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#help-0
tacit arch
lone heartBOT
lone heartBOT
Available help channel!
verbal compass
A ball is tossed into the air from the roof of a building. Its height, h metres above the ground after t seconds is modeled by the relation
h = -3.5(t – 3)² + 60
What is the height of the building
gray isle
what have you thought about
verbal compass
what have you thought about
Well at first I tried substituting t for 0 and that gave me
h = -3.5(t – 3)² + 60 h = -3.5(-3)² + 60 h = -3.5(-9) +60 h = 31.5 + 60 h = 91.5
I feel like this is wrong
ocean sealBOT
ℝamonov
verbal compass
Oh it's +9
h = -3.5(t – 3)² + 60 h = -3.5(-3)² + 60 h = -3.5(9) +60 h = -31.5 + 60 h = 28.5
This then?
gray isle
yes
gritty veldt
quick question
lone heartBOT
quick question
gritty veldt
what do you call factoring, but into additions instead of multiplications?
for example
a=b+c
gray isle
not sure how
a=b+c
shows what you're trying to describe
wdym by
into additions instead of multiplications
can you show me examples of what you mean by
factoring into additions and
factoring into multiplications
gritty veldt
oh, I think I got it,
I think the word I'm looking for is decomposition
like fourier decomposition
so
what I want is something like this
f(a,b) = g(a) + h(b) + m(a,b)
would you call this decomposition?
tacit arch
That wasn't so hard, was it
alpine sable
...
alpine sable
lone heartBOT
bitter vault
Not quite. The slope of the tangent is given by $\dfrac{dy}{dx}$. First write $y = r\sin(\theta) = 2\sin(2\theta)\sin(\theta)$, then find $\dfrac{dy}{d\theta}$. Similarly, find $\dfrac{dx}{d\theta}$. Now apply the chain rule to obtain $\dfrac{dy}{dx}$
ocean sealBOT
1345631
supple tundra
I know it's not the intended method, but you could always multiply both sides by $r^2$, and then get convert to cartesian and then implicit differentiation
ocean sealBOT
azeem321
alpine sable
Not quite. The slope of the tangent is given by $\dfrac{dy}{dx}$. First write $y...
Oh i see
supple tundra
I.e. $(x^2+y^2)\sqrt{x^2+y^2}=4xy$
alpine sable
So u convert polar to parametric
ocean sealBOT
azeem321
alpine sable
And go from there
lucid wadi
Hi
lucid wadi
isn't their answer wrong?
why did the negative disappear and ln of x change to ln 1/x
karmic rapids
why did the negative disappear and ln of x change to ln 1/x
$$-\ln{x} = -1 \cdot \ln{x} = \ln{x^{-1}} = \ln{\frac{1}{x}}$$
ocean sealBOT
illuminator3
tame hound
Carl has 15 colored balls in his pocket. The balls have three different colors. Carl randomly take the balls out of his pocket. What is then the smallest number of balls that Carl has to pick up to surely get at least one ball of each color?
Information given:
(1) 1/3 of the number of balls are black.
(2) 7 balls are red and 3 balls are blue.
Can we solve this with info 1, info 2, separately, or combined?
tame hound
(1) B = 15*1/3 = 5
5+X+Y = 15
(2) R = 7, Y = 3, X = 5
=> R+Y+X = 15
I was thinking in information (1), we don't know how many of the balls are of different colors.
Information (2), we know the color of every ball, so the information is sufficient to solve the question.
Any comments?
drifting hull
of course we can solve it in every case, we just get different answers
tame hound
Please explain how we can solve it with information one only.
drifting hull
The balls have 3 different colors, so there is at least one ball of each color. If he picks up all 15 balls, he clearly has one of each color
tame hound
Well the answer is that it can only be solved with information (2) alone, (1) is insufficient.
gray isle
15 isn't necessarily the smallest
tame hound
What do you mean by ’smallest’?
tame hound
You think my reasoning was ok?
gray isle
yes
ember token
Im stuck with these equation (factorization)):
-16t²+48t+488 = 0
ember token
I've tried to factorize it
-8(2t²-6t-61)
but i cant find common factor between the three terms
short cobalt
61 is prime
ripe rain
,w -16t^2 +48t +488
ocean sealBOT
ocean sealBOT
ember token
i did that
ripe rain
ember token
is that the furthest it can be done?
ripe rain
Yes
short cobalt
yes, but it must be with the quad formula , right?
ripe rain
yes, but it must be with the quad formula , right?
