#help-36
final saddleBOT
south lily
if you find the derivative of $f(x)=kx^3$ to $f'(x)=3kx^2$\
then since the normal is perpendicular to $f'(x)$ this must be true:\
$f'(2) \cdot \frac{1}{6} = -1$\
$12k \cdot \frac{1}{6} = -1$\
$k = -0.5$
soft zealotBOT
chrelleren
cosmic zinc
Why do you make it = to -1
south lily
if two lines are perpendicular the product of their slopes is -1
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native sparrow
why is, in the image, colored that blue part in the last graph? how (from the first disequation) we know what part need to be colored?
final saddleBOT
why is, in the image, colored that blue part in the last graph? how (from the fi...
gloomy ferry
why is, in the image, colored that blue part in the last graph? how (from the fi...
Since it should be larger than 0, it means that you are only considering the graph above the x-axis
native sparrow
Since it should be larger than 0, it means that you are only considering the gra...
and why i dont consider value that are beetween x1 and x2?
gloomy ferry
When you have values between x1 and x2, the solution is negative, the idea behind you sketching the graph is "for a certain value of x, your output is going to be y", now you want your inequality to be larger than or equal to 0, so you want the graph that is above instead of below
you can see values between x1 and x2 is below the x-axis (or the line drawn), which indicates a negative solution
native sparrow
When you have values between x1 and x2, the solution is negative, the idea behin...
sorry i dint understand, can you explain in simpler terms?
gloomy ferry
sorry i dint understand, can you explain in simpler terms?
blue line is your graph and green area is y>0, if you have an inequality and you want it to be larger then 0, it means their solution needs to be a positive value
native sparrow
blue line is your graph and green area is y>0, if you have an inequality and you...
yes so every value that starts from the red point?
gloomy ferry
Yes
and also if you notice, the graph on the left also lies in the green area, so it also includes
native sparrow
why is, in the image, colored that blue part in the last graph? how (from the fi...
the solution of my equation are 2, i draw them and accept only the one who is >= 0
native sparrow
and also if you notice, the graph on the left also lies in the green area, so it...
but isnt it less than 0?
gloomy ferry
do you know what is a function? I'll try explain that way
native sparrow
do you know what is a function? I'll try explain that way
no sorry, i only use f(x) as "a series of operstions with and x"
gloomy ferry
why is, in the image, colored that blue part in the last graph? how (from the fi...
basically for A:
Your f(x) is x^2+2x-16 and you want f(x) >=0
so you are drawing out f(x) and y>=0, and you are finding the places where both the graph and the region touches each other
native sparrow
basically for A:
Your f(x) is x^2+2x-16 and you want f(x) >=0
so you are drawing...
what is y in this case?
stuck mirage
why is, in the image, colored that blue part in the last graph? how (from the fi...
In general, when you have a number, to know if it is positive or negative you need to write it as a product (multiplication) of numbers whose signs you know
If you take the example
$x^2+2x-16 \geq 0$
soft zealotBOT
Daddy_314
stuck mirage
Notice it can be factored into
$(x + 1 - \sqrt{17})(x+1+\sqrt{17}) \geq 0$
soft zealotBOT
Daddy_314
stuck mirage
This is a multiplication of two numbers
$(x + 1 - \sqrt{17}) \times (x+1+\sqrt{17})$
native sparrow
**Daddy\_314**
you applied the delta formula, right? (to find the 2 solution)
soft zealotBOT
Daddy_314
stuck mirage
Its positive only when both of those numbers are positive or both are negative
So $x + 1 - \sqrt{17} \geq 0$ AND $x+1+\sqrt{17} \geq 0$
soft zealotBOT
Daddy_314
stuck mirage
Or
Both are <= 0
Once we solve each case, we can know which region to color
This is the true way to solve these questions
Any other way is a shortcut
That you will forget within a week
stuck mirage
you applied the delta formula, right? (to find the 2 solution)
Not necessarily but you can
I completed the square
Take a simpler example
Without square roots
To see the method I explained
native sparrow
Not necessarily but you can
then how did you find out that it became x+1-sqrt 17?
stuck mirage
$x^2+2x-16
= x^2+2x+1-17
= (x+1)^2 - 17
= (x+1)^2 - \sqrt{17}^2
= (x+1 - \sqrt{17})(x+1+\sqrt{17})$
soft zealotBOT
Daddy_314
stuck mirage
This is how
native sparrow
oh ok, i understand the process but not why and how you managed to think that
soft zealotBOT
Daddy_314
native sparrow
i also did but i didnt even think about that ahaha
stuck mirage
Well now you will
native sparrow
or i can use the formula, right?
