so then the limit DNE
#help-28
wide sundial
pliant quarry
ivory birch
my bad
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ivory birch
...
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unreal garden
i have the following expression in dnf form $\lnot q \lor r \lor \lnot p$
glossy valveBOT
metnal
unreal garden
is it "legal" for me to turn it into $(\lnot q \lor r \lor \lnot p) \land (\lnot q \lor r \lor \lnot p)$ to get cnf form?
glossy valveBOT
metnal
unreal garden
this feels like cheating..
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@unreal garden Has your question been resolved?
drowsy sky
$(\lnot q \lor r \lor \lnot p) \land (\lnot q \lor r \lor \lnot p)$
glossy valveBOT
maikelmatica
unreal garden
? @drowsy sky
hexed zephyr
How
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1
rapid rain
do you know how to find eigenvalues of a matrix?
what is the method that your teacher gives you?
wind needle
use the lambda approach is probably the easiest way for the eigenvectors
@hexed zephyr
|B-λI| = |[5,-1,3,1]-[lambda,0,0,lambda]| = 0
rapid rain
'lambda approach' is calculating the caracteristic polynomial but yes
$\chi_B = \begin{vmatrix} X - 5 & 1\ -3 & X-1 \end{vmatrix}$
glossy valveBOT
rafilou2003
rapid rain
but i saw this formula m+-sqrt(m^2 - p)
yes, this is exactly finding the solutions of X^2 - 2mx + p
which is what you get when you compute $\chi_B$
glossy valveBOT
rafilou2003
wind needle
hey
fast peak
do you know what mod is
tight glen
What do you not understand?
wind needle
yes i know what mod is
how did they construct the sets S and T from the information given
fast peak
can you tell me one number x with x = 2 mod 3
wind needle
2
fast peak
can you tell me another?
hexed zephyr
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short siren
Check the last determinant
hexed zephyr
Where
I didn't write - 3
I sound stupid but I really can't spot it 😂
Ok I found it, I'm too tired
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distant moth
help
distant moth
I tried to do that, but all my attempts became very long procedures
distant moth
one sec
amber hemlock
in place of A put 3x and take 4th power both sides, you will get your identity
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slow sleet
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craggy verge
Not up to date on law of cosines and on mobile rn sorry, can’t really help check rn
slow sleet
Not up to date on law of cosines and on mobile rn sorry, can’t really help check...
oh my bad for taggin man 😭
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dull thicket
does anyone know what the transtion matrix is?
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does anyone know what the transtion matrix is?
dull thicket
im working with in linear algebra with vector spaces
im fairly certain its the the change of coordinate matrix but im not quite sure
dull thicket
its in my assignment, the task says as follows: what is the transtion matrix P_B<-C from the basis C to the basis B
simple totem
then yes it's just the change of coordinate matrix
dull thicket
Okay, so
i had the question:
let V be a vector space with basis B = [b1,b2] let T: R^2 -> R^2 be a linear transformation such that T(b1)=b1 - 5b2 , T(b2)= -3b1 + 9b2, find the matrix [T]_b with consideration to the basis B. which is just pic below.
now get another basis C = [c1,c2], c1= 2b1 + b2 c2= b1 + b2. Im supposed to find the change of coordinate matrix, and i feel like i am doing something wrong
dull thicket
also C is in the vector space V
all of this would mean c1 = (2,1) and c2=(1,1) right?
and i would just take the augmented matrix and reduce it to row echelon form
also it P_B<-C
forgot to mention that
the augemented matrix would also just be [b1,b2:c1,c2] right?
my next question is what really makes me question things (although i haven´t finished this yet as of writing this), its simply find [T]_C to T with consideration to the basis C. which feels to easy
if anything at all is unclear feel free ask ^^
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limpid ocean
Where did i go wrong
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Where did i go wrong
limpid ocean
Or if i didnt go wrong whats my next step
viral jasper
Yourm could've simplified $\log_5 (3x^2)$ to $\log_5 {3} +2\log_5{x}$
glossy valveBOT
SWR
viral jasper
Not sure if that's easier, but just a thought
You also made a mistake with $\ln(3x^2)^2$
glossy valveBOT
SWR
limpid ocean
You also made a mistake with $\ln(3x^2)^2$
o ok i corrected this where do i go from there?
