thewizardofOU
#help-23
flat frigateBOT
mortal sandal
Does it make sense why
manic heart
im a little confused on what u mean by that
flat frigateBOT
thewizardofOU
mortal sandal
Yeah related to 3 and 4
If you know how to do 4 then I'm not sure where the problem is
How are you doing it?
manic heart
If you know how to do 4 then I'm not sure where the problem is
so all these questions are related to 4?
mortal sandal
Yes
minor barn
Get your own help channel
all the info is already in this channel
manic heart
It is not correct
what did I do wrong
mortal sandal
Well, without any work I'm tempted to just say "got the wrong answer"
But I imagine to get your x term you added the two things on the right together
That happens to work in part 4 but isn't correct in general
manic heart
ok ill explain what i did
first i added the a1 and a2
= a2
and then i did -3 × -5
and then I did -3+-5
mortal sandal
what's a1 and a2?
steep vessel
but wht "+"?
isn't it multiplication?
i have a question for you
What is
a*a=?
@manic heart
viscid bronze
thats a^2
manic heart
ur supposed to multiply?
viscid bronze
yes sir
viscid bronze
use the FOIL method
steep vessel
ur supposed to multiply?
Whenever you see parenthese with nothing between them, it means that you have multiplication right there
( )( )
viscid bronze
basically do $x * 2a$, then $a*-5$, then $-32a$, then finally $-3-5$
flat frigateBOT
Courtesy
viscid bronze
and that will give you
manic heart
ohh
steep vessel
and then expand normally
viscid bronze
should I say the answer
manic heart
so u always multiple a?
steep vessel
should I say the answer
no i think you should let her answer
viscid bronze
so u always multiple a?
Google up the foil method
viscid bronze
no i think you should let her answer
k
there's also something called FOIL method if that helps..
wait let me screenshot
steep vessel
there's also something called FOIL method if that helps..
exactly
manic heart
Google up the foil method
would that be allowed?
delicate sphinx
this is what ive done before
How were you able to do question 4 here? Because that process you applied here, is the same for the problem you are stuck on
manic heart
How were you able to do question 4 here? Because that process you applied here, ...
that was easy
delicate sphinx
It's no different
delicate sphinx
that was easy
So how did you do 4a?
viscid bronze
Don't add-
manic heart
= 6x
viscid bronze
Multiplyy
viscid bronze
I mean add at the end once you break the parnthesis
multiply first and once you finish breaking up the (n) then you add all the terms
delicate sphinx
first i added the x1 + x2 = x2
What are you using as x1 and x2?
delicate sphinx
and a×5=....
She's explaining how she did 4a, not this problem
viscid bronze
$2a*a$ not equal to $2a$
steep vessel
oh ok
viscid bronze
how do you put a not equal sign?
steep vessel
use \neq
viscid bronze
first i added the x1 + x2 = x2
here
viscid bronze
first i added the x1 + x2 = x2
did you know something called the expontent rule?
where
$a^b * a^c = a^$(b+c)$$
flat frigateBOT
Minds&Moves
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
viscid bronze
omg
viscid bronze
it's always multiply?
no add
if your multiplying the same number with a different expontent, then you add both expotent
and leave the number alone
$a^b * a^c = a^{(b+c)}$
flat frigateBOT
Courtesy
viscid bronze
there\
delicate sphinx
it's always multiply?
No, not quite, there is adding in one of the steps
flat frigateBOT
Courtesy
viscid bronze
it even works with variables too
manic heart
ohh
viscid bronze
omg
viscid bronze
so numbers get multipled
this only works when if there's the same numbers
and if they are different.
like
$5^4 * 7^{25} \neq{(5*7)^{(25+4)}$
then it's not true
flat frigateBOT
Courtesy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
manic heart
ohh
viscid bronze
so did you get it?
viscid bronze
read this
delicate sphinx
what about the others
I don't think you are understanding how to distribute/FOIL/expand properly, here's a video that would help https://www.youtube.com/watch?v=Dn6f_fL79Ws&ab_channel=TabletClassMath
manic heart
alr let me watch it
safe radishBOT
@manic heart Has your question been resolved?
manic heart
i watched the video and i understood everything
would i also use foil method for 1,2,3
or like when do i know that I need to use the f.o.i.l method
lapis pecan
you use foil when your multiplying
so for number 2 you would use it
but not when your adding or subtracting them
delicate sphinx
would i also use foil method for 1,2,3
FOIL is just a mnemonic for expanding two binomials like in question 4. Question 1 and 2, there's no expanding
manic heart
what did i do wrong 😭
delicate sphinx
what did i do wrong 😭
Where did -3 come from?