Yes
ember token
because after that i did:
2t²=0
t²=-2
And the square root of -2
And with the other
-6t = 0
t= 6
and i supposed that 6 was the answer i dont know if im correct
ripe rain
because after that i did:
2t²=0
t²=-2
Wth did you do here?
ripe rain
2t^2-6t-61=0 doesn’t mean 2t^2=0, -6t=0 and so on
hallow sparrow
How would I solve for the first five terms? The homework suggests that we need to reach the binomial series using the factoring I did in the beginning. I’m not sure how to account for variable a if I’m not doing the original Taylor series
hallow sparrow
However if I do use the original taylor series, how would I build out the terms using the original (or the factored version)?
lone heartBOT
@hallow sparrow Has your question been resolved?
hallow sparrow
<@&286206848099549185>
tacit arch
Does it say to calculate the Taylor series ? Show the instructions
What you did looks fine. I don't get why you want to use Taylor series
hallow sparrow
It asks for the first five terms
@tacit arch I'm just confused because I feel like it needs to be in a Taylor form since the center isn't 0.
The professor hinted the factor 3^(1/3) in the beginning
Which makes sense, but to use a binomial series here throws me for a loop
lone heartBOT
@hallow sparrow Has your question been resolved?
hallow sparrow
<@&286206848099549185>
shell widget
@hallow sparrow Replace x by 4x for the first one, for the second you can write it as (1+4x) (1+4x)^(1/3)
you know (1+4x)^(1/3) from the first part, multiply by (1+4x)
shell widget
ah
hallow sparrow
I ended up writing out terms using the original taylor series, despite my professor's "hint" to set it up to binomial series form
Because the binomial series form afaik doesn't account for a
I left a comment on the problem asking how to account for it
lone heartBOT
@hallow sparrow Has your question been resolved?
lone heartBOT
@hallow sparrow Has your question been resolved?
tacit arch
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violet canopy
Can someone please help me with this, the word cut at the start is “using”
limpid spade
a^(b/c) =cthrootof(a^b) right?
lone heartBOT
@violet canopy Has your question been resolved?
lost briar
hello! my question is:
Find the range of values of k if the curve y=kx^2−2x+(2k−1) lies completely above the x−axis.
I don't know where to start in answering this question, thank you!
rotund plank
hello! my question is:
Find the range of values of k if the curve y=kx^2−2x+(2k−...
It is clear that k must be positive (assuming we want a quadratic curve), since otherwise the graph would open negatively
Now what property must the graph have for it to not go below the x-axis?
(And is it sufficient)
lone heartBOT
@lost briar Has your question been resolved?
cursive badger
hint: ||what kind of roots would it have?||
bigger hint: ||what kind of roots would it have if it never touches the x axis||
biggest hint: ||since your roots are y=(-b±sqrt(b^2-4ac))/2a, for there to be no roots, b^2-4ac must be negative, making your roots imaginary (thus no intersection). plug in your a b and c values and find the k values that make the roots imaginary.||
lone heartBOT
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wary stream
Don't open multiple channels
eternal hedge
Ok
wary stream
So close this channel
mystic sinew
Why would adding x *I to a matrix not change the eigenvectors?
merry depot
work it out. What does it mean to have an eigenvector/value?
mystic sinew
work it out. What does it mean to have an eigenvector/value?
Doesn’t change the direction
But does adding xI not change dorection
oak perch
Ay=λy then (A+xI)y=(λ+x)y
lone heartBOT
@mystic sinew Has your question been resolved?
mystic sinew
Ay=λy then (A+xI)y=(λ+x)y
I don't think that's obvious
That if Ay=λy then (A+xI)y=(λ+x)y
lone heartBOT
@mystic sinew Has your question been resolved?
indigo dock
How do you write in algebraic form
lone heartBOT
How do you write in algebraic form
simple turtle
How do you write in algebraic form
with some variables x, y, z...?
lone heartBOT
@indigo dock Has your question been resolved?
indigo dock
with some variables x, y, z...?
Not what I mean
simple turtle
Not what I mean
Sorry. What do you mean?
simple turtle
Not what I mean
lone heartBOT
@indigo dock Has your question been resolved?
swift shore
@indigo dock wdym
ocean spindle
lone heartBOT
tacit arch
but the answer is -3
What about f(0)
tacit arch
in this cause would i solve for critical numbers
That's part of it yes.
ocean spindle
so i found the derivative which ended up to be
3(x+3)(x+1)
critcal values
x=-3 x=-1
tacit arch
The other part is evaluating at the boundaries
ocean spindle
so i would have to esstentially guess and check
by plugging in -4, -1 , 0, 3
into the f(x)
f'(x)*
tacit arch
That's not guessing, that's enumerating
ruby hinge
nah f(x) itself
ocean spindle
sorry f(x)*
would that process be correct
do the critical values not always tell u the ABSOLUTE max/min?
tacit arch
do the critical values not always tell u the ABSOLUTE max/min?
