is the answer is not KM, KL, LM
unreal anvil
because it's from smallest to largest
tranquil pine
I need help, how is the answer is not KM, KL, LM
Smallest to Largest
NOT: Largest to Smallest
oh wait ok
is KL also 24?
i know LM is 24 and KM is 98 but im not sure if KL would be 24
That information is not provided anywhere in the picture
You are confusing angles with sides
oh
do i just ignore the angles and look at the trianlge itself ?
unreal anvil
do i just ignore the angles and look at the trianlge itself ?
nope
hint: how are an angle and it's coorespdoning opposite side related?
tranquil pine
the angle is the angle of the opposite side?
hushed flax
Am I crazy or does the question not make sense?
final saddleBOT
Am I crazy or does the question not make sense?
hushed flax
Wait
I might be slow
What I did was I formed the equation into like P=y((y-4)/4) and then I didn’t really know what to do after that
Then I thought to myself how to solve this logically, and I thought that I could use the fact it’s multiple choice to my advantage
But idrk rn
I feel like this question is supposed to be easy but I’m slow
blissful meadow
What does P look like as a function of y?
hushed flax
I took the equation and solved for x, and x = (y-4)/4
Then plugged that into the function P=yx, where I am trying to minimize it
blissful meadow
Yeah I get that, but let's just consider the product to be a function of y, so you have $p(y) = y\frac{y-4}{4}$
soft zealotBOT
Azyrashacorki
blissful meadow
It's a parabola yes?
hushed flax
Yea
blissful meadow
And is it opening upwards or downwards?
hushed flax
Upwards
blissful meadow
So where do parabolas opened upwards generally have a minimum?
blissful meadow
You could do that.
You could also complete the square since this is at the vertex.
hushed flax
Rightt
blissful meadow
Either is fine.
silk marlin
blissful meadow
$$y(y-4)/4 = \frac{1}{4}y^2 -y = \frac{1}{4}(y^2 - 4y) = \frac{1}{4}((y-2)^2 - 4) = \frac{1}{4}(y-2)^2 - 1.$$
soft zealotBOT
Azyrashacorki
hushed flax
So does that mean the answer is 1?
blissful meadow
-1
blissful meadow
Yeah, y=2, but p is the product.
hushed flax
Am I crazy or does the question not make sense?
After plugging it back here I get -1/2
Oh wait why did I think that was a positive number
blissful meadow
In this case y is the "x-axis", so you want the value of height of the vertex.
i.e. -1
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shell copper
I had a math problem on today's regional Olympiad that I sadly didnt have time to solve 😦 Could you pls help me?
So I need to find out is there a natural number n that is bigger than 10^100 and so n^2 and (n+1)^2 are the same but with the numbers rearranged, for example 13^2 and 14^2 are 169 and 196
But I need n to be more than 10^100.
final saddleBOT
I had a math problem on today's regional Olympiad that I sadly didnt have time t...
shell copper
I had a math problem on today's regional Olympiad that I sadly didnt have time t...
Or I can prove that there is no such a number
trail crest
You needed to existence or to find it
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brisk spade
Im not that good but can u use math proof by induction method ?
shell copper
Yes I think
shell copper
BrBruh don't tell me it's that simplesimple
brisk spade
I mean you can try
shell copper
What is happening wwith my keyboard lol
brisk spade
not every helper here is a prof
shell copper
I mean you can try
yea, thanks a lot
shell copper
Thanks again
shell copper
.close
fringe root
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autumn geode
WOAH
what an amazing q
now
let's rewrite this a little and I think you can do this
$log(3a) + log((\frac{a}{6})^2)$
soft zealotBOT
nosqldb
soft zealotBOT
! What the hell am I doing here?
fringe root
then what would it be
cold gorge
3a * (a/6)^2
This
fringe root
then?
cold gorge
What then?