maybe start with them
#help-36
tiny gorge
tranquil pine
okay but how do u do that
tiny gorge
what is the area of a rectangle?
tranquil pine
lxw
tranquil pine
90
tiny gorge
yep and there are two of them, so they contribute 180 total
the other four faces will take more work
which one do you want to start with?
tranquil pine
ad
tiny gorge
all right, so the top of the tunnel
tranquil pine
yh
tiny gorge
any thoughts on how to compute that?
tiny gorge
notice that it's half of a cylinder
do you know how to compute the area of a cylinder
say of radius r and length l
tranquil pine
2 pie r l + 2 pie r ^2
tiny gorge
where do the two terms come from
tranquil pine
x+1/x+2=0,75 so how we can fınd x?
final saddleBOT
x+1/x+2=0,75 so how we can fınd x?
tranquil pine
<@&286206848099549185>
soft zealotBOT
Ann
tired walrus
!15m
final saddleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
tranquil pine
how can ı find x?
tired walrus
that depends on what equation you meant.
tranquil pine
ı mean x+1:x+2=0,75
tired walrus
did you mean $$x+\frac{1}{x}+2=0.75$$ or did you mean $$\frac{x+1}{x+2}=0.75?$$
soft zealotBOT
Ann
tranquil pine
yes
tired walrus
start by multiplying both sides by (x+2). this will turn your equation into a linear one.
optional: also multiply both sides by 4.
tranquil pine
it's 2x+2:2x+4 rn right?
tired walrus
ok first off
when you write fractions in plaintext
you have to put parentheses around the numerator and denominator
so your original equation must be written as
(x+1)/(x+2) = 0.75
this way there is no miscommunication of the kind that happened with us
tranquil pine
so your original equation must be written as
(x+1)/(x+2) = 0.75
here
tired walrus
but you definitely didn't follow my instruction.
tranquil pine
yes i didnt understand
tired walrus
start by multiplying both sides by (x+2). this will turn your equation into a li...
.
multiply both sides by (x+2).
like this:
\
$\frac{x+1}{x+2} \cdot (x+2) = \frac34(x+2)$
soft zealotBOT
Ann
tranquil pine
where did the 3/4 come
tired walrus
it's the 0.75
tired walrus
ok and now the right side is 2x+2/2x+4
no
tranquil pine
😨
tired walrus
you are missing parentheses again and you are also multiplying very incorrectly
i have to go, sorry
stoic temple
wicked hinge
$hi$
soft zealotBOT
David K.
wicked hinge
$\frac{x+1}{x+2}•(x+2) //. \. $
half salmon
$\frac{(x + 1)(x + 2)}{x + 2} = \frac{3(x + 2)}{4}$
soft zealotBOT
dragonbreath
wicked hinge
$\frac{x+1}{x+2}•(x+2) = \frac{x²+3x+2}{x+2}$
soft zealotBOT
David K.
half salmon
when multiplying with things in the parenthesis you have to multiply by everything in the parenthesis independently
wicked hinge
**dragonbreath**
$\frac{(x+1)(x+2)}{x+2}$
half salmon
I am going to guess you are on phone or a computer/laptop that has access to use powers and special symbols for math
soft zealotBOT
David K.
wicked hinge
Cancel out x and 2
half salmon
@tranquil pine
wicked hinge
$x-1$
soft zealotBOT
David K.
soft zealotBOT
David K.
final saddleBOT
@tranquil pine Has your question been resolved?
lunar forum
final saddleBOT
lunar forum
anyone worked with this before?
spent all day on it, im just reading the book myself. i did the two problems before this
final saddleBOT
@lunar forum Has your question been resolved?
final saddleBOT
@lunar forum Has your question been resolved?
brisk charm
final saddleBOT
@lunar forum Has your question been resolved?
final saddleBOT
how do i do this
quick flax
hemlo, im not sure how to say this in english properly so tell me if there's something you need further clarification on
item c wants you to factor the given polynomial
this simply means to find all the smaller polynomials that have a product of x^3 - x^2 - 5x - 3
to explain further, here is an example:
( x +1 ) and ( x + 2 ) are factors of ( x^2 + 3x + 2 ) since the product of ( x + 1 ) and ( x + 2) is ( x^2 + 3x + 2 ),
therefore if we want to factor the expression ( x^2 + 3x + 2 ), the answer would be
( x^2 + 3x + 2 ) = ( x + 1 ) * ( x + 2 )
final saddleBOT
@vocal grove Has your question been resolved?
vocal grove
hemlo, im not sure how to say this in english properly so tell me if there's som...
what would be right in this case?
quick flax
im sorry, can you rephrase the question?
vocal grove
im sorry, can you rephrase the question?
You gave an example
but instead of using an example
vocal grove
how do i do this
how do you do it in task c
quick flax
i see i see
kindly refer to the last 2 lines in my previous message as basis but to reiterate:
problem: factor the expression ( x^2 + 3x + 2 )
answer in sentence form: the factors of ( x^2 + 3x + 2 ) are ( x + 1 ) and ( x + 2 )
answer in equation form: ( x^2 + 3x + 2 ) = ( x + 1 ) * ( x + 2 )
i hope this helps
vocal grove
hemlo, im not sure how to say this in english properly so tell me if there's som...