They do not
ruby hinge
wait u might need to take the double derivative as well
ocean spindle
sorry
then what does a critical number tell u?
when the points change direction
okok
i used desmos and noticed
ripe rain
Wait you need to understand the curve
ripe rain
i used desmos and noticed
Umm don’t desmos already bruh
ripe rain
the critical numbers 1
Do you mean point of inflection?
oak perch
Could u explain this?
Which option do you want to select
lone heartBOT
@ocean spindle Has your question been resolved?
alpine sable
help
safe needle
Write down the area of the triangle formula using known variables
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
no
lmao
mf
there are very unhelpful people and this server is innactive
cuz america is currently asleep
opaque inlet
Write down the formula for the area of a triangle
lone heartBOT
@alpine sable Has your question been resolved?
real wolf
small brain moment... why is it b and not a
lone heartBOT
small brain moment... why is it b and not a
real wolf
found the tangent of y=4x-4 not sure what they did after this to obtain (3,8)
tight locust
What
Why would the tangent be 4x-4
Do you understand the concept of differentiation?
real wolf
is the tangent rule not y=4x - 4
real wolf
oh what the answers said it was lol
tight locust
The derivative is 2x
real wolf
yes...
vital crown
found the tangent of y=4x-4 not sure what they did after this to obtain (3,8)
How did you get a from y=4x-4
tight locust
4x - 8 + 4 = 4x - 4
real wolf
get what sorry
vital crown
,calc 3*4-4
ocean sealBOT
Result:
8
Result:
0
oh
i didnt even think of that lmao wtf
testing values ahhh i see
thank you fellas
.close
lime igloo
lone heartBOT
indigo flint
What’s the name of this topic
I forgot what the | means
But I think it’s just u put 0 into x and becuase of that function ur answer turns positive
lime igloo
Modulus
indigo flint
So ur min val is 1?
lime igloo
For that I think we would have to use differentiation
indigo flint
Yeah I think it’s 1
lime igloo
Answer is 59 I suppose
indigo flint
Nah it just asks for what’s the min value u can get right?
Acc ur right
One sec
So to go from x-1 to 119x-1 we have gone 120 times
And if the minimum modulus of each function is 1, then the answer should be 120
Because the lowest real number u can put in to the function to get a low number is x=0
lime igloo
120 was coming as my answer too but exercise sheet says 59 is the answer
lime igloo
Nah
indigo flint
I don’t think differentiating will help
Does the question tell u how many marks it is
lime igloo
Ya
lime igloo
Ya
indigo flint
Is there a way u can differentiate the equation
It wouldn’t make sense tho would it
U would just get 1,2,3 and so on
lime igloo
Yes
indigo flint
I think there’s a different formula maybe but I rly can’t recall bro I’m sorry
indigo flint
wait i think figured something out
Lmk if u work it out because I kinda wanna know 😂😂😂
lime igloo
<@&286206848099549185>
lone heartBOT
@lime igloo Has your question been resolved?
rotund plank
One way to go about this is to use the absolute value inequality $\mid x - a \mid + \mid x - b \mid \ge \mid a - b \mid$
ocean sealBOT
dk.dkn
vale wigeon
One way to go about this is to use the absolute value inequality $\mid x - a \mi...
just type |. \mid wasnt made for that
rotund plank
just type `|`. `\mid` wasnt made for that
Alright, I’m used to doing it on a computer where I don’t have that button
vale wigeon
\vert is also an option
lone heartBOT
@lime igloo Has your question been resolved?
soft cosmos
Hello
soft cosmos
I have a hwfor stats and prob
i get a z score which is -25, and it is abnormally big
<@&286206848099549185>
lone heartBOT
✅
lone heartBOT
@soft cosmos Has your question been resolved?
lone heartBOT
@soft cosmos Has your question been resolved?
lone heartBOT
@soft cosmos Has your question been resolved?
alpine sable
Hi
gray isle
what have you tried?