im trying to end up with this but i cant figure out how
viral jasper
Show me your correction
limpid ocean
Show me your correction
i just left it as it was before
minor basalt
Where did i go wrong
Yoour last two steps are wrong,
You didn't cancel out the term √(x+1) from the second half of numerator
And in the last step you forgot to 3x²
limpid ocean
o i just divided (x+1)1/2 from the second half and got (x+1)
minor basalt
Ohh okok sorry i didn't see that
limpid ocean
And in the last step you forgot to 3x²
what do u mean by this?
minor basalt
But you forgot the 3x²
limpid ocean
But you forgot the 3x²
where do i put the 3x^2?
limpid ocean
Btw I tried solving it a bit differenttly, and got the answer should I share it?
yeah could i see that
minor basalt
Give me a minute
limpid ocean
o i changed it to this
minor basalt
No i don't think so
limpid ocean
so where do i go after this?
minor basalt
My answer is wrong too lol
minor basalt
so where do i go after this?
Let me see
limpid ocean
one sec
minor basalt
In the last step instead of writing ln(5) you wrote ln(x+1)
It should be -2ln(5)3x²(x+1)^3/2
limpid ocean
Let me see
minor basalt
Now cancel the 3x
limpid ocean
Not yet
limpid ocean
Ye doing it rn
minor basalt
Okok
minor basalt
Now (-2*2x) = -4x
minor basalt
The numerator is right now
Yesss
And after this multiply both denominator and numerator by -1 to get your answer
minor basalt
Glad to help out 😊
limpid ocean
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limpid ocean
Glad to help out 😊
Wait after i distribute the -4 into the (x+1) it becomes -4x^2 + 4x
minor basalt
Yesss
limpid ocean
But even so wouldnt it still be -4x + 4?
limpid ocean
But the answer needs a 4x+1
Hm
Well there are typos sometimes
are u sure its 4x + 4? It might be a typo then
minor basalt
Give me a moment I'll try solving it to see if i get the same answer
limpid ocean
okok
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median terrace
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kind jay
!status
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@median terrace Has your question been resolved?
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late grail
What do you need help with?
late grail
Do you understand what domain means?
median terrace
Yes
im fully understand all parts of question but i dont know the methodology for critical points
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smoky isle
Can someone help with the laurent series? This is one topic i cant seem to get my head around atm
smoky isle
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rapid rain
Can someone help with the laurent series? This is one topic i cant seem to get m...
Start with a fraction decomposition
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smoky isle
yeha, ive split the fractions, but i just dont really understand the process from there tbh
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minor isle
Peter is standing on a beach bank and has thrown a stone to a pole sticking out of the water. Now he wants to
he wants to find out how far it is. He measures the distance between the throwing spot and a
small rowing boat further along the shore. He also measures the two angles shown in
in the figure.
a) Use the figures to determine the length of the throw.
b) Then calculate the area of the triangle formed by the three dashed lines in the figure.
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Peter is standing on a beach bank and has thrown a stone to a pole sticking out ...
minor isle
i did not understood how to make it
i need to give it to the teacher after 2 hours ;((
minor isle
not really
slender totem
Wait a sec
minor isle
Wait a sec
waiting
minor isle
ahh bro
i know that
i think
but it is fine
try to tell me so i can understand it 100 percent
slender totem
Ok
minor isle
wtf
slender totem
Do u know the equation for sine rule
minor isle
wait i am finding the notes
slender totem
Yesh
slender totem
minor isle
if we say the pæl is B, so b is 84 m. Kastested(A) is 51°, and lille robåd (C) is 62°
minor isle
but bro how do i get the a) Use the figures to determine the length of the throw.
@slender totem
minor isle
could we first say 62+51=180-answer=C?
minor isle
if we got little b, and used this later could we do that?
like this from another homework
@slender totem
minor isle
ok
slender totem
minor isle
is it directly the answer for a?
slender totem
Yea
minor isle
ok thanks bro
slender totem
We can directly put it to the equation
minor isle
for the help
slender totem
And we also need to find the area right?
slender totem
Peter is standing on a beach bank and has thrown a stone to a pole sticking out ...