stuck mirage
You can, at your own risks
Also the formula
Came from exactly this method
If you read the proof of it
native sparrow
oh ok, perfect
native sparrow
**Daddy\_314**
so we have this, both of them need to be >=0 at the same time, right?
stuck mirage
Or both negative !
native sparrow
so we have this, both of them need to be >=0 at the same time, right?
what do we do after this point?
stuck mirage
We solve the inequalities
Case 1.
x + 1 + sqrt(17) >= 0
And x+1-sqrt(17) >= 0
So
x >= -1-sqrt(17)
And x >= -1+sqrt(17)
(draw this)
On a line
Or:
Case 2.
x+1+sqrt(17)<= 0
And x+1-sqrt(17) <= 0
Draw this as well
And you will see for yourself
native sparrow
sorry but why also both negative?
stuck mirage
Because the product of two negative numbers is positive
And the product of two positive numbers is positive
So since we know their product is positive, we can be in either one of those cases
If I tell you
$ab = 20$
soft zealotBOT
Daddy_314
stuck mirage
With a and b two integers
You can have a = 4 and b = 5
But also a = -4 and b = -5
native sparrow
yeah true
stuck mirage
Notice this method we are doing
Might seem a bit longer
But it is important to do it entirely
A few times
Then you can use shortcuts
When you figure out where they come from
So try to do what I said
native sparrow
So
x >= -1-sqrt(17)
And x >= -1+sqrt(17)
ok so i put this on geogebra?
stuck mirage
What upper part
stuck mirage
Im asking for drawings like this
One drawing for each Case
(each case has two inequalities, so two lines to draw per case)
native sparrow
i am not understanding anymore sorry
stuck mirage
Lets try it with a more basic example
Without square root of 17
Imagine you want to solve
$(x-1)(x+2) > 0$
soft zealotBOT
Daddy_314
stuck mirage
Case 1.
x-1>0
And x+2 > 0
Case 2
x-1<0
And x+2 < 0
Case 1:
x > 1 AND x> -2
Case 2:
x < 1
AND x <-2
So now we plot each case on the real line
Case 2 gives us this
x is less than 1 and x is less than -2
So x is < -2
This is the solution for case 2
We do the same for case 1
Do you understand ?
If not, there is no point doing degree 2 polynomial inequalities
final saddleBOT
@native sparrow Has your question been resolved?
light violet
stiff condor
notice that the particle is moving in a circular path
light violet
notice that the particle is moving in a circular path
This is what I’ve tried to do
Idk if this is correct
stiff condor
so we apply centrifugal force on particle for the outward radial direction for the equilibrium
stiff condor
lemme see
light violet
i got sn theta wrong
stiff condor
i got sn theta wrong
im quite confused myself :/
stiff condor
no worries
i think you should use this equation
mgsin 0 + µN = mrw²cos θ
light violet
i think you should use this equation
mgsin 0 + µN = mrw²cos θ
ive never seen this
how do i get to it?
stiff condor
how do i get to it?
equilibrium of particle (static friction)
light violet
is that mgsin theta or mgsin 0
stiff condor
is that mgsin theta or mgsin 0
theta sorry, my bad
stiff condor
let me know if you get the answer
I tried it with this equation and i got an answer
stiff condor
okay thank you
note here, µN is µ(mgcos θ+ mrw² sinθ)
light violet
note here, µN is µ(mgcos θ+ mrw² sinθ)
im not 100% sure where this equation comes from
stiff condor
im not 100% sure where this equation comes from
well, now you know
About the derivation...
Im not sure how to
light violet
ok
light violet
yessssssssssssssss
lets go
cmon
yes yes yes
thank you bro
(im slightly excited)
light violet
note here, µN is µ(mgcos θ+ mrw² sinθ)
why did my teacher not let me know about this
stiff condor
you prolly wanna check that equaation with your prof or your teach, and confirm if its valid
stiff condor
w^2=326.86
w=18.07
w=18.1
stiff condor
maybe u have saved my whole class
glad to help
im sure there might be another way to do it but i think this is the easiest
light violet
wo when is the formula valid
light violet
im sure there might be another way to do it but i think this is the easiest
10000x easier than what i did
stiff condor
for equilibrium of particle in static friction
final saddleBOT
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void cipher
hello, this is probably a silly question but im not sure if im right or not
void cipher
"Plot some points that are 5 units from the origin in the taxicab metric. What does the entire set of such points look like? Sketch it. Also sketch the set of points that are 5 units from the origin in the Euclidean metric. Call this set C for later reference."