gray isle
consider using the substitution
u = x^3
also don't forget your dx
alpine sable
oh yea
but the point is
i wanna know
how to get rid of the 3x^2
i realised i stuck at every question with the variable behind when it isn't a constant
cuz then i can't simply pull out
and thats what confuses me
@gray isle
gray isle
go through the whole process of integration by substitution starting with the substitution
u = x^3
gray isle
i know
go through the whole standard process and it'll become clear
from
u = x^3
find the relation between dx and du
rotund plank
@alpine sable Have you learnt the reverse chain rule?
alpine sable
my teacher said there is no chain rule in integration
rotund plank
reverse
gray isle
chain rule is everywhere in calculus
gray isle
u = x^3
du/dx = ?
alpine sable
3x^2
gray isle
yes
alpine sable
????
gray isle
and then du = ?
gray isle
yes...
gray isle
you have du/dx
rotund plank
What have you actually learnt in integration?
What methods do you know for integrating
gray isle
$\dv{u}{x} = 3x^2 \implies \dd{u} = , ?$
ocean sealBOT
ℝamonov
alpine sable
What methods do you know for integrating
i just know we need to reverse the differentiation method
from - *
to + divide
alpine sable
**ℝamonov**
x^3?
alpine sable
i don't seem to understand
gray isle
this is really basic algebra
gray isle
like really really basic algebra 1 algebra
gray isle
yes
rotund plank
Yea I’m not sure he’s manipulated derivatives before
gray isle
which is present in your original integral
rotund plank
You’ll learn about it soon enough
alpine sable
You’ll learn about it soon enough
nah i don't depend on my teacher
lol
also
@gray isle
what about du?
gray isle
wdym
gray isle
indicates which variable you are not integrating with respect to
alpine sable
im totally not with you lol
but its okay
:((( maybe the methods we come across are totally diff
@gray isle
gray isle
look up integration by substitution
alpine sable
IG I NOW KNOW
T HANKS TO MY FAV TEACHER
EDDIE WOO
thanks @gray isle
ughhh my teacher never taught this before
I SWEAR
rotund plank
I sort of always viewed them as separate things before
gray isle
you're starting with
$$\int \sin(x^3)\cdot 3x^2 \dd{x}$$
using the substitution: $u = \red{x^3}$ leads to $\dd{u} = \blue{3x^2\dd{x}}$
$$\int \sin\underbrace{(\red{x^3})}{u}\cdot \underbrace{\blue{3x^2 \dd{x}}}{\dd{u}}$$
$$\int \sin(u) \dd{u}$$
ocean sealBOT
ℝamonov
gray isle
which gets you something that you should definitely know how to integrate
sly mantle
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lone heartBOT
Available help channel!
wet spindle
lone heartBOT
wet spindle
okay, 88 and 888 are just trial and error right?
we only need 8 8s to get to 1000
but we still don't know how many digits we should put in a row
gray isle
consider
1000 = 8 * 125
888 = 8 * 111
88 = 8 * 11
8 = 8* 1
gray isle
have a think about it
wet spindle
hmmm
add the ones
and you'll get 125
888 = 8 * 111
88 = 8 * 11
8 = 8* 1
8 = 8* 1
8 = 8* 1
it still doesn't explain how we know it's 888 + 88 + 8 + 8 + 8 instead of 88 + 88 + 888 + 8 for example
gray isle
if you think about it properly it will
1000 = 8 * 125
adding a total of 125 8s gets you 1000
888 = 8 * 111
by adding 888 you're effectively adding 111 8s
same idea for the rest
888 = 8 * 111
88 = 8 * 11
8 = 8* 1
8 = 8* 1
8 = 8* 1
how many 8s are you effectively adding by adding
888 + 88 + 8 + 8 + 8
and compare that to
88 + 88 + 888 + 8
wet spindle
> 888 = 8 * 111
> 88 = 8 * 11
> 8 = 8* 1
> 8 = 8* 1
> 8 = 8* 1
how many 8s are y...
125
gray isle
yes
wet spindle
here why do we stop at 10?
why doesn't he continue adding 1 with nth number of 8s like he did with 40 and 20?
gray isle
they're getting to the closest multiple of 10
and in this case they must get 10 for the final sum to be 1000
wet spindle
trying the same thing with number 4
and I just realized that if you multiply an even number by 5, you'll get 0 as the last digit of the sum
with 4, I understand that you need 250 4s to get to 1000
but I still don't know how many digits I should put in a row
gray isle
consider positive integer solutions to
$$111a + 11b + c = 250$$
ocean sealBOT
ℝamonov
gray isle
for efficiency you'd want a as high as possible
lone heartBOT
@wet spindle Has your question been resolved?