I still dont know how I do task c
quick flax
before I proceed, may i ask if you are familiar with long divison in polynomial?
vocal grove
before I proceed, may i ask if you are familiar with long divison in polynomial?
I know how to do polynomial divison
thats how i did task b
This is task b
quick flax
that's great, we can utilize your solution in b to answer c
i'll refer to my example again as basis but this time i'll incorporate your process in b
example b. solve the equation ( x^2 + 3x + 2 )
answer: -1 and -2 (i won't provide the solution here for now but if you need it, just ask)
example c. factor the expression ( x^2 + 3x + 2 )
answer:
from b, we have ( x = -1 ) and ( x = -2 ), then we have
x = -1
-> x + 1 = -1 + 1 (added 1 to both sides)
-> x + 1 = 0
and
x = -2
-> x + 2 = -2 + 2 (added 2 to both sides)
-> x + 2 = 0
Therefore,
the factors of the expression ( x^2 + 3x + 2 ) are ( x + 1 ) and ( x + 2 )
i.e ( x^2 + 3x + 2 ) = ( x + 1 ) * ( x + 2 )
in your case, your answer in b are -1, -1, and 3
vocal grove
i'll refer to my example again as basis but this time i'll incorporate your proc...
but can you solve the task, because I've tried many times and still dont get it
quick flax
have you tried the approach i've introduced in answering c?
vocal grove
have you tried the approach i've introduced in answering c?
Ive tried but i couldnt do it
quick flax
may i see your attempt?
vocal grove
I erased it all
quick flax
let's start with x1
we need the right hand side of the equation to be 0
thus we need to turn -1 to 0
we can do this by adding 1 to -1 since -1 + 1 = 0
if we add 1 in one side of the equation, we'll have to add 1 to the other side of the equation
thus from x1 = -1
this will turn to x1 + 1 = -1 + 1
and then will become x1 + 1 = 0
this is our first factor ----> ( x + 1 )
have you followed?
quick flax
to clarify, + 1 is not a factor,,, the factor is x + 1
vocal grove
to clarify, + 1 is not a factor,,, the factor is x + 1
so its the opposite of the answers?
because they need to cancel each other to get 0
so
quick flax
that's the idea yes
vocal grove
(x+1)(x-3)(x+1)
quick flax
(-1+1)(3-3)(-1+1)
this is not necessary anymore
quick flax
(x+1)(x-3)(x+1)
you can stop here
vocal grove
you can stop here
How do i do task d
quick flax
how do i do this
bump
quick flax
i think shorten here means to simplify
vocal grove
there should be a x^3
quick flax
also i think there's a typo here, does the first x in the numerator not really raised to 3?
vocal grove
vocal grove
also i think there's a typo here, does the first x in the numerator not really r...
yes
quick flax
okay okay
so what we do is to answer d is
we factor both the numerator and the denominator
luckily we already know the factors for the numerator
which is just the answer to c
so now, find first the factors for the denominator
vocal grove
(x+1)(x+1)(x-3)
quick flax
yep that's the factors for the numerator
vocal grove
yep that's the factors for the numerator
deno is (x-1)^2 no?
vocal grove
idk
vocal grove
yeah
quick flax
are you familiar with the ff:
vocal grove
yes
quick flax
this formula will help you in finding the solution to deno
quick flax
a: coefficient of the variable with degree 2, in other words, the number beside x^2
b: coefficient of the variable with degree 1, in other words, the number beside x
c: coefficient of the variable with degree 0, in other words, the number without an x
vocal grove
both are -1
quick flax
yep
quick flax
because they need to cancel each other to get 0
then using what we have learned in c, what are the corresponding factors?
vocal grove
wait
vocal grove
the factors need to have "x" with them
what
quick flax
the solution to the demo is
x1 = -1
x2 = -1
vocal grove
yes
quick flax
then the corresponding factors are
( x + 1 ) ( x + 1 )
vocal grove
oh yeah
quick flax
right, we just added 1 to both sides so that the right hand side of the equations would be 0
now going back to d
since we now have the factors for both the numerator and denominator
we replace the expressions with their factors
the result would be
$((x^3-x^2-5x-3)/(x^2+2x+1))=(((x+1)(x+1)(x-3))/((x+1)(x+1)))$
vocal grove
Do I cancel out
quick flax
Do I cancel out
yep this is accurate
now we will shorten or "simplify" the expression by canceling similar terms in the numerator and the denominator
vocal grove
quick flax
yep go ahead
vocal grove
quick flax
im not sure of the language being used here
quick flax
this is quite a jump from our previous topic xD
vocal grove
Well
quick flax
but are you aware of the symbols being used in the given?
quick flax
∈
this symbol is also read as "is an element of"
so we read "k ∈ R" as "k is an element of R"
this means that k can have any value in R
do you follow?