manic heart
Where did -3 come from?
okay let me explain
firstly i did a × 2a
= 2a^2
then
a × -5
= -5a
-3 x 2 = -6a
delicate sphinx
-3 x 2 = -6a
You mean 2a
manic heart
so if i know how to use the foil method would i be okay doing binomials then
delicate sphinx
As mentioned, FOIL is a mnemonic for expanding two binomials
So if you see it in the form like question 4, you can use FOIL
manic heart
so do i use foil when it says expand?
delicate sphinx
Not necessarily. Because question 3, says expand but you didn't really apply FOIL
lean otter
Really confused about this, why am I multiplying 2k by the 2? They aren't like terms?
safe radishBOT
Really confused about this, why am I multiplying 2k by the 2? They aren't like t...
delicate sphinx
Really confused about this, why am I multiplying 2k by the 2? They aren't like t...
You can multiply them
lean otter
I just did combining like terms and it told me to seperate them and add them individually, like -2k -(-5)+1 is simplified to -2k+6
delicate sphinx
It's not adding
lean otter
So if I'm multiplying, whether the terms are alike or not doesn't matter?
delicate sphinx
Nope does not matter since you want like terms for adding and subtract. Since you are multiplying, you don't need like terms
lean otter
Oh ok, so I multiply by whichever number comes before the bracket, and add the first number to the like terms?
If it were 2 -k (-2k - 5), would it be 2k +7?
delicate sphinx
Not quite, so -k * -2k = 2k^2
lean otter
-k can also be written as -1k?
delicate sphinx
Yes
lean otter
Why to the power of 2 at the end? Doesn't it just turn into +2k?
lavish urchin
Because it's -k * -2k, when you multiply, you add the exponents
no the question he sent was -k+2(-2k-5)
delicate sphinx
If it were 2 -k (-2k - 5), would it be 2k +7?
@lavish urchin
So yes you do add exponents for -k * -2k
lavish urchin
so the 2 before the bracket needs to be multiplied by -2k
lavish urchin
<@765921567976194068>
close but wrong
lean otter
So by that logic, -2(-5n+6) +5(2-7n)
Turns into -10n -12 +10 +35n?
Which is 25n-2?
I just multiply by the number infront of the brackets?
delicate sphinx
so the 2 before the bracket needs to be multiplied by -2k
What are you looking at?
2 -k (-2k - 5) = 2 -k * (-2k - 5) so 2 + -k * -2k + -k * -5
Are you reading 2 -k (-2k - 5) as (2 -k)(-2k - 5)?
lavish urchin
So by that logic, -2(-5n+6) +5(2-7n)
Turns into -10n -12 +10 +35n?
so this will be 10n -12 +10 +35n =45n-2
lavish urchin
Are you reading 2 -k (-2k - 5) as (2 -k)(-2k - 5)?
no
delicate sphinx
So by that logic, -2(-5n+6) +5(2-7n)
Turns into -10n -12 +10 +35n?
-2 * -5n = 10n
-2 * 6 = -12
5 * 2 = 10
5 * -7n = -35n
Combine like terms so 10n - 35n = -25n
-12 + 10 = -2
So -25n - 2
lean otter
Tf
So I did it wrong but still got the right answer
I messed up signage for -10 and 35
delicate sphinx
no
If you reread, the original problem is -k + 2(-2k - 5) but then the OP asked, what if it was 2 - k(-2k - 5) hence why I said -k * -2k = 2k^2
lean otter
Uhh I'm gonna do 1 more here just so I can understand
lavish urchin
oh
lavish urchin
If you reread, the original problem is -k + 2(-2k - 5) but then the OP asked, wh...
mb
delicate sphinx
I messed up signage for -10 and 35
`+ * + = +
-
-
- = -
-
-
-
- = -
-
-
-
- = +`
From basic multiplication concepts
- = +`
-
lean otter
19 - 6 (-k -2)
-6 x -k = 6k
-6 x -2 = 12
12 + 19= 31
6k +31?
delicate sphinx
Yes
lean otter
I think I understand thanks, what I'm doing is called the distribution property?
delicate sphinx
Yep
tawdry salmon
What did I do wrong
safe radishBOT
What did I do wrong
tawdry salmon
One minute
^ answer is right btw
Ok so I did
4 + sin(2 * 11pi/12)
That uses the sum formula
thin bridge
where's 4 + coming from
tawdry salmon
Bro
2 * 3
Ayy lets go that was the secret
Yo @thin bridge
Can u even write it like that
3 * 2sin
No?