wet spindle
for efficiency you'd want `a` as high as possible
wait
ok for 8, we need 8 8s to add together
for 4, we need 7 to get to 1000
right?
since
gray isle
huh?
wet spindle
Did the same with 8
8 8s is needed to get to 1000
tried the same with 4 but I couldn't get an answer
wet spindle
here we have 8 8s
here we have 7 4s
but I couldn't find any other way to get to 250
gray isle
use more 4s
gray isle
I only need 7
where's that coming from
wet spindle
just like this right?
gray isle
i don't see how that leads to the conclusion that you can get to 1000 using 7 4s
gray isle
set up the addition table properly
wet spindle
set up the addition table properly
the 4 one?
gray isle
yes
gray isle
see what happens when you try and follow their approach
note that i dislike their approach and would recommend that you just use what i set up
wet spindle
the first problem in Gelfand's Algebra and boy is it hard
lone heartBOT
@wet spindle Has your question been resolved?
wet spindle
yeah I can't solve it
lone heartBOT
@wet spindle Has your question been resolved?
ripe ore
lone heartBOT
karmic rapids
what have you done so far
alpine sable
,rotate
ocean sealBOT
graceful juniper
karmic rapids
don't spoonfeed
lone heartBOT
@ripe ore Has your question been resolved?
rotund plank
Is that $2\sqrt{2}\cdot x$ or $2\sqrt{2x}$?
ocean sealBOT
dk.dkn
sage rain
It’s telling me this is wrong
lone heartBOT
It’s telling me this is wrong
leaden shadow
I think you forgot to divide both sides by -1
sage rain
At which point do I do that?
leaden shadow
At -x²-6x=-1
sage rain
Now why do you do that?
I had an earlier problem that I didn’t have to do that
I don’t remember the professor showing us an example like that
leaden shadow
Because if you complete the square, it's not going to be correct.
lone heartBOT
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@alpine sable Has your question been resolved?
orchid path
Hello I am a student who speaks Spanish, but I do not have the help of a teacher due to the economic situation and in my school the teachers cannot help with the homework, perhaps for some this is easy, but it is difficult for me to be able to understand it, geometry has always been a weak point of mine, I have tried to solve it but it is difficult, I don't know if someone could help me with this, I have translated it, I even translate this to be able to communicate, I hope to have your help
orchid path
<@&286206848099549185>
lone heartBOT
@orchid path Has your question been resolved?
frigid fulcrum
Yes?
orchid path
Hello I am a student who speaks Spanish, but I do not have the help of a teacher...
....
dull storm
is teaching students by professors considered waste of time
since they just repeat same things and same explanations over and over again
do they consider they could spend that time more productively on research and stuff like that, science?
or do they always keep getting something out of teaching students like new ideas, new insights - stuff like that
i mean they do have time for science and everythinb but i am talking about these couple extra hours specifically
orchid path
Everything is complicated, but do you know how to solve it? In spite of everything, it is a task and if I do not deliver it I will be failed, I do not ask you to solve it, only your help to be able to solve them together
lone heartBOT
@orchid path Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
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idle spindle
anyone has tips on how to easily know if it is a one tailed or two tailed test?
hybrid skiff
surreal sinew
anyone has tips on how to easily know if it is a one tailed or two tailed test?
A one-tailed test is when you are testing if the population value is less then or greater than the null, but a 2 tailed is when you are testing if the population value is simply different from the null
idle spindle
my teacher said if its finding the paramaters its a two tailed test
is that always correct?
.close
balmy gale
If we have two independent events in probability (A and B). How do you calculate the smallest value of P[A n B]? Isn't it always 0?
lone heartBOT
If we have two independent events in probability (A and B). How do you calculate...
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sour dew
Sort of an abstract question - I have a scenario where I'm applying k++ means clustering, but I want to define each area of a centroid in the fashion of a square (doesn't necessarily have to be a square, as long as I can get some definable area) - can anyone point me to any literature or definitions that can achieve something like this?
lone heartBOT
Sort of an abstract question - I have a scenario where I'm applying k++ means cl...
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sour dew
<@&286206848099549185>
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@sour dew Has your question been resolved?
last tendon
Without really thinking about it that carefully, it just sounds like you are replacing the usual euclidean metric with the taxicab metric. I doubt scikit-learn or anything has that built in so it'd be a bit of work to code yourself.
lone heartBOT
@sour dew Has your question been resolved?
sour dew
Without really thinking about it that carefully, it just sounds like you are rep...
hm, do you have an example of what the taxicab metric would look like in clustering? how would i get the lengths of the sides for each centroid grouping
is there anyway I can ensure in that each grouping the lengths of the area are identical? even if the areas overlap
last tendon
I haven't thought enough about the problem to comment further. I would expect you would find very little literature because it will be unpleasant at best.