vocal grove
yea
quick flax
I'm slightly confused on the second sentence, im not sure what "amount of solution" means, this might be an error in the translation
but amount of solution might refer to number of solution, do you agree?
vocal grove
"solution set" or "set of solutions"
quick flax
ahh i see
so we just solve for k for each value of L as x
do you follow or would you like me to explain further?
vocal grove
i would like to see it visualised
quick flax
formula: ( x + k )^2 = 9
since the problem wants us to find k, we'll isolate k in the equation, i.e. k will be left alone in the left-hand side of the equation, we do this below:
( x + k )^2 = 9
----> sqrt [ ( x + k )^2 ] = sqrt [ 9 ]
----> x + k = 3
----> x + k - x = 3 - x
----> k = 3 - x
this is now the formula we will be using.
we now have L = { 1, 7 }
then we compute for k when x is 1 and when x is 7
in other words, solve for k
k = 3 - (1)
k = 3 - (7)
do you follow?
vocal grove
yes
quick flax
is everything good?
vocal grove
yyes
quick flax
formula: ( x + k )^2 = 9
since the problem wants us to find k, we'll isolate k ...
until what part in this message did u understand?
quick flax
!nosols
final saddleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
vocal grove
this is not homework
quick flax
still you are asking me to finish this task. though i am willing to help you throughout the learning process, if you feel that you are not absorbing my explanations right now, it is okay to rest for a while
!done
final saddleBOT
If you are done with this channel, please mark your problem as solved by typing .close
final saddleBOT
@vocal grove Has your question been resolved?
ashen sail
ok
ashen sail
.close
final saddleBOT
final saddleBOT
Available help channel!
golden basin
final saddleBOT
golden basin
sorry for the image quality
i assumed the side of the cube to be of 1 unit length, O is the origin and you can see the axis
so,
,,\bar{OD} = \bar {i + j}
,,\bar {OG} = \bar {j + k}
,,\bar {OF} = \bar {i + k}
no latex for you sinners, please bear
golden basin
so,
,,\bar{OD} = \bar {i + j}
,,\bar {OG} = \bar {j + k}
,,\bar {OF} = \ba...
anyways, then i calculated the unit vector for these and multiplied them with a,2a,3a (given in question)
but the solution multiplied a,2a and 3a with a different unit vectors
i.e, i did
a*(i+j/ root 2)
while he did
2a* (i+j/ root 2)
so upon addiction the coefficients of i cap, j cap and k cap change, BUT both our answers are correct right?
<@&286206848099549185>
sturdy stream
did you find the resulatant
golden basin
did you find the resulatant
yes
sturdy stream
how much
golden basin
but the problem is that the resultant of the solution is different from mine
sturdy stream
yeah how much did you get
golden basin
since i considered different vectors to be multiplied by a,2a,3a
golden basin
yeah how much did you get
wait
golden basin
(a/ root 2) * ( 4 i cap + 3 j cap + 5 kap)
golden basin
because i got the answer 5a
what..
how is ur resultant not a vector
a vector resultant has to be a vector..
golden basin
that was rhe magnitude of their resultant
thats correct
5 is the magnitude
its useless to waste so much time on this, it has to be correct
thanks for your time
.close
final saddleBOT
final saddleBOT
Available help channel!
split quiver
(x/x-3) + (x2 + 9/ x2 - 9) = (2x/x+3) what does x =??
I got x=3 but the answer sheet was x = -1
final saddleBOT
(x/x-3) + (x2 + 9/ x2 - 9) = (2x/x+3) what does x =??
I got x=3 but the answer ...
cold gorge
x can not be 3, it makes the denominators zero.
split quiver
x can not be 3, it makes the denominators zero.
yea should have thought of that
yo thx
.close
final saddleBOT
final saddleBOT
Available help channel!
placid musk
this was my task and I have two questions can I say since V3 is linearly dependent we have Dim = 2 and I wasn't sure if this is the correct way of finding a basis.
final saddleBOT
this was my task and I have two questions can I say since V3 is linearly depend...
placid musk
you mean show more steps of the augmented matrix?
dense coral
yeah, though you don’t have to i suppose
tranquil pine
<karnaugh-map>
\begin{karnaugh-map}[4][4][1][$CD$][$AB$]
\minterms{1, 2, 4, 7, 13, 8, 11, 14}
\end{karnaugh-map}
are there any implicants that can be formed here
or am i stuck with like a bunch of terms with 4 literals each
soft zealotBOT
robust mulch
It might help if you explain what that means
tranquil pine
thats a k-map
amber holly
Should be since you have 7 and 8 in the minterms
tranquil pine
Should be since you have 7 and 8 in the minterms
wait wdym
robust mulch
But my guess would be that youre looking for (A XOR B) XOR (C XOR D)
amber holly
I was about to say minterms of two binary numbers whose values are consecutive always form an implicant but realized there are counterexamples
Yeah 7 and 8 is a counterexample nvm
Ah it works when the smaller integer is the even one ig
0001
0010
0111
1000
1011
1110
Yeah I guess you are just stuck with those literals
tranquil pine
okay thats fine
but
im meant to represent it in terms of like
uh
xors
so i like
picked the 2x2 square in the top left
and u have like
[
A'B'C'D+A'BC'D'
]
soft zealotBOT
robust mulch
Also C'
soft zealotBOT
soft zealotBOT
tranquil pine
so now repeating it for the rest gets you uhhhhh
amber holly
Yeah correct
tranquil pine
Okay doing it in my head is not a good idea
amber holly
You should get A'B'(C xor D) + (A xor B)CD + A(B xor C)D I think?