I don’t think 2sin is sin(2x)
thin bridge
6 = 3 * 2
you can first rewrite that as
$$3 \cdot \blue{2\sin\br{\frac{11\pi}{12}}\cos\br{\frac{11\pi}{12}}}$$
then apply the double angle identity for the blue part
flat frigateBOT
ℝαμΩℕωⅤ
tawdry salmon
Right right
(cos^2)^3
How do we do power to the 3rd..
How to reduce to first power?
thin bridge
what are the exact instructions of the original question
thin bridge
well first simplify that whole expression
applying the defintiion of sec and exponent laws
thin bridge
skipping ahead
before doing anything with double angle identities
first simplify what you have
applying the defintiion of sec and exponent laws
thin bridge
you have something in the form
p^3/p
tawdry salmon
I don’t see it
thin bridge
you have some "thing" cubed divided by that thing
tawdry salmon
cos^2(x)^3
I don’t see anything dividing?
Oh
…
cos^2(x)^3/cos^2(x)
Whatever the hell that means
Just
cos^4(x)?
thin bridge
yes
tawdry salmon
thanks
safe radishBOT
@tawdry salmon Has your question been resolved?
tawdry salmon
So
This is interesting
1 + 2cos(10x) + cos^2(10x)
4
Both dividing
So we know cos^2(10x) will give us a denominator of 2
Can we straight up take it out
1 + 2cos(10x) + 1 + cos(20x)
8
Or
Do we have to do 1/4 + 2cos(10x)/4
And take out that 2 separately
fair crane
soemone help pls
safe radishBOT
soemone help pls
safe radishBOT
soemone help pls
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
I don't know where to begin.
<@&286206848099549185>
.close
delicate pumice
safe radishBOT
delicate pumice
Did i do this problem right
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
pleaaaase
someone
safe radishBOT
@delicate pumice Has your question been resolved?
safe radishBOT
@delicate pumice Has your question been resolved?
open tulip
Did i do this problem right
what is the purpose of the problem?
plucky elk
Your answer should be in terms of sines and cosines
Error or typo here
You took the Laplace transform of x'
worldly elbow
Hello!
I am working on a homework assignment that is due shortly and I would like for someone check and make sure that my work makes sense, and to help me solve the final problem of the assignment.
I am unsure on if I should solve it the same way I did with the other parts of the problem and if so, what numbers should I plug in where?
safe radishBOT
Hello!
I am working on a homework assignment that is due shortly and I would lik...
granite flower
in the first picture
that you have write 200, 150, 180 in it
a&b are the measure of the length of the 2 sides that are next to the angle and not opposite to them
here you chose a & b to be 180 & 200. which is wrong because the 180 meters side opposite to the angle you want to get
it is easier to see that from the map you have
a & b should have been 150 & 200
worldly elbow
a & b should have been 150 & 200
Thank you, I’ll fix that right now!
Does everything else look alright?
granite flower
in the second picture you also fell for the same error
You want the angle of a certain point (which here is the second building)
then search for the sides that are connected to that point (which are in this case the first building to the second building, and the third building to the second building)
and they will be a & b
the third side that has remained in the end will be c
worldly elbow
in the second picture you also fell for the same error
So in the second equation, a & b should be changed to 100 & 120 instead of 120 & 150?
granite flower
i want you to look at the 120 side, is it connected in any way to the second building?
worldly elbow
No, because it’s the estimated measure for the distance between the first and third building?
granite flower
yes then it can't be a or b
then it should be c
For the final question you have to not use the value that you have written in the previous question
and depend on the angles and sides that you have calculated or measured before to calculate the distance from the Kidder hall to the third building.
search for a triangle that connects the third building to Kidder Hall to another building that has an angle of the angles you have calculated.