Part (b)?
minor isle
yeah
slender totem
.
Ummm i wish if i could
But i have to go to bed now
Its 12 at my place
Im a little sleepy
minor isle
But i have to go to bed now
fine thanks for help
slender totem
Ur welcome
minor isle
done
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minor basalt
Put the value of x as zero
You'll see that y>5
And since x is always less than 0, that means y will always be greater than 5
You can simply put x as any value that satisfies the question
Since x<0
onyx glen
so you have y > 5 - 2x, but you also know x is negative thus -2x is positive
thus 5-2x > 5
you don't need to choose any numbers
minor basalt
thus 5-2x > 5
Do this then
Like do you understand what we did here?
Sorry i dont understand?
onyx glen
what you did is valid but not helpful @torn jolt
you want to compare y with 5
(or find out that such a comparison cannot be made)
minor basalt
Since the question is asking about y, it would be easier to make y the subject of your inequality rather than x
If i dont need o show my working i usually put an easy value of x and check the options
Okok
Since question says x<0
I will choose any number that is less than 0
For example -2
So
2x+y>5
2(-2)+y>5
-4+y>5
y>5-(-4)
y>5+4
y>9
And therefore, A is bigger than B
I just replace x with the value i chose, and check with option matches with the results i got
Usually it doesnt take more than 2
austere carbon
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austere carbon
How do I do this?
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1
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austere carbon
<@&286206848099549185>
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@austere carbon Has your question been resolved?
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@austere carbon Has your question been resolved?
late perch
You can try using double angle formula for sin and cos
For example cos2x + 1 = (2cos^2(x) - 1) + 1 = 2cos^2(x)
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stuck island
how do i keep simplifying 2y²-9=y²
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how do i keep simplifying 2y²-9=y²
inland viper
To simplify the expression 2y² - 9 = y², we can start by bringing all the y terms to one side of the equation and the constant terms to the other side:
2y² - y² = 9
Simplifying the left-hand side, we have:
y² = 9
Taking the square root of both sides, we get:
y = ±3
Therefore, the solutions to the equation 2y² - 9 = y² are y = 3 and y = -3.
inland viper
we had 2y² - y² this means you'll be left with y²
paper lagoon
Is this correct niether for first 2 and two for last
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Is this correct niether for first 2 and two for last
@paper lagoon Has your question been resolved?
real steppe
how do you know how many basis steps will be needed in a strong induction proof
simple totem
intuition
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simple totem
your question is very generic, it's tough to say how many basis steps you'll need for any random strong induction proof
if you can narrow the question down or give an example then maybe we can help
real steppe
uhm, okay, I think a common example is the stamp problem
I guess I will just try to re-read the example in my textbook
I've been staring at it for like, what feels like hours
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craggy verge
if you share the problem it can be helped with specifically
it may help you in learning it, while general questions tend to be better for confirming what you already know
real steppe
at the highlighted part is where I get lost
like, the possible combinations of stamps seem to be 4c and 5c
so you have some n
in math terms, shouldn't n = 3a + 4b
like if you express the problem in symbols rather than english
and why would you even think about it that way, i.e. "we consider two cases, when at least one 4c stamp has been used and when no 4-cent stamps have been used" what?
seems like the idea here is to consider two possibilities with P(k)
that P(k) i.e. the amount of postage k is either made of 4c stamps or 5c stamps
but like, can't it be both?
wtf
like there doesn't seem to be any rhyme or reason to what is happening here
case 1: 4-cent stamps were used to form k, thus, k+1 can be reached by replacing a 4c stamp with a 5c stamp
case 2: if no 4c stamps were used, then we form postage of k cents using only 5c stamps... but that seems like a wild leap of logic
seems like case 2 is just an assumption
craggy verge
that `P(k)` i.e. the amount of postage `k` is either made of 4c stamps or 5c sta...
no no no
basically, this is a proof by induction, yes?