tranquil pine
[
A'C'(B\oplus D) + A'C(B\oplus D)' + AC'(B\oplus D)' +AC(B\oplus D)
]
soft zealotBOT
tranquil pine
hopefully this didnt fuck up
amber holly
You can introduce more xors lol
Factor (B xor D)' out of the middle two terms
And (B xor D) for the others
Ah wait no it's just one more xor
amber holly
,w truth table of ((not A) and (not C) and (B xor D)) or ((not A) and C and (not (B xor D))) or (A and (not C) and (not (B xor D))) or (A and C and (B xor D))
soft zealotBOT
amber holly
Let's see
1, 2, 4, 7, 8, 11, 13, 14
0001
0010
0100
0111
1000
1011
1101
1110
@tranquil pine Yeah you got it
amber holly
So what I was saying that's also the same as $A'C'(B \oplus D) + (A \oplus C)(B \oplus D)' + AC(B \oplus D)$
soft zealotBOT
A Lonely Bean
amber holly
i think it ends being a xor b xor c xor d
No?
Or
Wait
Oh okay yeah
How didn't I see this lol
robust mulch
But my guess would be that youre looking for (A XOR B) XOR (C XOR D)
With or without the parens?
robust mulch
Oh cool
tranquil pine
yeah alright thanks everyone
there is a bit more to the question but its like coding related
so ill figure that out on my own
.close
remote crane
Hi everyone 🙂 Coud someone give me a hint?
$$
\int \cos^3 x \left( 1+\sin^7 x \right) , dx
$$
I managed to do $$\int \cos^3 x , dx$$ by hand, but $$ \int \cos^3 (x) \sin^7(x) , dx $$ looks like a nightmare 
soft zealotBOT
Sweet Tea 🧋
trim lance
Wait what
remote crane
?
trim lance
Which one is your intégral is it the top one
remote crane
yea
$$
\int \cos^3 x \left( 1+\sin^7 x \right) , dx
$$
So I broke it down into
$$
\int \cos^3 x \left( 1+\sin^7 x \right) , dx = \int \cos^3 x , dx + \int \cos^3 (x) \sin^7(x) , dx
$$
soft zealotBOT
Sweet Tea 🧋
remote crane
by the linearity of the integral
remote crane
hmmmmmmmm, iirc u-sub is just 'putting things under the differential':
$$
\int \cos^2 x \left(1+\sin^7 x \right) , d(\sin x)
$$
you meant this?
soft zealotBOT
Sweet Tea 🧋
remote crane
I'm from europe and we don't call it u-sub 😦
floral nova
Both cos^3x and cos^3xsin^7x are just integration by parts. If you can solve the integral of cos^3x, the other one is just a similar grind
remote crane
Both cos^3x and cos^3xsin^7x are just integration by parts. If you can solve the...
thanks 🙂
.close
low night
How to do part b?
final saddleBOT
How to do part b?
low night
Also did I do part a correctly?
Idk if setting covariance = 0 would be valid in this case
If it is independent then covariance is 0 but covariance of 0 doesn’t guarantee independence so idk if setting covariance = 0 would be the right approach
final saddleBOT
@low night Has your question been resolved?
final saddleBOT
@low night Has your question been resolved?
crystal wing
I have this question:
There exists 2 lines with the equations, respectively, 4x+2y-4=0 and 4x-3y+12=0
Are they:
a) Parallel
b) coincident
c) concurrent but not perpendicular
d) intercept in the 1st quadrant and are perpendicular
e) intercept in the 4th quadrant and are perpendicular
final saddleBOT
I have this question:
There exists 2 lines with the equations, respectively, 4x+...
crystal wing
The theme is analytic geometry.
I'm not sure how to start. I've tried using an equation system to find out the variables but i'm not sure if that will do anything
High school math
blissful meadow
If you try to solve the system of equations, you should be getting your answer. Nvm it's just easier if you think of it as general equations of lines.
solar glade
Do you know when two lines are parallel?
crystal wing
If you try to solve the system of equations, you should be getting your answer. ...
I think I found one of the variables, y = 16/5
blissful meadow
Well at least you know they meet, so they're not parallel.
crystal wing
Well at least you know they meet, so they're not parallel.
How do I know they meet?
blissful meadow
How do I know they meet?
Since you found a solution.
There's various ways of going at this problem. If you're more familiar with that, you could always just write the line equations in the more "common" way as y = mx + b
And then compare those equations to know what's going on.
solar glade
Also you can play with the slopes
Get the slope of both equations and you’ll say they are different so they are not parallel
crystal wing
Get the slope of both equations and you’ll say they are different so they are no...
alright, i'll try that also
blissful meadow
then, y = (-4x-4)/2?