Then use the same cos law that you have used such that:
the c side will be the side that is opposing the angle you will use.
a & b are the other sides of the triangle.
worldly elbow
So if c is 120, then a & b for the second equation are 200 and 120?
granite flower
do you mean for the final question or for the one before it?
worldly elbow
For the second question, not the final one, my apologies
granite flower
So if c is 120, then a & b for the second equation are 200 and 120?
this missed up a little bit
why you used the same side twice?
also he want the angle the forms on the second building, by connecting the triangle of the first, second, and third builidings
so why you included the Kidder hall to it
worldly elbow
The way you’re trying to help is kind of confusing me more
granite flower
to make it easier for you.
you have the map right
draw the triangle that is ordered from you
label the angle you want to get as "C"
the side that is opposite to that angle (or not connected to it) will be labeled as "c"
the other two sides will be "a" & "b"
then use the law
worldly elbow
Did I fix this problem?
granite flower
Did I fix this problem?
that is almost correct
but you used c as 150
i think you forgot to change it
granite flower
here we are talking about the first question, c is 180
granite flower
yes that is correct
worldly elbow
Thank goodness
granite flower
,calc 150^2 + 200^2 - 180^2
flat frigateBOT
Result:
30100
This is the second question, I think I may have fixed it? Most likely wrong though ^^’
granite flower
drawing the question will help you solve it better
granite flower
This is the second question, I think I may have fixed it? Most likely wrong thou...
yes it is correct
worldly elbow
Okay so, now with these two being correct, how do I go on to solve the final problem?
granite flower
,calc 150^2 + 100^2 - 120^2
flat frigateBOT
Result:
18100
For the final question you have to not use the value that you have written in the previous question
and depend on the angles and sides that you have calculated or measured before to calculate the distance from the Kidder hall to the third building.
search for a triangle that connects the third building to Kidder Hall to another building that has an angle of the angles you have calculated.
Then use the same cos law that you have used such that:
the c side will be the side that is opposing the angle you will use.
a & b are the other sides of the triangle.
worldly elbow
Do I use the same formula for the last two questions? c^2 = a^2 + b^2 - 2ab • cos(theta)?
granite flower
yes
you may edit it a little bit when you know what variable or unknown you want to get from the equation
it is funny but non of the angles that you have calculated would be helpful to solve this question here
worldly elbow
So is this a good start?
worldly elbow
it is funny but non of the angles that you have calculated would be helpful to s...
Is that bad?
granite flower
So is this a good start?
the unknown here would be the length of a side not the angle
do you know?
you are correct for now
umm wait, i don't think that you will have to use this law
do you have a picture for the map
worldly elbow
This is the map we have to use
granite flower
so i don't see first building, second building, or third building here, is it because you are the one who choses them?
worldly elbow
Yeah, but I just need to know how I should solve the final problem now that I have the angles and distances correct. How do I compute the distance between the third building and Kidder Hall? The distances I have a very rough estimates as the paper says they might be because the website doesn’t have a proper measurement tool, just something that gives us a general idea of the space apart
granite flower
oh i knew
you will use the same law
you have the distance from the second building to the third building
oh wait
they form a quadrilateral right?
can you draw the shape the building make and the sides and angles you have
worldly elbow
Here’s a better quality photo with the drawing
safe radishBOT
@worldly elbow Has your question been resolved?
worldly elbow
I’m working on the final question now
granite flower
that is what you got
that is better
now we have the whole angle on the second building
if we got the angle marked blue
we can subtract it from the whole angle to get the angle between
worldly elbow
This is what I have for the third problem
granite flower
This is what I have for the third problem
what is that law
it doesn't make sense
the sides you use on the right hand side should be only 2 sides
you have used 4 different sides
worldly elbow
What should I be doing then. This was due 30 minutes ago 🥲
I’ve been sick so I’ve had no other time to do it
granite flower
do as i said here
i approximated the angles to the nearest integer value, so if you want more accurate results use the values you wrote
worldly elbow
do as i said here
I can’t figure that out
granite flower
use the cos law to get the value of the blue angle
or you know what
you can use the sin law instead
it would be easier
to use
as we have a singed angle already then we can get the value of the blue angle like this
$$\frac{180}{\sin(60)}=\frac{200}{\sin(\theta)}$$
flat frigateBOT
Sherif Player
granite flower
,wolf calc \arcsin(\frac{200\times\sin(\arccos(\frac{301}{600}))}{180})
the result here is in radian
worldly elbow
So my answers are wrong?
safe radishBOT
@worldly elbow Has your question been resolved?
worldly elbow
.close
gusty ferry
safe radishBOT
gusty ferry
how
lean otter
1 - (Addition of all other fractions)
gusty ferry
so add 3/5 and 1/3?
lean otter
Ye
gusty ferry
14/15
gusty ferry
1 minus 14/15?
lean otter
Yep
gusty ferry
1/15
gusty ferry
yes
gusty ferry
yes
lean otter
Non adult is child and senior
Yeah
So
Let us assume
X number of people visited
Yeah?
gusty ferry
yep
lean otter
⅗ of them were adults
So ⅗x were adults
⅗x * 130 = Ticket revenue from adults
gusty ferry
woahahaha what
lean otter
Similarly,
⅖x * 100 = Ticket revenue from non-adults
gusty ferry
why 3/5 times x?
lean otter
If suppose
There were total of 100 people, ⅗ were adults
Then how many adults were there?