i think i understand the euclidean metric part of the question, it's a circle with a radius of 5 from the origin
the taxicab metric i think of like a knight in chess, if the knight could move X number of squares in any up/down/left/right combination of moves
so would that look more like this? (one sec sketching this fast)
just imagine 4 of those
but that's the general idea as i understand it. am i right?
desert mantle
well ok you drew some boxes. but what are the points you need to draw
void cipher
with the taxicab if the points are 5 from the origin they need to be (5,0) (4,1) (3,2) (2,3) and so on?
desert mantle
is there something between those?
desert mantle
yes
void cipher
taxicab = square centered on the origin, euclidean would be 5 from the origin but in a circle instead of a square?
void cipher
no
i'm in precalc and it's my first math in 22 years, i'm using khan academy to try to catch up and patch holes in my knowledge
yesterday i realized i'd completely forgot about the pythagorean theorem. totally forgot all about it.
you probably get this all the time but i cannot thank you enough
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delicate nebula
help
delicate nebula
final saddleBOT
@delicate nebula Has your question been resolved?
prime mason
is anyone able to help with part 2
final saddleBOT
is anyone able to help with part 2
prime mason
i think that means that the normal force is doing all the radial force?
like friction doesnt play a part in contributing to radial force?
mental roost
Get the centripetal force and the normal force. Get their components in the direction of the slope. Then see for which angle they cancel each other out
prime mason
im confused about the normal force
cause if this is my fbd
how did my teache get this
final saddleBOT
@prime mason Has your question been resolved?
smoky oracle
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tulip coyote
Do you have any idea as to how to start?
smoky oracle
Do you have any idea as to how to start?
currently i found the iqr of class x and class y
which is 3x for x and y-1 for y
then i did 3x=3(y-1) since its 3times more
but im not sure what to do anymore
tulip coyote
Yep, good looking, then of course you can also then say as a result you know x = y - 1
What about the median statement?
smoky oracle
do i do x^2-3= y^2-y/2
tulip coyote
Yep, that’ll do 
You have that, but at the same time, that x = y - 1
Can you cook with that? 
tulip coyote
im thinking do i solve for y and then substitute the x in?
Yep basically 
smoky oracle
ok so i got x= -2 or 3 and y=4 and -1
im not sure how to calculate the percentage
actually i get it
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tired horizon
Yo
tired horizon
<@&286206848099549185>
I’m in 8th but reviewing topics from last year we take a test in them
I’m reviewing 6.10 but know how to do it
But I need practice problems to study
It’s circle graphs
For my test tomorrow
hearty vector
hybrid heath
<@&286206848099549185>
!15m
final saddleBOT
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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.
@tired horizon Has your question been resolved?
void cipher
So im making some headway with understanding things since my last question
void cipher
But this has me stumped
I think its a circle with the origin at -3,-9
And a radius of 5
But im not going to lie, i pulled that out of my backside
hybrid heath
I think its a circle with the origin at -3,-9
Close
Double check your origin
Radius is right tho
void cipher
How do i double check my origin
Up until now ive mostly been doing problems with an origin of 0,0
Ive been at this math work for four hours today and im just short of the halfway point, i feel so discouraged
languid yoke
How do i double check my origin
You have the signs flipped
hybrid heath
Since squaring something cant be negative
No. That's not why
(x+3)²+(y+9)²=5² would have an origin of -3,-9
void cipher
Why do you flip the signs?
hybrid heath
(x+3)²+(y+9)²=5² would have an origin of -3,-9
Imagine this was our function. If we choose x=-3, then we're solving 0²+(y+9)²=5², which has solutions y=-9+5 and y=-9-5. In short this means the extreme y points are 5 units away from the coordinate -9. Likewise, if we choose y=-9, then we would get x=-3+5 and x=-3-5, which is 5 away from the coordinate -3. These four points we've found describe a circle of radius 5 centered around the point -3,-9
Another good way to find the origin is to just solve (x-h)²+(y-k)²=0. There's only one solution, and it will be the origin
void cipher
One sec reading
Did you mean if x=3 instead of -3?
For the second part where you gave the formula what do you plug in for h and k? Is it the same as (x2-x1)^2 + (y2-y1)^2= 0
I'm struggling to understand
Did i lose you
I'll just try again later
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grim siren
7b
grim siren
how do u do b
severe canyon
There's several ways, such as using the classical quadratic formula, x = -b ± √..
feral ginkgo
that's right
you see that the discriminant (number under the square root) is negative
which suggests the quadratic has no real solutions
it does have *complex * solutions though but if you haven't learnt about complex numbers then stopping at no real solution is good enough
grim siren
this is the solution?