It looks like the MATLAB statistical toolbox has a cityblock argument: https://www.mathworks.com/help/stats/kmeans.html
If you have a license you can just open up the source code and tinker with it
sour dew
ok thank you
indigo dock
Sorry. What do you mean?
I apologise, I had a math class. What I meant was how to write algebraic equations in discord e.g. @oak perch usually writes some kind of code and then the bot reads it as an equation, like x/(x+3) except it writes it how you would on paper if you know what I mean. How do you do that?
regal schooner
it's using texit
#resources the last message here
you can use #bots for trying it out
lone heartBOT
@indigo dock Has your question been resolved?
indigo dock
it's using texit
lmfao you pinged the wrong person
lone heartBOT
lmfao you pinged the wrong person
regal schooner
lmfao you pinged the wrong person
OH my bad xD
indigo dock
<#488106178094694400> the last message here
oh thanks
Lemme try though I am still unsure
.close
lone heartBOT
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vague iris
Is dy/dx the final answer or d/dx?
lone heartBOT
Is dy/dx the final answer or d/dx?
indigo dock
Is dy/dx the final answer or d/dx?
?
indigo dock
Like this
I'm not understanding what the question is sorry? Also what level of maths is this?
Is there a question?
vague iris
Is there a question?
im asking if I should use dy/dx or d/dx for the final answer
is there a difference between the two?
indigo dock
im asking if I should use dy/dx or d/dx for the final answer
is there a differen...
I might be stupid but to me d/dx would imply that there is no y. But I cannot say for sure what you are asking without seeing the original question.
coral moss
when you differentiate you are using d/dx on both sides. For example, y=x differentiated is d/dx y = d/dx x. You are basically multiplying d/dx by y which is why you have dy/dx iirc
Because you are differentiating with respect to x
So you can either say d/dx (y) = 1 or dy/dx = 1 for y=x
It will probably make more sense when you do implicit differentiation
lone heartBOT
@vague iris Has your question been resolved?
tawny fable
Hey there
bitter vault
=> Assume T is invertible. It is thus injective and surjective. Use injectivity to conclude {T(b_1) ,..., T(b_n)} is llinearly indepedent, and use surjectivity to conclude that it also spans W.
<= Assume T sends a basis of V to a basis of W. Conclude from this that dim V = dim W, so T is an isomorphism and thus bijective.
Hope this helps you get started
round stump
all the complex numbers z such that z^2 = -5+12i
bitter vault
all the complex numbers z such that z^2 = -5+12i
No thank you.
round stump
I need the solution
bitter vault
I need the solution
That's fascinating, but it's quite rude to order people to do your homework.
vale wigeon
@round stump this channel is occupied, and also we don't give out answers.
bitter vault
not homework
Still, it's rude to order people to do what you want. Phrase your question in a more neutral way, such as "Can someone help me with the question about ...". Just saying "Find all complex .." means you are ordering people to do your work for you.
vale wigeon
Math help (AVAILABLE)
bitter vault
where I find channel
vale wigeon
^ also that
vale wigeon
@alpine sable do not encourage channel stealing.
round stump
I write . reopen but nothing changed
vale wigeon
it's when someone insists on posting their question in someone else's channel
alpine sable
Ah I see
vale wigeon
@round stump you have opened your own channel #help-14 by posting in it
now you wait for someone to come along and help you
round stump
ok
alpine sable
it's when someone insists on posting their question *in someone else's channel*
I will keep that in mind in the future
round stump
I will there
vale wigeon
@tawny fable are you still here?
alpine sable
I recognise the question he asked. It is from Linear Algebra done right book lol
Very difficult book in general
lone heartBOT
@tawny fable Has your question been resolved?
tawny fable
=> Assume T is invertible. It is thus injective and surjective. Use injectivity ...
first of all thanks
now for the =>
I am struggling on understanding how can I use the surjective to show it spans W
@bitter vault
tawny fable
We know that for every vector in W there is a vector in V s.t T(v) = w
vale wigeon
w in W, and v in V
tawny fable
yeah
vale wigeon
don't omit names when introducing things
okay, yes
and what would it mean if {Tb_1, ..., Tb_n} were to span W?