their basis is p(12) can be made by 3*4
their inductive is p(k)->p(k+1), ok
they prove p(k)->p(k+1) in two cases, case is p(k) is made using at least 1 4 coin, or otherwise. (p(k) is made not using at least 1 4 coin)
in case 2, we know p(k) uses no 4c coins, therefore p(k) is made entirely of 5c coins (therefore since k>12 we know there are at least 3 5c coins)
therefore we can remove 3 of those 5c coins and use 4 4c coins instead to make p(k+1)
there's only one basis here, they split the inductive bit in two
real steppe
so k is greater than or equal to 12
if k = 12 then we have 3*4c
to get to k+1 if you have 4c stamps, you replace one 4c stamp with a 5c stamp
to get to k+1 if you have only 5c stamps, you replace three 5c stamps with four 4c stamps?
that seems, weird
how do you know you will always have enough 5c stamps
or you just don't worry about it because it's an induction proof
xD
craggy verge
how do you know you will always have enough 5c stamps
bc k>12 yes?
at 12 we have 3c stamps left (4 of them) so at 13 we have 2 left
so at 14 we have 1 left
so at 15 we have 0 left to make k+1, 16 (omg my writing today)
15 is made of 3 5c though, so we make k+1, 16, with 4 4c
and from there we always have enough 5c left as shown
make sense or would you like futher clarification?
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real steppe
make sense or would you like futher clarification?
that makes sense ty
thorny ledge
Hey would anyone be able to help with the following problem: "Find the flux of F=<5z, 4y^2, 3x>
out of the closed cone y=sqrt(x^2+z^2) with 0≤y≤3"
thorny ledge
so I need to use the divergence theorem, and computing the divergence is fairly straightforward. div(F)=8y
however, I am struggling a bit with setting up the region for the triple integral
I can visualize it in my head, I believe it looks like a cone of height 3, but rotated 90 degrees from the Z axis origin
so like a cone with it's center through the y-axis
would anyone be able to help me think through setting up the region?
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vapid barn
use cylindrical coordinates with y as your height
(x,y,z) -> (rcost, y, rsint)
@thorny ledge
toxic aspen
how do i find the maximum of this
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how do i find the maximum of this
cloud moon
there are either no maximums, or an infinite amount
see that at π you have another maximum
toxic aspen
yes
toxic aspen
oh okay
toxic aspen
okay thanks
cloud moon
no problem
toxic aspen
how do i find the maximum and minimum of this
heres the graph
i thought the maximum was (3pi,5)
keen spruce
and the opposite is -5
toxic aspen
yeah
isnt the maximum the first positive point on the graph though
so it would be (3pi, 5)
but its not
keen spruce
oh
if its going from left to right then it would be -8pi
but they are both the max of 5
unborn quarry
heres the graph
(-8pi, 5) and (3pi, 5) are incorrect
For example, the maximum at the right is between 0 and 5pi, exactly at the middle
That's not 3pi
unborn quarry
why would that not be the maximum
It's a maximum, but it's not at 3p8
*3pi
That's what I meant
toxic aspen
what is the maximum then
toxic aspen
how would i write that in the coordinate form
unborn quarry
The x value is not 3pi
unborn quarry
For example, the maximum at the right is between 0 and 5pi, exactly at the middl...
.
unborn quarry
It's between 0 and 5pi, exactly at the middle
At the middle of the segment that goes from 0 to 5pi
What is exactly in the middle of 0 and 5pi?
toxic aspen
it says its wrong
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true dagger
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twin wolf
So I'm trying to solve this
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So I'm trying to solve this
twin wolf
i have this so far
but im not sure what im trying to find
unless im trying to find the length of the red line?