grim siren
thats what my teacher put
soft zealotBOT
lgkoo
feral ginkgo
thats what my teacher put
they made a mistake then
they forgot to keep the square root for 11
grim siren
ok i see
gentle zephyr
It is currently $3!:!00!:!00 \text{ p.m.}$ What time will it be in $6666$ seconds? (Enter the time in the format "HH:MM:SS", without including "am" or "pm".)
final saddleBOT
It is currently $3\!:\!00\!:\!00 \text{ p.m.}$ What time will it be in $6666$ se...
soft zealotBOT
938c2cc0dcc05f2b68c4287040cfcf71
fallen vigil
how many hours are in 6666 seconds?
gentle zephyr
60secs are 1 minute
60 minutes are one hour
6666/(60 x 60) gives the number of hours
fallen vigil
and that is?
soft zealotBOT
Result:
1.8516666666667
almost two hours
fallen vigil
ok so
what u normally do here is you round down and take 1 hour
and from there u continue to find the number of minutes after u minus one hour from the start
fallen vigil
yes
soft zealotBOT
Result:
3066
yes
gentle zephyr
,calc 3066/60
soft zealotBOT
Result:
51.1
round down
fallen vigil
alway round down and work with the remainder
gentle zephyr
,calc 3066 - 51 * 60
soft zealotBOT
Result:
6
6 seconds
fallen vigil
yes
fallen vigil
yes
final saddleBOT
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rocky juniper
Hello I have a statistics-related question.
I'm trying to justify using a pearson's correlation coeffecient over spearman's correlation coeffecient to test the relationship between poverty rates and disease incidence rates.
The data does have an outlier but appears to have a normal distribution.
I have tested for both coeffeicients and I have found spearman's coefficients to be generally lower (but not by much) to the pearson coefficients. Is that enough justification to choose Pearson's test?
lethal estuary
what does the scatterplot look like?
rocky juniper
lethal estuary
those don't exactly look linear to me (esp. the second one) so IMO Spearman is more appropriate
rocky juniper
so it doesn't matter that much whether either value is higher or lower?
since I know that having an outlier is already pretty indicative of using a spearmans correlation
lethal estuary
it depends on how you define "an outlier". but Pearson's correlation is for a linear relationship, and I don't think those look close enough to linear. looks like an exponential decay, kinda
but I don't know if there's a one-size-fits-all rule. you can see some of the answers here for example: https://stats.stackexchange.com/q/8071/42597
there's more useful information here as well: https://stats.stackexchange.com/q/3730/42597
rocky juniper
I see thank you very much
I think I'll do both tests but only analyze the ones using spearmans
based on what I'm reading
the gap between the two values probably means that the data I have doesn't completely fit some conditions for pearsons
thank you again
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late sinew
i wanna figure out if i got the right answer, i will type out my though process in a second
final saddleBOT
i wanna figure out if i got the right answer, i will type out my though process ...
late sinew
so the method i used was just process of elimination
first i saw all periods were 2pi/65 so that doesnt help
i then saw you are looking for height/ vertical position, this made me cross out both cos answers leaving me with only B or D
next i saw the max height and min height, 48 and 8 respectivly
if i did D i would see the middle point/ start point is 20, with an amplitude of 28, this means that max height is 48 but min height is -8, and that does make any sense logically and for the problem
but for B, you start at 28 with an amplitude of 20 leaving you with max height of 48 and min height of 8 whioch mathces the description
so i chose B
late sinew
first i saw all periods were 2pi/65 so that doesnt help
is there a reason you put an X on this, what does not make sense about that?
ivory vessel
i did not x'd the 2pi/65, you are correct in that aspect
what i x'd is the reason you eliminated the options a and d
ivory vessel
the way the options gave cos and sin is to determine the starting phase, it has nothing to do with horizontal or vertical, i believe you are confusing the wheel for a unit circle
what i recommend is drawing a simple diagram
late sinew
wo if it isnt B, which one would you say it is?
ivory vessel
thats for you to decide, im simply telling whats wrong and right
if it isnt obvious already, this is a harmonic oscillation problem
ivory vessel
we will use the upward direction as the positive direction, we would have this diagram, where A is the amplitude
ivory vessel
amplitude is 20, the middle is 28 indeed
so we eliminate C and D first and foremost
$A\cos(\omega t + \phi) + y$
soft zealotBOT
ivory vessel
this is your usual oscillation function, where A is the amplitude, omega is the angular freq, phi is the starting phase, y is the vertical displacement
we determined amplitude to be 20 and vertical displacement to be 28, so we eliminate c and d
late sinew
so wait, wouldnt either B or A work?