⅗ * 100 right
Yes or no?
gusty ferry
why times tho
gusty ferry
yes
gusty ferry
but why do we 3/5 times 100
lean otter
What else would we do?
lean otter
I dont have an explanation for why we do ⅗ times 100
But thats what we do
gusty ferry
oh ok
lean otter
Yeah so
⅗x130 = revenue by adults
⅖x100 = Revenue by non adults
Adding them should equal to 136290
Find x -> total number of people
Find 1/15 of x -> Number of seniors
gusty ferry
3/5x * 130 right
lean otter
Yeah
chrome orbit
safe radishBOT
solar hazel
A is coarser than B means A is a subset of B
chrome orbit
ohh that simple ?
chrome orbit
the word is a math term or just an english word i have first time encountered ? 😛
safe radishBOT
solar hazel
coarse means rough in plain english
split fulcrum
chmonkey!!11!1
chrome orbit
i didnt know that 😛
safe radishBOT
Available help channel!
fierce inlet
this is how i did it
solve for n and m
n = 1/2
m = 5
substitute n and m in option b
both powers will turn out to be 1
since linear eq can have only 1 as max power
option b correct
but when you substitute 1/2 in 2n - 1 it's not 1, making it not a linear equation
how do i do this?
hazy elbow
this is how i did it
solve for n and m
n = 1/2
m = 5
substitute n and m in opti...
well n can be (1/2) as well as 1 and m can be 4 as well as 5
fierce inlet
that's what's confusing
if n is 1/2, it doesn't satisfy the equation of 2n - 1 = 1
2n-1 = 1 because it is a linear equation and power must be 1
hazy elbow
are you sure
a linear equation has MAX power of variable(s) as 1
so 2n-1 can be 0 as well as 1
and m-4 can be 0 as well as 1
now check the options with these conditions
fierce inlet
wait is it because anything to the power of zero is one
hazy elbow
yes
fierce inlet
a linear equation has **MAX** power of variable(s) as 1
from what i've learnt the power is only 1 for a linear equation
unkempt salmon
The graph of cube root of x looks awfully similar to cube of x but just rotated
unkempt salmon
So I was wondering if there was any way to rotate the graph of cube root of x to get the graph of cube of x
junior smelt
,w plot y=x^3, y=x^(1/3), y=x
Wait huh 
Never mind that then 
anyways note that the cube root and cube are inverses of each other
final halo
It's just flipped, you don't need any rotation
unkempt salmon
It's just flipped, you don't need any rotation
What?
dapper gazelle
it's the inverse function
final halo
Flip the blue in y=x you get the red
dapper gazelle
x^(1*3) is the inverse function of x^3
or in other words it is mirrored over the first bisector
unkempt salmon
Flip the blue in y=x you get the red
Can you send the equation
final halo
What equation?
unkempt salmon
Like modify the graph of cube root of x to get x cubed without any cubes or exponents
Only rotations, flips and translations
dapper gazelle
y = x^3
to get the inverse function we switch y and x =>
x = y^3
<=> y = x^(1/3)
oops
unkempt salmon
Not inverse function
Like modifying the same function
Isn't there any way to rotate and flip the graph
To get the same thing
final halo
A reflection in y=x is precisely swapping x and y in the equation
final halo
You can't do this by rotation
final halo
Because x³ and x^1/3 aren't related by a rotation
safe radishBOT
@unkempt salmon Has your question been resolved?
noble thicket
noble thicket
safe radishBOT
safe radishBOT
@noble thicket Has your question been resolved?
noble thicket
<@&286206848099549185>
lean otter
x is greater than or equal to 1
safe radishBOT
@noble thicket Has your question been resolved?
severe moon
Can someone help me with this question pls
safe radishBOT
Can someone help me with this question pls
severe moon
I know they are isosceles triangles
safe radishBOT
@severe moon Has your question been resolved?
white girder
I know they are isosceles triangles
Get as many angles as you can in terms of x and choose another variable y, which will get you all of the other angles
zinc gull
safe radishBOT
zinc gull
Can someone help me with this?