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torn jolt
how did they arrive at e^(2x) = 1 here
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how did they arrive at e^(2x) = 1 here
torn jolt
help
torn jolt
i dont understand the question
The company sells the screws in packages of
10 and offers a money-back guarantee that at most 1 of the 10 screws is defective
what it means at most 1
and if we should replace when X = 1 then why we subtract it from 1
does it mean when x>=2 we should replace and not for x = 0 or x = 1
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sinful totem
for the first one i think there is a break in the line on the graph at x=2
or is there a vertical asymtote?
torn jolt
Point 3 implies that it's a vertical asymptote at 2
sinful totem
Point 3 implies that it's a vertical asymptote at 2
i dont have to draw that do i
@torn jolt
torn jolt
I'm confused as to what you're supposed to do then
If you're not supposed to draw the graph
sinful totem
I'm confused as to what you're supposed to do then
i do needto draw the graph
i just dont have anything down because i dont know where to start lol
torn jolt
Well some of those points are giving you direct points on the graph you can at least mark down
Focus on what the limits are saying
Like for example point 6
What is that saying
sinful totem
Focus on what the limits are saying
is that a horizontal line at y=4
sinful totem
oh, so a point at (4,5)?
sinful totem
and that would be a hollow circle right
sinful totem
oh
torn jolt
There are multiple correct answers to this question
sinful totem
okay, so it doesnt matter?
torn jolt
Nope, though you probably want it to look nice so you can assume it's a line of any slope going through that point
sinful totem
Nope, though you probably want it to look nice so you can assume it's a line of ...
now for number 4, is that another point at 0,1
torn jolt
Yes, although this time you should consider whether it can be filled or not when you take into account 2 and 5
sinful totem
Yes, although this time you should consider whether it can be filled or not when...
im assuming filled
sinful totem
What does #5 say
as x gets close to 5, the corresponding value of f(x) approaches 4
sinful totem
What does #5 say
as x approaches 0 from values less than 0, the corresponding values of f(x) approach the value of f(0)
torn jolt
Ok, and you are claiming by saying that #4 implies that (0,1) is filled that f(0)=1
Does this contradict #2?
torn jolt
I can't give you answer due to the rules of this server but I think if you can convince yourself of it that should be enough
sinful totem
hollow circle at (0,1)
torn jolt
Anyways the only part of this that's tricky is f(-2)
I think you have enough understanding at this point to get everything else
sinful totem
I think you have enough understanding at this point to get everything else
not really
torn jolt
For help with that one I recommend you look at the graph for sin(1/x)
torn jolt
not really
It isn't intended that you get it immediately
Work with it for a bit and try to solve things on your own
If you get stuck for too long then come back
solid saffron
Is there any difference between solving quadratic equation in view of function, and solving quadratic equation in view of variable?
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Is there any difference between solving quadratic equation in view of function, ...
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muted delta
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muted delta
how to solve this ?
wild sleet
expand
muted delta
3-i + 3i-i * i ?
willow sedge
3-i + 3i-i * i ?
Your expansion is wrong
muted delta
a right
willow sedge
still wrong
muted delta
what would it be ?
muted delta
willow sedge
Use i^2=-1
muted delta
i just need to solve the complex number problem
willow sedge
i just need to solve the complex number problem
You mean just expand?
muted delta
expansion is one step
muted delta
maybe 3 - 1 + 3i-i^2
.
this might be correct
because 3-1+3i- (-1)
3-i+3i+1
4+2i
then i change + into -
so 4-2i
muted delta
so if i gave you (3-2i)(i+1), do i just expand and do the same thing ?
willow sedge
Yes
muted delta
3i+3-2i * i-2i ?
willow sedge
Yeah that's correct
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faint bobcat
how to solve?
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faint bobcat
how to solve?
how can i solve this quest
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wind prism
how come he multiplied the 2 with 2x+5 and not 3 as well???
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how come he multiplied the 2 with 2x+5 and not 3 as well???
gritty rose
how come he multiplied the 2 with 2x+5 and not 3 as well???
3 is in the denominator
$\frac{a}{b} \cdot c = \frac{ac}{b}$
glossy valveBOT
riemann
gritty rose
So this is the rule i must follow
wind prism
Thanks very much
stray raven
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stray raven
Can someone please help me with part c and d
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@stray raven Has your question been resolved?