ivory vessel
now the problem also gave an interesting information, that is at t = 0, the person is at the top of the wheel
ivory vessel
yes, though not explicitly
late sinew
ohh, t seconds after the top
so you are finding verticel position after passing the top
ivory vessel
now the problem also gave an interesting information, that is **at t = 0, the pe...
meaning, if you sub in t = 0 into the function, the person is at A + y height
late sinew
yeah, okok, i just missed that small detial
but it means a lot
thank you, i get what i did wrong now, the way i did it was if you calculate vertical postions from the center of the wheel, at 28 feet
but you need to start at 48
ivory vessel
yes, you need to analyze every information given, sometimes they can be subtle like that
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coral thistle
struggling with surjective in particular
final saddleBOT
struggling with surjective in particular
coral thistle
i got all the other ones just not the surjective ones
final saddleBOT
@coral thistle Has your question been resolved?
final saddleBOT
@coral thistle Has your question been resolved?
final saddleBOT
@coral thistle Has your question been resolved?
final saddleBOT
@coral thistle Has your question been resolved?
coral thistle
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uneven bridge
How come I can forget about the absolute value sign in this step?
final saddleBOT
How come I can forget about the absolute value sign in this step?
cursive rain
because the exponential function can only take
on positive real values
it's a bijection between R and (0, infinity)
@uneven bridge
uneven bridge
because the exponential function can only take
on positive real values
Ohh right! Thank you
Also, what is the reason the absolute value pops up again right at the end of this?
Is it just a mistake or is there a reason?
It’s solving a differential equation
final saddleBOT
@uneven bridge Has your question been resolved?
cursive rain
Also, what is the reason the absolute value pops up again right at the end of th...
i feel there should be an absolute value already after the integrating step
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@uneven bridge Has your question been resolved?
plush umbra
log x = log |x| always
uneven bridge
i feel there should be an absolute value already after the integrating step
But I used u=lnx to do it
The lnx was from the question
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@uneven bridge Has your question been resolved?
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@uneven bridge Has your question been resolved?
hollow spindle
Can someone help me with part c please?
final saddleBOT
Can someone help me with part c please?
final saddleBOT
@hollow spindle Has your question been resolved?
unkempt shale
is there any reason to use radians instead of angle when using sin functions?
little burrow
for any trig function, you can use either degrees or radians to evaluate it
if you are given measurements given in terms of pi, it would be far easier to use radians
but if you are given measurements in degrees, like an angle measure, use degrees
tranquil pine
is there any reason to use radians instead of angle when using sin functions?
use whatever ur more comfortable with, radians just comes out neater half the time imo
unkempt shale
but if you are given measurements in degrees, like an angle measure, use degrees
I guess that makes sense
unkempt shale
use whatever ur more comfortable with, radians just comes out neater half the ti...
fair
do any of you know how to change what the sin in geogebra uses?
little burrow
well the sine function just represents the the opposite length from the angle over the hypotenuse
that’s the only way it can be used
and it must be a right triangle
unkempt shale
but in geogebra the sin function looks like this
sin(rad)
little burrow
yes
unkempt shale
how do I make it look like this
sin(angle)
little burrow
oh well you can convert radians to degrees by multiplying a radian measurement by 180/pi
little burrow
well pi is equivalent to 180° on the unit circle
unkempt shale
when we're talking radius
little burrow
yeah you can just convert sin(rad) to sin(deg) by multiplying rad by 180/pi
and inputting that value back into the sin function
For example: Let’s say I want to evaluate the function: sin(pi/2)
I can convert pi/2 to degrees by multiplying it by 180°/pi
When multiplying them, the pi cancel out and you are left with 180°/2, which is 90°
So now, we can use sin(90°) instead of sin(pi/2), which is equal to one
forest ember
do any of you know how to change what the sin in geogebra uses?
Click on the gear icon > settings > graph icon on the rhs > set angle unit to degrees
unkempt shale
Click on the gear icon > settings > graph icon on the rhs > set angle unit to de...
thank you ^^
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severe moth
is there another way of getting 3 than whatever the fuck that was
final saddleBOT
is there another way of getting 3 than whatever the fuck that was
sturdy cypress
each permutation corresponds to 10 numbers that add up to 4
severe moth
but its like i dont think id come up with a solution like that on my own
sturdy cypress
e.g. **||||*|||*|| means 2 + 0 + 0 + 0 + 1 + 0 + 0 + 1 + 0 + 0
so 13! / 4! / 9!
i don't think so either
surreal vault
this the most complicated solution ive ever seen for a stars and bars problem
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arctic hill
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arctic hill
I don't know how to solve it I just want to know the approach
idle kayak
@arctic hill did you attempt anything at all?