I've gotten as far as finding the quadratic nth term of the stopping distanced 6, 14, 24
potent seal
The one under "challenge"?
zinc gull
Yes
potent seal
Ok
obtuse plover
U can do some polynomial curve fitting
zinc gull
Idk what that is
zinc gull
Oh okay
obtuse plover
What topic are u learning rn
zinc gull
I'm doing quadratics with real life applications
potent seal
You could use the equations of motion as welp
Well
Coz the car is constantly accelerating
Acceleration is just the second derivative of the d(s) function
zinc gull
Oh okay, is that something I should just know or can you figure it out from the question?
potent seal
But i think there's a simpler way
zinc gull
Also, can you show me how to do it without differentiation too?
potent seal
I just don't know what it is
obtuse plover
Yea it’s polynomial curve fitting
potent seal
Also, can you show me how to do it without differentiation too?
Ye ill try to find out
obtuse plover
Here’s an example
zinc gull
Okay
obtuse plover
This is a similar example
Given n points, you can find the equation of a polynomial of degree n-1 that passes through those points
zinc gull
Oh okay
How can I do that for this question?
I've said that the stopping distance can be calulated using n^2 +5n but idk if that even helps
potent seal
I misread it again, I thought it was a function of time, but it's a function of speed
Then ig you can just substitute values... You'll get 3 equations and you have 3 variables
obtuse plover
So you wanna set up the system p(20), p(30), p(40)
zinc gull
Oh, then solve as a system of 3 equations?
potent seal
Yeah
obtuse plover
Yea that’s what this is
zinc gull
So you wanna set up the system p(20), p(30), p(40)
Oh okay thank you
Thanks @obtuse plover
obtuse plover
Np
zinc gull
.close
tawny seal
If $\sum a_{n}$ and $\sum b_{n}$ both diverge, then $\sum a_{n} + b_{n}$ diverges
safe radishBOT
If $\sum a_{n}$ and $\sum b_{n}$ both diverge, then $\sum a_{n} + b_{n}$ diverge...
tawny seal
I've thought of the counterexample a_n = n and b_n = -n
both sum an and sum bn diverge in this case
but sum (an + bn) is the convergent series which equals zero
this is a valid counterexample right
?
flat frigateBOT
texaspb
tawny seal
.close
sweet hinge
safe radishBOT
sweet hinge
idk where to go after x=y-10
potent seal
Do you need AC in terms of x and y or...?
sweet hinge
I need to find ac which is just ae+ce
zinc gull
I think that you can equate coefficients to solve this. If you let AC be k lots of AE, then find a different route from A to C that is r lots of a different distance, you can equate coefficients and solve for AC
sweet hinge
it’s a number
potent seal
Ah kk
zinc gull
I can link you a nice video for stuff like this if you want?
sweet hinge
uh sure
zinc gull
sweet hinge
Thx
zinc gull
No problem
burnt umbra
[Linear Algebra - Eigen values & vectors]
I'm trying to find an eigen vector using eigen value 2, assume that transformation 0 is correct (2 is already substituted into the original matrix).
I'm wondering whether the result of this gauss is wrong?
I have 2 answers:
a. (-1, 1, 1)
b. (-1, 0, 1)
I assumed that in the second result, x3 would be 1, and x2 does not have any value, so it's zero
- note: bebas means free on the right side
safe radishBOT
**[Linear Algebra - Eigen values & vectors]**
I'm trying to find an eigen vecto...
@burnt umbra Has your question been resolved?
raven heart
it happens that you get 2 (linearly independent/free) eigenvectors for a single eigenvalue, it's not a problem
looking at the initial matrix, that's what I'd expect
raven heart
ah
burnt umbra
thanks
raven heart
well what's the full problem then ?
burnt umbra
wait
raven heart
are there other issues with it ?
burnt umbra
We were tasked to find P^-1 * A * P
Where matrix A:
0 0 -2
1 2 1
1 0 3
We already calculated the eigen values, that is
= (λ -1) (λ - 2)^2
= (λ -1) (λ - 2) (λ - 2)
λ = 1
λ = 2
λ = 2
raven heart
ok yeah
burnt umbra
we've found eigen vector for 1, but can't find 2
raven heart
well you found them for lambda = 2
both the answers are correct
the goal of diagonalization is to find a basis of eigenvectors
burnt umbra
yah... I have tried calculating the P, but since its determinant is zero. We can't find the inverse
raven heart
the goal of diagonalization is to find a basis of eigenvectors
you'd hope to get 2 eigenvectors here [your polynomial is (λ -1) (λ - 2)^2, if you don't have two eigenvectors for eigenvalue 2 your matrix wouldn't be diagonalizable]
raven heart
yah... I have tried calculating the P, but since its determinant is zero. We can...