This isn't exactly right, but that's the idea.
crystal wing
And then compare those equations to know what's going on.
What affects the equation behaviour? the only thing I know is that the last independent term affects the y-intercept
blissful meadow
If you have two lines y = ax + b and y = cx + d, then they would be parallel if a=c but b and d are different (so they have the right inclination, but they're not exactly the same line).
If b=d (and a=c), then you would have concurrent lines. This is easy to see because they would just have the same equation.
Now if a is not equal to c, that means that they aren't parallel. You can check if they're perpendicular : in that case, a = -1/c. If they aren't perpendicular, then you have the answer, if they aren't you can solve for their intersection like you would normally and you'll know in which quadrant it happens.
crystal wing
right. here when i try to rewrite the equation i mentioned
4x+2y-4=0
how come isn't it y=(-4x-4)/2?
i'm pretty sure when moving the 2 multiplying the y variable, it becomes a division instead and it divides the other side of the equation as a whole
forget it, i forgot to change the signal on the independent term
"If b=d (and a=c), then you would have concurrent lines. This is easy to see because they would just have the same equation."
Here, do you mean concurrent or coincident?
final saddleBOT
@crystal wing Has your question been resolved?
crystal wing
.close
polar obsidian
Why doesnt this method work to solve this integral?
final saddleBOT
Why doesnt this method work to solve this integral?
polar obsidian
,tex $$ \int_{1}^{2} \frac{4} {x^{2}} dx$$ $$ \int_{1}^{2} (\frac{2}{x})^{2} dx$$
half salmon
\ddx?
polar obsidian
And now why cant i use ln
soft zealotBOT
@polar obsidian
solar glade
And what do you do with the power
polar obsidian
And what do you do with the power
Uh
I thought you take care of it afterword
4 * ln(x)^3 / 3
half salmon
4 * ln(x)^3/3 does not derive to (2/x)^2
polar obsidian
It’s not proportional to 1/x
Cause of the square?
solar glade
Give me the definition of the derivative of lnx
final saddleBOT
@polar obsidian Has your question been resolved?
next pagoda
For theorem 1.10 c, wouldn't I just use the definition of 1.9 to show that a-b would not he an element of N naught?
final saddleBOT
For theorem 1.10 c, wouldn't I just use the definition of 1.9 to show that a-b w...
@next pagoda Has your question been resolved?
next pagoda
^
next pagoda
blissful meadow
You can do that. i.e. since a <= b, it means that b-a is in N_0. Then you can conclude something about a-b, as you suggested.
next pagoda
This makes sense to me! But I'd like someone to double check.
final saddleBOT
This makes sense to me! But I'd like someone to double check.
next pagoda
My only concern here is maybe the or statement below definition 1.9. Because its not true that b-a wouldn't be an element of N naught. But I thin it is true that a = b.
tidal pumice
$a,b \in \mathbb{Z}$ is given
soft zealotBOT
LF
next pagoda
You're saying I don't need to write that?
tidal pumice
you need to write that, but in the next sentence
next pagoda
Okay
Ummm
Can I write applying the definition 1.9, if a<=b then b -a is an element of N naught......... and then write a, b is an element of the set of integers?
tidal pumice
no write a,b element of Z first
you can say By hypothesis, $a,b \in \mathbb{Z}$
soft zealotBOT
LF
tidal pumice
yes
next pagoda
Oh okay
tidal pumice
and then the rest
next pagoda
Let me give it another shot
tidal pumice
i dont get why you use definition 1.9 at all
you dont use the fact that b-a is in N_0
it is technically correct but it just clutters your proof if you dont use it
tidal pumice
your last sentence is good tho
it is just not clear how you got there
did you use c)?
tidal pumice
it would be a much nicer proof yes
next pagoda
Should I abandon starting with By Hypothesis a, b is an element of the set of integers?
Since I'm not going to use deff 1.9
And just use c?
This is what I came up with
tidal pumice
not really
does this proof convince you?
hm actually its very close
you just need to state why you can apply theorem 1.10 c) (we know $a \leq b$)
soft zealotBOT
LF
tidal pumice
and make the conclusion a bit clearer
next pagoda
Okay
Is it unjustified to apply theorem 1.10 if we assume a <= b?
Or is there something I need to add to get to a <= b
tidal pumice
no you can apply it
you just need to state why
thats how i would write the proof :
By hypothesis, $a,b \in \mathbb{Z}$. By (c), it follows from $a \leq b$ that $a \ngtr b$. Since $b \leq a$ and $b \nless a$, we must have $a = b$.
soft zealotBOT
LF
next pagoda
By hypothesis, $a,b \in \mathbb{Z}$. By (c), it follows from $a \leq b$ that $a ...