try to solve for a
and read the question carefully and maybe something will click
if your still stuck, let me know
its better if you try to think your way through this problem though
but i can give you a hint: carefully read and understand the question
final saddleBOT
@arctic hill Has your question been resolved?
arctic hill
<@962206606341337088> did you attempt anything at all?
yes
@idle kayak
I solved for a but it became a radical in terms of b
idle kayak
what root is the radical?
arctic hill
3
idle kayak
and what does the question say that a is?
arctic hill
a positive integer
idle kayak
well a and b
arctic hill
ye
idle kayak
you need to find a positive integer B that would end up turning everything inside of the radical to be a perfect cube
arctic hill
oh ok
idle kayak
and the cube root of that value is the least possible value of A
arctic hill
oh ok
how would you find it fast?
because that's a lot of guess and check in the end
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tranquil pine
ab/cd = 0,c4.
The letters represent the digits not multiplication
final saddleBOT
ab/cd = 0,c4.
The letters represent the digits not multiplication
clear moon
what are you asked to do, find out what a,b,c, and d are?
so you have a 2 digit number ab divided by another 2 digit number cd to give you the decimal number 0.c4?
covert tree
$$\frac{10a+b}{10c+d}=\frac{10c+4}{100}$$
soft zealotBOT
qwertytrewq
covert tree
@tranquil pine try rearranging by cross multiplying to get rid of the fractional part first
tranquil pine
1000a+100b = 100c+4d
clear moon
double check that multiplication
covert tree
1000a+100b = 100c+4d
(10c+d)(10c+4) is not 100c+4d
covert tree
Uh
try this: (10c+d)(10c+4)=10c(10c+4)+d(10c+4) by distributive property
apply the distributive property again to get what neil got
covert tree
10 c*10c = 100 c^2
clear moon
10c * 10c is 100c²
clear moon
10c * 10c + 10c * 4 + d\*10c + d\*4
look very closely at each term of the multiplication here
tranquil pine
100c^2 + 40 c + d10c + 4d
covert tree
100c^2 + 40 c + d10c + 4d
So we have $$1000a+100b = 100c^2+40c+10cd+4d$$ Notice the left side of the equation is divisible by 10, when is the right side of the equation divisible by 10?
soft zealotBOT
qwertytrewq
tranquil pine
im lost
tranquil pine
yes
covert tree
but the equation we established tells us that 100c^2+40c+10cd+4d is divisible by 10
clear moon
those first three terms are always divisible by 10, so it comes down to figuring out when 4d is divisible by 10
tranquil pine
but d can have so many values
clear moon
there are digits
covert tree
but d can have so many values
its a digit so its only from 0 to 9
clear moon
d is an integer between 0 and 9
clear moon
there’s one more option
tranquil pine
0?
clear moon
yeah
tranquil pine
so now what
covert tree
we can now do these case by case
clear moon
though hold up
d can’t be 0
because you’d be dividing ab by cd to get 0.c4
if d is 0, then cd looks like 10 or 20 or 30 or something
covert tree
d can’t be 0
27/50?
clear moon
fuck
tranquil pine
wait
clear moon
never mind
tranquil pine
you got the answer
clear moon
i was onto nothing
tranquil pine
no
this is the only solution
i checked my math book
it gives the answer without solving it
clear moon
okay d is either 0 or 5, let’s assume d is 0
covert tree
doesnt make sense but no
because when a=0 b=6 we get 06=6
tranquil pine
a cant be 0
covert tree
HOW DID YOU GET HERE
we casework on d=0 or d=5
tranquil pine
a is null
clear moon
**qwertytrewq**
then in this equation if d is 0, you get 1000a + 100b = 100c² + 40c
covert tree
a cant be 0
ok then ignore the other solution
clear moon
if the left is divisible by 100, so is 100c² + 40c
100c² is always divisible by 100
when is 40c divisible by 100, when c is a number from 1 to 9
tranquil pine
0 and 5
clear moon
yeah so c = 5 and d = 0 for this case
covert tree
can you find ab now given cd=50?
clear moon
now ab / 50 = 0.c4
covert tree
0.54
clear moon
oh oops, yeah
covert tree
ok, but we are not done yet
tranquil pine
how
clear moon
that’s the case when d = 0
covert tree
we need to conclude that d=5 yields no solution
clear moon
if d = 5, 1000a + 100b = 100c² + 90c + 20
covert tree
now left hand side is a multiple of 4
clear moon
now left hand side is a multiple of 4
could we repeat the same reasoning with the left being a multiple of 100 and checking when 90c + 20 is a multiple of 100?
covert tree
could we repeat the same reasoning with the left being a multiple of 100 and che...
i think so
tranquil pine
so 90c is a multiple of 80
clear moon
not necessarily
tranquil pine
..