graceful rivet
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stone cliff
I can try to help for b
I guess first is to find the frequency from the bottom graph
quaint prawn
<@&286206848099549185>
!15mins
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stone cliff
It makes 1 cycle every 2.8 seconds
graceful rivet
indeed
stone cliff
Wouldn’t that mean a frequency of around 0.36
graceful rivet
how did you get that number
stone cliff
It would be great if you had the answers but I’m pretty sure it’s like that
graceful rivet
oh shit yeah
stone cliff
So use the information
graceful rivet
💀
stone cliff
Of 0.80m
Probably divide it by 6 parts
And one wavelength would be 4 parts I think
stone cliff
Uh
graceful rivet
how can I find it i dont have v
stone cliff
One wavelength should be 0.8/6*4 right
I went from the peak of hill 1 and peak of hill 3
graceful rivet
hmm
graceful rivet
Idk
stone cliff
One wavelength would be 2/3 of the total length
graceful rivet
why tho
stone cliff
Wdym why
graceful rivet
it doesnt mention anything abt harmonics
stone cliff
A wavelength is just how long the wave is when traveling one cycle
I didn’t do anything with harmonics
stone cliff
Yes
stone cliff
Yes
sharp flame
$\log_x \left( \frac 52 - \frac 1x \right) > \frac 52 - \frac 1x$
glossy valveBOT
NEONPerseus
sharp flame
I need the solution set
Finished off all the conditions to make sure everything is defined
How would I start solving the actual inequality?
torn jolt
,w log_x(5/2 - 1/x) = 5/2 - 1/x
sharp flame
Nice
torn jolt
How would I start solving the actual inequality?
I dont think there would be an algebraic way
sharp flame
So I'd have to graph and look at it?
torn jolt
yeah, do it numerically
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minor turret
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minor turret
ok so first we need to prove that the two vectors are independent right
viral jasper
fair start
minor turret
so giving it coefficients a and b and equaling that to 0 gives a =b=0
since a+2b =0 , 2a+6b=0 and -3a-3b=0
viral jasper
yup
minor turret
so solving for b with the first two equations we get -2b =0
b=0 and thus -3a = 0
so a =0
now i know there are different ways to find the basis
our professor wants us to first find the spanning list of the Vector space and use those vectors to make the basis
so we have (1,00) (0,1,0) and (0,0,1) that span F^3
or sorry the spanning list of F^3
and now we can consider the list (1,2,-3) , (2,6,-3) and (0,0,1)
since (0,0,1) is not in the span( (1,2,-3), (2,6,-3))
minor turret
and now we can consider the list (1,2,-3) , (2,6,-3) and (0,0,1)
this list is indepndent
but now i'm not sure how to go from here
viral jasper
Sounds like a basis to me if you've shown they're independent
minor turret
in another example
our professor has "So (v1,e1,e2) spans e1,e2,e3"
as the final step
e1 e2 and e3 being the spanning list of F^3
and v1 being the vector given
quiet stirrup
It helps if you write down what a basis is.
minor turret
a spanning list with all linearly independent vectors right
quiet stirrup
I was going to be a little bit more pedantic but yes.
So given a space, you need to show your set of elements is a spanning set for that space, then once you establish that, you need to show they are linearly independent.
It's not clear that {v1, e1, e2} spans F^3, but you can show {v1, e1, e2} spans {e1, e2, e3} relatively easily since you only need to show that e3 is in that span
Then you just need a transitivity argument that if {v1, e1, e2} spans {e1, e2, e3} and {e1, e2, e3} spans F^3, then {v1, e1, e2} spans F^3 too. This is long winded but it avoids having to take an arbitrary element of F^3 and write it as a linear combination of {v1, e1, e2}
minor turret
so if i have {v1,v2,e3} i need to show it spans {e1.e2,e3}
which can be done by showing that e1 and e2 are in that span?
quiet stirrup
You could show {v1, v2, e3} spans {e1, e2, e3} by showing e1 and e2 are in the span and as a consequence they span the same space as {e1, e2,e3}
The other option is to take an arbitrary element of F^3 and show that you can write it as a linear combination of {v1, v2, e3}, which is probably marginally more annoying.
minor turret
i was trying to show e1 was in the span
but i'm having a hard time writing e1 as a linear combinatoin of v1,v2,e3
v1 being (1,2,-3) v2 = (2,6,-3) and e3 = (0,0,1)
quiet stirrup
Just throw it in a matrix and do Gaussian Elimination then
minor turret
ok
by looking at the matrices does it look like e1 is a linear combination of those vectors
im not sure if i'm missing some easy steps
quiet stirrup
I expect if you take any one of e1, e2 or e3 and combine it with v1 and v2 it will be a basis but I haven't tried.