write this out formally too
tawny fable
if span{Tb_1, ..., Tb_n} = W
vale wigeon
...not what i wanted tbh
tawny fable
Then alpha_1Tb_1 + alpha_2Tb_2 + ... + alpha_n*Tb_n = 0 iff alpha_1....alpha_n = 0
tawny fable
oh sorry
vale wigeon
i wanted "every vector in W is a linear combination of Tb_1, ..., Tb_n"
tawny fable
then every vector in W can be written as a linear combination
tawny fable
But that is all assuming that it spans W
vale wigeon
you can never say "a linear combination" on its own
vale wigeon
But that is all assuming that it spans W
no, we aren't assuming anything.
i'm asking you to translate the statement "span {Tb_1, ..., Tb_n} = W" into something we can work with
and the translation i expected is: $$(\forall w \in W)(\exists c_1, \dots, c_n \in K)(w = c_1Tb_1 + \dots + c_nTb_n)$$
ocean sealBOT
Ann
tawny fable
Yeah ok
I get it
I just don't understand how does that help me with the question
like
ofc it is
assuming towards a contradiction?
Is that the way you are aming for?
@vale wigeon
wait
if {Tb_1,...Tb_n} is LI
- T is surjective
Ok I have one side
T is invertible
thus dimV = dimW
thus that set {Tb_1, ... , Tb_n} is LI with the size of n
thus a basis for W
vale wigeon
sorry am in class
tawny fable
in class?
You're a student?
You're like a hundred times better than my teacher
lol
.close
leaden tiger
need some help proving a trig equation
so i have
lone heartBOT
need some help proving a trig equation
so i have
gray ingot
how do you think you can get tan from sin and cos?
leaden tiger
yes
gray ingot
what is it
gray ingot
close, but that's the identity for tan(a+b)
leaden tiger
the bottom sign should be +
gray ingot
alright now replace 1 with tan(pi/4)
leaden tiger
i think i get it now
leaden tiger
yep, got it
theres always litterally 1 step in these question that i dont think about and i lose the entire thingg
anyway, thanks for the help!
.close
quiet sinew
is this correct? i didnt know u could cross multiply addition of fractions
quiet sinew
you need to prove 1/1-cosp + 1/1+cosp = 2cosec²p
gray ingot
is this correct? i didnt know u could cross multiply addition of fractions
yes it is correct
lone heartBOT
@quiet sinew Has your question been resolved?
tame moss
is $(k+1)!(k+1) = (k+2)!$
lone heartBOT
is $(k+1)!(k+1) = (k+2)!$
ocean sealBOT
Ziggy
blissful temple
Try k = 0, does the equality hold?
tame moss
yes
blissful temple
No, why?
tame moss
oh no it doesnt
gray isle
recall the basic definition of the factorial
blissful temple
$(k+1)!(k+2)=(k+2)!$ though by definition
ocean sealBOT
Zanarcane
normal wing
no, but (k+1)!(k+2) is
tame hound
tame hound
What part of this whole figure is shaded?
knotty spire
What have you tried?
hollow shale
What are the areas of the semicircle and the circle?
knotty spire
What two shapes do-
tame hound
What are the areas of the semicircle and the circle?
πr^2/2 and πr^2
knotty spire
is the radius of the circle r?
hollow shale
Are you sure?
tame hound
r/2
$$A_{semicircle}=\pi r^{2}\times \frac{1}{2}$$
$$A_{semicircle}=\frac{\pi r^{2}}{2}$$
$$A_{circle}=\pi (\frac{r}{2} )^{2}$$
$$A_{circle}=\frac{\pi r^{2}}{4}$$
knotty spire
good, now you can probably solve it
ocean sealBOT
AuHasard
tame hound
@knotty spire How do I find out how much is shaded now?
knotty spire
Well, you want to find out what part of the semicircle is shaded by the circle.
What would that be?
tame hound
Do I divide them?
knotty spire
Which by what
tame hound
The circle divided by the semicircle.
knotty spire
yup
tame hound
This? $\frac{\frac{\pi r^{2}}{4} }{\frac{\pi r^{2}}{2} } =\frac{2}{4} =\frac{1}{2}$
knotty spire
yes
ocean sealBOT
AuHasard
tame hound
@hollow shale Is this right?
hollow shale
Yes.
tame hound
So half of it is shaded?
hollow shale
Yes.
knotty spire
That's why we use math, and don't just eyeball it.
hollow shale
It doesn't look like 1/2, but the numbers don't lie.
lone heartBOT
@tame hound Has your question been resolved?
tame hound
The cleaner Yngwe has 4,000 less in monthly salary than the teacher Arber. Arber has two thirds as much salary as the doctor Chandra. Together, the three have as much in salary as the Member of Parliament Joar, who has 66,900 in monthly salary.