clear moon
90c + 20 could be 200
tranquil pine
wait
covert tree
i think so
i just rather brute force at this point
tranquil pine
9c + 2 = 10
clear moon
so 100a + 10b = 10c² + 9c + 2
covert tree
9c + 2 = 10
= a multiple of 10, but not just 10
clear moon
yeah so when is 9c + 2 a multiple of 10, more casework for c being somewhere between 1 and 9
clear moon
yes
covert tree
and?
clear moon
there’s another?
tranquil pine
no
tranquil pine
so c is 2
clear moon
okay so when d = 5, c = 2
so ab / 25 = 0.24
wait
that just gives ab = 6
and i’m assuming that’s not allowed
tranquil pine
definitely not
clear moon
great so the solution we found earlier is the only one
tranquil pine
ok
clear moon
27/50
covert tree
ab/cd = 0,dc
we do a similar thing here
tranquil pine
got it
tranquil pine
how to write in texit
clear moon
$$\frac{10a+b}{10c+d}=\frac{10d+c}{100}$$
soft zealotBOT
neil
covert tree
how to write in texit
🤔 you can pull up some videos on how to use latex
tranquil pine
?
covert tree
1000a+100b= 100cd + cd
what is (10c+d)(10d+c), again remember to use distributive property
its not just 10c*10d+c*d
tranquil pine
100cd + 10c^2 + 10d^2+ cd
clear moon
yes
covert tree
100cd + 10c^2 + 10d^2+ cd
good!
clear moon
so 1000a + 100b = 101cd + 10c² + 10d²
covert tree
what number can we use to check divisibility?
tranquil pine
10
clear moon
good so now it’s a question of when 101cd is a multiple of 10
it might be useful to know that 101 is a prime
covert tree
it might be useful to know that 101 is a prime
or we reduce it to 1cd💀
tranquil pine
how
clear moon
^
or if you use the prime reasoning, the only way 101 * cd would be a multiple of 10 would be if cd contained 2 and 5 as factors
by the fundamental theorem of arithmetic
so either way cd must be multiple of 10
covert tree
by the fundamental theorem of arithmetic
😂 this seems too advanced for this question lol
clear moon
i realized after lol
clear moon
how do you know that
tranquil pine
the answers
covert tree
cd is not a multiple of 10
by cd we mean c*d
tranquil pine
oh
tranquil pine
guyss this might be too complex for me
clear moon
well if c and d are one digit numbers that multiply to 10, one must be 2 and one must be 5
soft zealotBOT
qwertytrewq
covert tree
and cd to represent product
clear moon
well if c and d are one digit numbers that multiply to 10, one must be 2 and one...
does this reasoning make sense
tranquil pine
yes
covert tree
well if c and d are one digit numbers that multiply to 10, one must be 2 and one...
we gon case check 0 to 40? 💀
clear moon
13/25 and 13/52
clear moon
we gon case check 0 to 40? 💀
wdym?
tranquil pine
uhhh
tranquil pine
guys thanks for the help but this is way too complicated for me
clear moon
c*d could be any multiple of 10
fuck
tranquil pine
my math teacher will surely think i copied it
covert tree
my math teacher will surely think i copied it
what grade is this?
clear moon
idk how else you were supposed to solve it other than guess and check
tranquil pine
6th
clear moon
what the hell
tranquil pine
i turned 13 in april btw
tranquil pine
nope
covert tree
i turned 13 in april btw
congratulations
clear moon
no wonder the algebra and factoring and stuff seemed hard
tranquil pine
the thing is
clear moon
bro’s in 6th grade 😭
tranquil pine
my teacher gave everyone some tests
to solve until this week
she gave us 2 months
and each test has 5 subjects
its for a grade
so thanks for the help
.close
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
what does it mean by an indeterminate period?
final saddleBOT
what does it mean by an indeterminate period?
amber holly
Could you show the context?
soft zealotBOT
tranquil pine
here @amber holly
amber holly
Seems like they meant that period can't be determined
tranquil pine
but 4a is already a fundamental period yea?
the answer key says the answer should be option A
so do u think theres a misprint in the option itself?
shouldnt it be 4a and not 4
what do u think
amber holly
but 4a is already a fundamental period yea?