Can I make it more clear in the second sentence for myself that "By the same theorem, $b \leq a$ and $b \nless a$, therefore we have $a = b$
soft zealotBOT
unbearablefrequentist1
tidal pumice
no i didnt use the theorem in the second sentence
next pagoda
Oh really
tidal pumice
$b \leq a$ by hypothesis
next pagoda
Darn
soft zealotBOT
LF
tidal pumice
and $b \nless a \iff a \ngtr b$
soft zealotBOT
LF
tidal pumice
yes
tidal pumice
ty:)
next pagoda
I guess this just tells me didn't read what you wrote fully
tidal pumice
but do you get it now?
tidal pumice
youre welcome
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tranquil pine
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tranquil pine
so like i got a t-value of -3.86
how am i meant to interpert P(T < t) tho
like how am i meant to use this here?
i just got into this stuff so im not sure 
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flat flame
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flat flame
can someone double check 4 for me
And can someone help me with 5
x = y-1
And then u replace x with y-1
But I got y^2+2y-2
rocky tusk
4 is right
flat flame
Which isn’t in the answer
flat flame
4 is right
ohh ok ty
flat flame
yup that’s what I got
flat flame
ohhh
rocky tusk
so u just get y^2
rocky tusk
yes
flat flame
expanding your get y^2-2y+1+2y-2+1
Wait I don’t understand how u got two 2y
rocky tusk
the -2y or +2y
flat flame
-2y
rocky tusk
-2y comes from (y-1)^2
flat flame
how
muted cloak
If x+1=y
(x+1)²=y²
rocky tusk
(y-1)(y-1)=y^2-y-y+1
flat flame
ohhh
flat flame
ok tysm
orchid crescent
do i just find the piecewise of absolute value and plug into the whole function?
Q2/
Write the functions as piecewise functions and simplify.
(i) 𝑓(𝑥) = |5𝑥 − 7|
(ii) 𝑓(𝑥) = |5𝑥| / x
(iii) 𝑓(𝑥) = 5 − 𝑥/ |𝑥 − 5|
(iv) 𝑓(𝑥) = |𝑥 + 2| / 𝑥'2 + 𝑥 − 2
final saddleBOT
do i just find the piecewise of absolute value and plug into the whole function?...
tranquil pine
u don't have to plug. U have to find the point of discontinuity and then write the function so that it is always continuous in the give domain
for example f(x)=|x| can be written as f(x)=-x for x<0 and f(x)=x forr x>= 0
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@orchid crescent Has your question been resolved?
orchid crescent
for example f(x)=|x| can be written as f(x)=-x for x<0 and f(x)=x forr x>= 0
in that scenario
lets say its
f(x)=|x| /x
now that i know its either f(x)=-x for x<0 and f(x)=x forr x>= 0
tranquil pine
yes f(x)=-1 < 0. and f(x) = 1 for x>0
orchid crescent
and i just pick ANY value greater or equal to zero
doesnt matter if its 0 or a mil
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sacred lynx
(x-2)^2*(x-4)^2 equals 1 need help solving it
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(x-2)^2*(x-4)^2 equals 1 need help solving it
opal plinth
a^2 * b^2 = (ab)^2
sacred lynx
would that not make a ^4 equation?
opal plinth
It already is one
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@sacred lynx Has your question been resolved?
sacred lynx
so how do i solve that?
vital crag
so how do i solve that?
$(a^2)^2 = a^4$
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riemann
sacred lynx
idk how to solve ^4 equation tho
opal plinth
This is a special case
opal plinth
a^2 * b^2 = (ab)^2
Have you tried this yet?
sacred lynx
Special case wym??
opal plinth
It's a quadratic squared, not just any quartic
opal plinth
a^2 * b^2 = (ab)^2
This is one way to start solving it, I'm not going to solve it for you
Another way would be to find an obvious solution and do polynomial division
opal plinth
Yes
sacred lynx
Now what?
opal plinth
Like this?
What does that equal?
sacred lynx
0
opal plinth
Really?
sacred lynx
- And 4
opal plinth
(x-2)^2*(x-4)^2 equals 1 need help solving it
That's not what you said here
sacred lynx
Oh yea 1 forgot
opal plinth
How do you expect to find an answer if you forget the question...
Anyway, you have (x^2 - 6x + 8)^2 = 1
sacred lynx
Yes
opal plinth
What values can (x^2 - 6x + 8) take?
sacred lynx
Sqrt1?
opal plinth
Is that it?
opal plinth
Yeah, so again, what values?
sacred lynx
+- sqrt1
opal plinth
... come on, what's sqrt(1)
sacred lynx
Wym what are you asking?
sacred lynx
1?
sacred lynx
So -1 and 1 and solve both
opal plinth
Exactly
final saddleBOT
@sacred lynx Has your question been resolved?
jovial iris
Check whether function f(x) = log_2 (2x+5) is bijective on its domain.
If possible, find inverse function of it, and if not, describe why.
final saddleBOT
Check whether function `f(x) = log_2 (2x+5)` is bijective on its domain.
If poss...
jovial iris
Can someone tell me what does this "on its domain mean"?
I can find domain under the assumption that the function is real, so domain is (-5/2, +inf)
But what do I put as codomain? How do I go about finding that?