ah ok yeah that's a problem
raven heart
can you show your P then ?
burnt umbra
can i change it tho?
raven heart
you need to use both of them
burnt umbra
oh
burnt umbra
I'll try for
-2 -1 -1
1 1 0
1 1 1
Alright it's fine, thanks for helping
so that P inverse is:
-1 0 -1
1 1 1
0 -1 1
.close
strong bison
i need help w this
safe radishBOT
i need help w this
rough storm
!status
safe radishBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
!showwork
safe radishBOT
Show your work, and if possible, explain where you are stuck.
@strong bison Has your question been resolved?
safe radishBOT
@strong bison Has your question been resolved?
dusky crag
Hey
So, you're just asked to explain how you would find the instantaneous velocity of the skydiver at 2.0 seconds
You here @strong bison ?
Can you please @ mention me if you text back
safe radishBOT
@strong bison Has your question been resolved?
indigo tundra
safe radishBOT
delicate sphinx
Wtf is a furlong
,w what is a furlong
flat frigateBOT
indigo tundra
LOL WHAT ITS REAL
delicate sphinx
Yes it's a unit of measure
indigo tundra
Is the answer 18/35
Is this the answer
delicate sphinx
Idk probability so I can't help sorry, someone else will stop by if they can help
indigo tundra
😭 😭
indigo tundra
<@&286206848099549185>
torpid fable
use law of total probability
indigo tundra
use law of total probability
Never heard of it
torpid fable
Is the answer 18/35
yes
safe radishBOT
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Available help channel!
jovial sun
as surds how would I find the roots to $x^3+3x^2-33x-35$
safe radishBOT
as surds how would I find the roots to $x^3+3x^2-33x-35$
flat frigateBOT
sealpup321
jaunty owl
well
when dealing with non quadratics
I try to plug in some easy integer values to see if those equal 0
cuz then I can do division to reduce the degree of the polynomial
jovial sun
sorry XD
jaunty owl
np
flat frigateBOT
sealpup321
jovial sun
sorry about that
jaunty owl
well since I can tell that when it is expanded, the degree of the polynomial will be 2, I would just expand it and factor that
jovial sun
huh sorry i must be tired for some reason i completely forgot tha
thanks for the help and sorry for the confusion lmao
jaunty owl
no problem
vagrant ice
jaunty owl
ye
safe radishBOT
jovial sun
.reopen
safe radishBOT
✅
jovial sun
holup i got $x=5\pm29^(1/2)$
flat frigateBOT
sealpup321
jovial sun
the answer should be $x=1\pm(13)^(1/2)$
flat frigateBOT
sealpup321
jaunty owl
**sealpup321**
for this?
jovial sun
yup
jaunty owl
well idk what u did Lolo so I can't advise u
jovial sun
i simplified and got$x^2-10x-4=0$
flat frigateBOT
sealpup321
jaunty owl
I think that's wrong
jovial sun
then used the quadratic formula and got $5\pm root(29)$
flat frigateBOT
sealpup321
jovial sun
I think that's wrong
ah my bad
how so?
my workings seem ok
as $2(x+1)(x-4) = 2x^2-6x-8$
flat frigateBOT
sealpup321
safe radishBOT
jovial sun
i am really exhausted today usually im not so
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Available help channel!
fluid spoke
fluid spoke
idk what this question is talking about
or asking me to do
is it just asking me to find the antiderivative of v
weary lotus
storm berry
safe radishBOT
storm berry
How can I find the critical points
I already tried quadratic formula and factoring
no real solutions for quadratic formula
<@&286206848099549185>
😦
.close
steep gust
safe radishBOT
fleet condor
whats Km,n in this case
or is it just asking for you to descibe what the matrix dimensions would be and the meaning of the elements?
safe radishBOT
@steep gust Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
merry totem
I need help understanding this I know the T is supposed to be by itself, but I'm sure if I'm doing this correctly.
safe radishBOT
I need help understanding this I know the T is supposed to be by itself, but I'm...
merry totem
merry totem
Wait am I suppose to divide by 3 to get the T by itself?