How much does Arber have in monthly salary?
tame hound
Yngwe gets 4000 less Arber. Arber has 2/3 higher salary with doctor Chandra, right? Or how do I write?
tame hound
this is what I've got so far, can someone give me more advice?
normal wing
tame hound
@normal wing So 2x/3 - 4000 + 2x/3 + x = 66900, right?
normal wing
correct
tame hound
$$66900=\frac{2x}{3} -4000+\frac{2x}{3} +x$$
$$66900=\frac{4x}{3} +\frac{3x}{3} -4000$$
$$66900=\frac{7x}{3} -4000$$
$$70900=\frac{7x}{3}$$
$$70900\times 3=\frac{7x}{3} \times 3$$
$$70900\times 3=7x$$
$$30386 ≈ x$$
@normal wing Is that right?
ocean sealBOT
AuHasard
tame hound
$$\frac{2}{3} \times 30385.7=20257.14$$
ocean sealBOT
AuHasard
tame hound
@normal wing This is Arber's salary right?
normal wing
correct
kindred wing
lone heartBOT
kindred wing
can somone help me with this
why arent we including 3 and 4
so wont it be like 6x6x6
lone heartBOT
@kindred wing Has your question been resolved?
bitter vault
so wont it be like 6x6x6
Can't get skew-symmetric matrix with those, because there is no -3, -4.
kindred wing
Can't get skew-symmetric matrix with those, because there is no -3, -4.
ahhhh ok ok thanks a lot!
.close
serene moon
Hi
serene moon
I don't understand why you would subtract 120 from 180 to get the degrees
isnt it just 120?
lone heartBOT
@serene moon Has your question been resolved?
alpine sable
how to find the percent of markup
lone heartBOT
@serene moon Has your question been resolved?
lone heartBOT
@serene moon Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
unborn jewel
Hi
unborn jewel
I need some help with b
How do you represent a ratio as a pper of 2
Power of 2*
hollow shale
,rotate
ocean sealBOT
hollow shale
What is the sequence?
unborn jewel
What is the sequence?
2^3 , 2^2, 2^1, 2^0
hollow shale
Have you found the n-th term of this sequence?
unborn jewel
Have you found the n-th term of this sequence?
Mhm
hollow shale
What is the ninth number then?
unborn jewel
,rotate
ocean sealBOT
unborn jewel
What is the ninth number then?
This
hollow shale
What is the ratio of the first number and the ninth?
unborn jewel
What is the ratio of the first number and the ninth?
Wdym ratio
hollow shale
(first number)/(ninth number)
unborn jewel
(first number)/(ninth number)
Uh 2^3/2^-5
hollow shale
And that is equal to 2^(?)
unborn jewel
And that is equal to 2^(?)
Uh 9
hollow shale
Not quite.
unborn jewel
Not quite.
8?
unborn jewel
Oh okay
hollow shale
Evaluating that gets you 256
unborn jewel
Evaluating that gets you 256
How do we calculate the position of a number that is 4096 times bigger than another number
hollow shale
Express 4096 as a power of 2.
Set the ratio of the two numbers to 4096.
This is where having the n-th term (and not just a table) comes in handy, since n is just the position, so you can solve directly for it.
lone heartBOT
@unborn jewel Has your question been resolved?
violet iron
I didn’t really understand chain rule so I don’t understand that
lone heartBOT
@violet iron Has your question been resolved?
alpine sable
do you just need to find the derivative?
oh i understand the question
so let's name 6x-5=u
then the derivative of u^4
equals 4*u^3
then you should multiply this solution with the derivative of u
so the derivative of 6x is 6
in the first column you should wright 4*(6x-5)^3
and in the second (4*(6x-5)^3)*6
so it becomes 24*(6x-5)^3
let me know if you need some more explanation
violet iron
Yeah but with chain rule
Hmm let me think and try to understand
I didn’t understand the second column part
alpine sable
to take the derivative there are some general rules
there aint no rule for the first equation
but we do recognise u^4
of which we do know how to take the derivate
so we rewrite 6x-5 as u
but ones we've taken the derivative of u^4
we still have to take the derivative of u
but we know that u is 6x-5
so we have to take the derivative of it and that becomes 6
which we multiply with the derivative of u^4
lone heartBOT
@violet iron Has your question been resolved?
tame moss
HELLO
shell widget
@tame moss Yes
shell widget
Yes
tame moss
why?
shell widget
cause they're correct?