I think it's kind of all real values, but still, codomain is never mentioned + I am not sure what to do if "image" of domain and the codomain are not the same (and the codomain is not given)
Can someone help me about these semantics
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@jovial iris Has your question been resolved?
hybrid heath
I can find domain under the assumption that the function is real, so domain is (...
This is the correct domain, yes
hybrid heath
But what do I put as codomain? How do I go about finding that?
This requires understanding basic properties of log functions, but you are correct, it is all reals
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jovial iris
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jovial iris
This requires understanding basic properties of log functions, but you are corre...
Good
Now
What does it mean for a function to be a bijection "on its domain"?
Is it standard bijection check
Or is it something else?
tranquil pine
what is a standard bijection test to you
jovial iris
(1) Check if injective
(2) Check if sirjective
If (1) and (2), then it's bijective. Otherwise, not.
jovial iris
The problem I have here is the difference between codomain and image
There are some functions that have different codomains and images
But
That only seems to occur when the codomain is already given in function definition
Otherwise, when we are defining a codomain, we basically do find the image
And then it must be sirjective, right?
Obviously every "y" in codomain has its "x" in domain, such that f(x) = y
dense coral
i mean if you define the codomain of a function to be its image, then of course it will be surjective
but i believe log_2(2x+5) has a domain of (-2.5, inf)
and a codomain of R
dense coral
That only seems to occur when the codomain is already given in function definiti...
the thing is, asking for a function's image when defining a function is asking for too much
you often wouldn't know a function image, but would still like to know what its target space (codomain) is
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@jovial iris Has your question been resolved?
final saddleBOT
Would the answer for c) not be
soft zealotBOT
mj
tranquil pine
way I got this was
just putting a 1 over the entire thing
or in other words
inversing
$((\frac{8x}{x^2-1})^{-1})=\frac{x^2-1}{8x}$
soft zealotBOT
mj
tranquil pine
Would the answer for c) not be
on c) btw
soft zealotBOT
riemann
vital crag
which is not the same as $f(\tfrac1x)$
soft zealotBOT
riemann
soft zealotBOT
!
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riemann
tranquil pine
$\frac{8x^{-1}}{x^{-2}-1}$
soft zealotBOT
!
tranquil pine
$\frac{\frac{1}{8x}}{\frac{1}{x^2}-1}$
soft zealotBOT
!
tranquil pine
$\frac{\frac{8}{x}}{\frac{1}{x^2}-1}$
soft zealotBOT
!
tranquil pine
$\frac{\frac{8}{x}}{\frac{1-x^2}{x^2}}$
soft zealotBOT
!
tranquil pine
$\frac{8}{\frac{1-x^2}{x}}$
soft zealotBOT
!
tranquil pine
$8\cdot\frac{x}{1-x^2}$
soft zealotBOT
!
tranquil pine
$\frac{8x}{1-x^2}$
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!
tranquil pine
well lookie here
back to where qwe started lol
is there a way to tell that you'll get the same answer
as the question
or is it just something you have to dfo
vital crag
would have been faster to multiply top and bottom of f(1/x) by x^2
tranquil pine
I guess
vital crag
back to where qwe started lol
but f(1/x) != f(x) if that's what you're implying
tranquil pine
so it's just coincedence that it is here
tranquil pine
super obvious question: I understand how the radians cancel out but how do the pi's cancel out considering one is -pi?
final saddleBOT
super obvious question: I understand how the radians cancel out but how do the p...
tranquil pine
dense coral
i mean
if i gave you -2/2
you would cancel it out to get -1
in this case, you can think about -pi/3 as -(pi/3)
and then cancel the pi's
if you prefer that
tranquil pine
It's easier if you start considering the - prefix to denote multiplication by -1
dense coral
^
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@tranquil pine Has your question been resolved?
outer tide
How to integrate this??
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mortal hedge
Given is the following quadratic form
q(x1,x2,x3,x4)=x21 +x2 +x23 +x24 +2x2x3.
(a) Is this quadratic form positive (semi-)definite, negative (semi-)definite or indefinite? Explain briefly.
(b) Find all vectors w⃗ for which q(w⃗) = 0. Explain why you found them all.
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warm python
$\int \frac{1}{1+x^4}$ is it possible to do this using a trig u sub ?
warm python
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unborn vault
warm python
!xy
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
unborn vault
this is real problem
we need to find supremum and infimum
.ckose
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torpid sage
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torpid sage
i dont get the highlighted phrase
and i really dont know how to solve this problem....
pls ping me if u can help, TYSM
hardy wren
I think you have to calculate the Riemann sum which has this integral as a limit but you only sum the first 4 terms of the sum and see which of the following answers is correct
@torpid sage
torpid sage
I think you have to calculate the Riemann sum which has this integral as a limit...
yeah
i think so
this is really triggering my ocd
im not sure whether the "limit of sums" is basically the riemann sum or not?
hardy wren
It is
torpid sage
It is
oh it is?
sheshhhhhhhhhh
aight waity
imma try to find it
and then can u give it a check?
hardy wren
Sure
midnight sparrow
I have an increasing function f define on ]0,1[ and I need to show that if $f(]0,1[)$ is an intervall thus f is continuous on ]0,1[ but I wondered, R is an intervall and I didn't think lim f when x goes to 0 exist and is defined so f is not continuous in this case ?
final saddleBOT
I have an increasing function f define on ]0,1[ and I need to show that if $f(]0...