Some computations are going to be easier than others
Gaussian Elmination is going to terminate your computation after a few steps either way, so it doesn't materially matter.
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jovial herald
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fallow crest
why is the product rule used here and not the chain rule?
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why is the product rule used here and not the chain rule?
fallow crest
could u use the chain rule like this?
modern horizon
west prairie
why is the product rule used here and not the chain rule?
it's a multiplication, not a f(g(x))
west prairie
unless you threat a multiplication like a separate operation, like a series of additions... would that make sense?
not really 😄 ... well, just ignore that
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solid saffron
What's the measure of angle median forms with the opposite side in an isosceles triangle?
solid saffron
I'm talking about 2nd median
solid saffron
onyx glen
дана треугольная призма ABCA_1B_1C_1, чье основание -- равнобедренный треугольник ABC, где AB = BC = 25cm, AC = 30cm. через ребро AA_1 проведена плоскость, перпендикулярная ребру BC. вычислить в cm^3 объем призмы, если площадь сечения призмы плоскостью равна 72cm^2
я правильно перевела?
solid saffron
дана треугольная призма ABCA_1B_1C_1, чье основание -- равнобедренный треугольни...
Да, все верно
onyx glen
чертеж есть?
в стереометрии без чертежей никуда -- если не дан, значит, надо сделать.
@solid saffron ?
solid saffron
<@812307327977390141> ?
Пару минут, нарисую
onyx glen
прикольное, кстати, у этой задачки решение есть...
вот мой чертеж. под спойлером, ессно
solid saffron
onyx glen
а теперь вопрос на миллион: какой угол вам был нужен и зачем?
solid saffron
Уже он не актуален )
Я просто думал, что у равнобедренного триугольника 2-я и 3-я медианы перпендикулярны к противоположным сторонам вершин, от которых они идут, и получаеться что AH - это медиана ABC
onyx glen
а откуда такая нумерация медиан?))
onyx glen
это у вас K такие? я прочла как H
solid saffron
10 * 30 = 300 см^2
solid saffron
это у вас K такие? я прочла как H
Ну да )
onyx glen
10? откуда 10?
solid saffron
10? откуда 10?
(1/2) * 20 * 30
solid saffron
Ну BK
solid saffron
BK = sqrt( (25^2) - (15^2) )
onyx glen
вообще даже медиану BK проводить не нужно
ибо $S(ABC) = \frac{1}{2} \cdot AH \cdot BC$
glossy valveBOT
Ann
onyx glen
а объем призмы $V = AA_1 \cdot S(ABC) = \frac{1}{2} \cdot (AA_1 \cdot AH) \cdot BC$
glossy valveBOT
Ann
solid saffron
AH -это вторая медиана?
onyx glen
не знаю ни о каких "вторых" или "третьих" медианах, но говорю я о вот этом отрезке
и не медиана, а высота вполне
onyx glen
а она и не нужна!
onyx glen
ну если очень хочется, то можно
а так-то $AA_1 \cdot AH$ --- площадь сечения, а она дана напрямую
solid saffron
А я правильно сдела
glossy valveBOT
Ann
onyx glen
и BC тоже дано напрямую
solid saffron
Я правильно сделал, что:
Площадь ABC = (1/2) * 30 * 20 = 300
Также площать ABC = AH * BC * (1/2)
300 = AH * 25 * 1/2
AH = (300 * 2)/ 25 = 24
AA1 = 72 / 24 = 3
V = 3*300 = 900
?
onyx glen
ну можно и так
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solid saffron
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regal tiger
can somebody give a tip for rearranging formulas thanks
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can somebody give a tip for rearranging formulas thanks
vital shadow
as in x + 1 = y, x = y - 1?