gritty glacier
Yes t itself
merry totem
chilly lance
add 6 first ‼️
gritty glacier
I said you to make two cases bruh
$t = \begin{cases}
3t - 6 = +8\
3t-6=-8\
\end{cases}$
flat frigateBOT
Bettim
gritty glacier
now you can divide both sides by 3
you will get 2 values for t
both are correct
subtle matrix
Can someone explain to me how the formula is used to solve these questions
safe radishBOT
Can someone explain to me how the formula is used to solve these questions
@subtle matrix Has your question been resolved?
subtle matrix
<@&286206848099549185>
subtle matrix
.close
fair whale
safe radishBOT
fair whale
been staring at this problem for the last two hours
I am completely clueless
all I could figure out
safe radishBOT
@fair whale Has your question been resolved?
fair whale
<@&286206848099549185>
safe radishBOT
@fair whale Has your question been resolved?
crude sleet
What’s the definition of a linearly independence?
It’s this!
Since that set only has one vector in it you have to show that:
$a\bold{V}= \bold{0}$
flat frigateBOT
Karl
crude sleet
And what must the value of a be?
Oh shucks u got all of this
Alrighty
Extending a set to become a basis
There’s a process for this lemme Google
Badabing Badaboom
The hard bit is adding figuring out which of the tacked on basis is in the span of S
But since S consists of 1 vector, it shouldn’t be terrible right?
And the basis that you tack on can just be the standard basis for R5, i.e.
(1,0,0,0,0), (0,1,0,0,0), etc
@fair whale
lean otter
What am I doing wrong here?
safe radishBOT
What am I doing wrong here?
lean otter
flat frigateBOT
Matt
$50=100(b)^{1590}$, im using the equation $P(t)=a(b)^t$
cloud citrus
wdym by the rate
cloud citrus
Its not messed up
cloud citrus
wait for a bit
cloud citrus
**Matt**
```latex
$50=100(b)^{1590}$, im using the equation $P(t)=a(b)^t$
```
From this we have
$$b^{1590}=\frac{50}{100}$$
flat frigateBOT
Afi
cloud citrus
b should be (50/100)^(1/1590)=0.9995564153
flat frigateBOT
Matt
cloud citrus
Yeah
lean otter
The problem states at 1590 years, it contains 100 mg
so dont you agree
$100=a(b)^{1590}$
flat frigateBOT
Matt
flat frigateBOT
Matt
cloud citrus
yes that is correct
cloud citrus
i think you should just find the value of b first
lean otter
i think you should just find the value of b first
$50=100(b)^{1590}$
flat frigateBOT
Matt
cloud citrus
can you just give me the value of b?
flat frigateBOT
Matt
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
flat frigateBOT
Matt
cloud citrus
hmm go on
cloud citrus
wdym by that
cloud citrus
sure
cloud citrus
that should be correct
safe radishBOT
safe radishBOT
Available help channel!
kindred violet
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patent kindle
Do u know what sinx is
kindred violet
Do u know what sinx is
no i always get confused
i feel like i know but i don’t know
kindred violet
i know reference angles and rotation angles and all that
i know
sine cosine tangent and the reciprocal versions
and sin = y/r etc
i know unit circle
patent kindle
Ok
So we just have to plot the graph of sinx =y
Do u know how to plot graph of a function
kindred violet
Do u know how to plot graph of a function
honestly no not really
my mind goes blank when it asks me to do that
patent kindle
We have to get the value of y at a value of x and mark that on the graph
patent kindle
Is calculator allowed
kindred violet
on the test no, but sometimes they assign calculator questions for homework so i don’t know about this question
patent kindle
Idk how to explain this sorry
delicate sphinx
honestly no not really
Just make a table of values, and use the unit circle.
kindred violet
Just make a table of values, and use the unit circle.
i can make up any values i want?
delicate sphinx
It gives you the domain for both functions, -pi to 2pi
delicate sphinx
i can make up any values i want?
Not quite any. It has to be values in that given domain
kindred violet
Not quite any. It has to be values in that given domain
what’s an example of a value that is could use?
kindred violet
It gives you the domain for both functions, -pi to 2pi
anything between here?
delicate sphinx
That's why you also use the unit circle
It should be a value between -pi and 2pi and something on the unit circle since you know that
Like pi
kindred violet
i feel like this is a stupid question but if i pick an x value of pi for example what is my y?
delicate sphinx
i feel like this is a stupid question but if i pick an x value of pi for example...
You plug that into the function
kindred violet
i feel like this is a stupid question but if i pick an x value of pi for example...
i feel like i know what to do but nothing comes to my mind right now
delicate sphinx
You have y = sin x and y = cos x, you're plotting both