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phoestaclies
midnight sparrow
the intervall must be bounded ?
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@midnight sparrow Has your question been resolved?
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@midnight sparrow Has your question been resolved?
midnight sparrow
<@&286206848099549185>
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@midnight sparrow Has your question been resolved?
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fleet maple
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viscid fossil
fleet maple
why is that ?
spring haven
not necessarily. the sphere can have an equation of the form $$(x-\alpha)^2+(y-\beta)^2+(z-\gamma)^2=r^2$$ which does not have center (0,0,0)
soft zealotBOT
kheerii
fleet maple
So what do we do :/ ?
spring haven
not sure actually
maybe you can try what @viscid fossil says. if the sphere has center (0,0,0) then their statement would be correct i.e |r(t)| would be independant of t
you can simplify the x and y coordinates of r(t)
fleet maple
how do i do that
spring haven
do you know the triple angle formulae for sin and cos?
fleet maple
No
spring haven
fleet maple
Interesting
spring haven
can you tell me what the x and y coordinates then become?
spring haven
the 3 is in the power yes?
fleet maple
Yea
spring haven
yes. so we get $\vec{r}(t)=4\cos^3(t)\vec{i}+4\sin^3(t)\vec{j}+4\sqrt{3}\sin(t)\cos(t)\vec{k}$
soft zealotBOT
kheerii
spring haven
do you see how?
spring haven
well that's just double angle identity
fleet maple
Ob yhea
Nvm i had it written down with an exponent so it didint work
But yhea i see it now
spring haven
so try calculating and simplifying $|\vec{r}(t)|$
soft zealotBOT
kheerii
spring haven
I think it should come out as a constant
fleet maple
alr, Let me try
fleet maple
yes. so we get $\vec{r}(t)=4\cos^3(t)\vec{i}+4\sin^3(t)\vec{j}+4\sqrt{3}\sin(t)\...
Should be 2 instead of 4
In z
spring haven
why?
fleet maple
Nvm
final saddleBOT
@fleet maple Has your question been resolved?
lament reef
send it rotated plz
fleet maple
,rotate
soft zealotBOT
fleet maple
The trig part should = 1
spring haven
it does
fleet maple
How ?
sleek token
is that a quiz?
round matrix
That's not true because of the $7n^{2} * 4$ piece, or in other words, not every term has a common factor of n^2
soft zealotBOT
£ ςΓσΔηκεΓζ
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
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tranquil pine
or use this mehtod i forgot name
Oh you have to use the long division method?
drifting steeple
Oh you have to use the long division method?
athats one way other way is synttic
synthetic division
tranquil pine
Hmm never heard of it but Ill watch it on yt
drifting steeple
yeah its simpler than long divison and very cool can be used on polynomials of 100 degrees iwthout crazy theorums
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verbal steppe
$\frac{3x+1}{x+2} < 2 \
\implies 3x+1<2x+4 \
\implies x < 3$
final saddleBOT
$\frac{3x+1}{x+2} < 2 \\
\implies 3x+1<2x+4 \\
\implies x < 3$
verbal steppe
Where did i go wrong?
soft zealotBOT
Merineth
verbal steppe
Why does x > -2 ?
raw fiber
plug in x=-2 and see what happens
candid hull
if x < -2, x+2 is a negative number, so you multiplied by a negative number
i.e. the inequality reverses
verbal steppe
i understand that if x is -2 that would mean i'm dividing by 0 which isn't possible
however
why is the answer
-2 > x > 3
hearty tide
-2 < x < 3
hearty tide
putting x = -2 will be undefined..
Putting x < -2 will give us value that will be >=2
Try putting x = -3
See what you get
( 3(-3) + 1 ) / ( -3 + 2)
(- 8 )/ - 1
Equals 8
Which is greater than 2
Therefore, X can't be Lesser or equal to (-2)
In that case, It has to be greater than (-2) ...
Means , x > -2 or -2 < x
hearty tide
**Merineth**
On the other hand, here you got x < 3
Combine these last two .. you will get -2 < x < 3
@verbal steppe
jagged seal
Min of what function?
hearty zephyr
why is x^2 negative on the <0 interval?
vernal spindle
i think its always positive
hearty zephyr
the derivative of x^2 is negative on that interval, sure. But why do you have x^2 as negative?
it's also always positive, and can never be 0
not much, it's just always positive
tranquil pine
what are the main ways to count something besides inclusion exclusion, multiplication principle, addition principle
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what are the main ways to count something besides inclusion exclusion, multiplic...
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faint rock
I need help with the basics of derivatives, for example, f(x)=2x-5, what is the derivative? I used the equation we are supposed to use which uses lim(h>0)((f(x+h)-f(x))/h, but I don't understand what happens to h