torn jolt
You're gonna have to give an example dawg
There's like 50 different levels of "rearranging" formulas
vital shadow
liike rarranging divisions and multiplications, suares
when you "move" something that is multiplied to the other side, you divide with that number
xy = 1, x = 1/y
reverse for multiplication
torn jolt
The most general rule is that whatever you do on the left of the = you must also do to the right
slender finch
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slender finch
why does it say in the 2nd box the normal to the plane is ( 5 4 3 ) when shouldnt it be ( -2 1 1 ) ?
because the cartesian equation of plane is = to the normal direction vector of the plane so where did they get ( 5 4 3 ) from or am i missing something ?
i have a test tomorrow so pls help me clear this up😅
@ me if yk
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torn jolt
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torn jolt
torn jolt
how do you solve this integral?
torn jolt
i only got far to this step where you use substitutions to get t^8/(1-t^2)^2
sharp flame
I mean you just posted the solution
torn jolt
I mean you just posted the solution
yes, but what are the steps?
sharp flame
Partial fractions then I think
torn jolt
wait so I just divide t^8 by (1-t^2)^2?
sharp flame
Yeah you can do that I suppose
torn jolt
i already did that and I get t^4+2t^2+3+(6t^2-3)/(t^2-1)^2
is that correct? I could have made a mistake during the polynomial division
Help
torn jolt
Help
channel occupied go somewhere else
and this is a test
for which are not allowed to provide solutions for
sharp flame
,w long divide t^8/(1 - t^2)^2
glossy valveBOT
sharp flame
Are you sure you got 6t^2 - 3 and not 4t^2 - 3
torn jolt
my remainder is 6t^2-3 hum
torn jolt
Are you sure you got 6t^2 - 3 and not 4t^2 - 3
yes
sharp flame
Maybe check your work again
torn jolt
alright
i need some 5 minutes before i can close this channel if that's ok
yeah i forgot to subtract by -2t^2
but wait
how do we calculate the integral of (4t^2-3)/(t^2-1)^2 ?
also im sorry for not using LATEX, i'll be sure to do that next time I ask
sharp flame
Hyperbolic sub then 
torn jolt
nice troll
torn jolt
how do we calculate the integral of (4t^2-3)/(t^2-1)^2 ?
nope
ln(a)-ln(b)=ln(a/b)
the ln part was just refactored with logarithmic rules
and the 6t/(1-t^2) was calculated simply by multiplying the remained of that mini-integral with 12
case closed
also, with all due respect, don't suggest random things
because some people probably won't look stuff on their own and such
peace
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cobalt atlas
\
cobalt atlas
Can you provide more context?
I CANT
polar valve
what is the question? You have obviously the answer.
cobalt atlas
what is the question? You have obviously the answer.
the end of the book it has all answer i but a circle on the answer so you know
i dont know how i just have the answer
polar valve
lets ask me again. youre posting an picture without any information. not even a question. So please be so kind to ask what you want to know.
viral jasper
lets ask me again. youre posting an picture without any information. not even a ...
This is from an "eye queue" test. The problem is designed to test.. Well.. You know.
cobalt atlas
swr ... my english isn't that good can u explain
cobalt atlas
This is from an "eye queue" test. The problem is designed to test.. Well.. You k...
thanks
viral jasper
Yos prep, right?
viral jasper
Prep= prepare or study or practice
@polar valve, basically, you need to be "intelligent" enough to see the pattern and know the answer
cobalt atlas
Prep= prepare or study or practice
thats rıght
polar valve
<@836252175675818054>, basically, you need to be "intelligent" enough to see the...
no need to explain (to me). ameer wants help, so it should be able to write a question.
cobalt atlas
no need to explain (to me). ameer wants help, so it should be able to write a qu...
i can't understand what's wrong with u .. its just an i/q question what do i have to explain
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twilit leaf
hi @cobalt atlas i figured it out
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hi <@745774403991633993> i figured it out
twilit leaf
basically, the numbers in the shape are the tens digit and the number of sides of the shape is the ones digit
the stars in between are plus signs
wild sleet
blessed eye chad
twilit leaf
so the top equation is
33+44+24=101
so
23+64+66=153
i will let this channel close by timeout, if you are around, please ping me, if not at least the information is here for you
viral jasper
@cobalt atlas did you ever figure out the one asked earlier too? The K+L one?
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