Not necessarily
tranquil pine
but that's the min +ve integer
amber holly
Yeah looks like they have a typo in option a
amber holly
but that's the min +ve integer
How do you know there is no smaller positive period?
tranquil pine
cus now the values just keep increasing
that was the smallest one
am i wrong? 😭
oh it got cut from the above but basically i let 4a=T
to show
trail mango
yajat
tranquil pine
hello layla u should be sleeping rn
trail mango
correct
i just slept for 5 hours which was not enough but now i can't fall back asleep
tranquil pine
oh i know how it feels like, u feel like going back to sleep cus it feels weird low on sleep but at the same time u cant fall asleep for some reason
i hope u fall back asleep soon 😭
i think i my doubt is cleared
thanks bean
trail mango
my sleep schedule is perpetually fucked so i don't think i will
this still feels like an upgrade from waking up at 7 pm tho so i'll take it
trail mango
listen i tried
trail mango
math
tranquil pine
oh ok fair
trail mango
no i’m not in school anymore i just do math for fun
trail mango
in some sense
tranquil pine
ok well i guess if u feel like ur more effective at night then u should keep it up
trail mango
i don’t haha
tranquil pine
💀
trail mango
i like working in the day so i can use my outdoor chalkboard
but i haven’t been able to most days
getting up at 7 pm makes that difficult
tranquil pine
outdoor chalkboard that sounds rly fun
trail mango
it is!
trail mango
i like whiteboards too
tranquil pine
getting up at 7 pm makes that difficult
make it a indoor one so u can now start using it at night too lmfao
tranquil pine
personally i feel like the chalk one is better the writing sound just makes it fun
also its easy to erase
trail mango
only thing i don’t like is my hands getting covered in chalk
trail mango
never tried it
tranquil pine
lmao ok u should tho
trail mango
i only have one piece of chalk though and i forgot to steal some from school when i went in today
so rip me if i run out
tranquil pine
stealing chalks is fun fr they have so many nice ones
they even have so many colorful chalks
trail mango
my friend has a lot of colored hagoromo chalk he brings in but don’t wanna steal those from him
tranquil pine
do you use a chalk holder
trail mango
no
tranquil pine
have u ever tried it?
tranquil pine
my friend has a lot of colored hagoromo chalk he brings in but don’t wanna steal...
damn wym by hagoromo
ask him if he could get u some
trail mango
damn wym by hagoromo
it’s a famous chalk brand
trail mango
have u ever tried it?
yea i have one but it’s at my mom’s house. as well as a bunch of colored hagoromo chalk
trail mango
yea if not for the fact i don’t wanna step foot in there
tranquil pine
damn u dont like ur mom? 😭
trail mango
no 
tranquil pine
bruh why
i have an online friend and she doesnt like her mom too she always tells me how she wanna move out
trail mango
don’t really wanna talk about it
tranquil pine
yea ok no problem with that
ok imma close this channel now i have to leave for my classes now
bye
.close
final saddleBOT
trail mango
bye
final saddleBOT
Available help channel!
clever cradle
Given Matrix $A = \begin{pmatrix} -2 & -1 & 1 \ -1 & -2 & -1 \ 1 & -1 & -2 \end{pmatrix}$
final saddleBOT
Given Matrix $A = \begin{pmatrix} -2 & -1 & 1 \\ -1 & -2 & -1 \\ 1 & -1 & -2 \en...
soft zealotBOT
キマイラ
clever cradle
How can i approach calculating Eigenvalues and Eigenvectors?
Do i begin with doing $A - \lambda I = 0$
soft zealotBOT
キマイラ
amber holly
You begin by solving for lambda in det(A - lambdaI) = 0 rather than A - lambdaI = 0
soft zealotBOT
キマイラ
clever cradle
I dont know what to do after this
tranquil pine
use the rational root theorem
you want the solutions to this characteristic equation
clever cradle
oh i miscalculated
tidal cradle
SO its -x(x+3)^2
clever cradle
SO its -x(x+3)^2
and in order to get the Eigenvalues i have to find the Zeroes?
for this function
like $-x(x+3)^2 = 0$ ?
soft zealotBOT
キマイラ
tidal cradle
Yes
reef surge
Laplace transformation problem
Everything makes sense except the transition to the last line
final saddleBOT
Laplace transformation problem
Everything makes sense except the transition to t...
final saddleBOT
@reef surge Has your question been resolved?
reef surge
nevermind i figured it out
even at multivariable calculus i have forgotten how to perform basic greatest common factor substitutions
i should probably just stop trying to be an engineer
fast grotto
final saddleBOT
fast grotto
i believe they want you to use greens theorum
My question is can you explain why this is true
mainly why is the parametrzation x,y=t,0
mmm ok
and when you use greens theorum
ok wait nvm i
think i got it
ok
final saddleBOT
@fast grotto Has your question been resolved?
final saddleBOT
proper wren
normal goblet
final saddleBOT
normal goblet
I know how to do most of it but I don’t understand the part where it’s from D to E
brazen plume
Find the lengths of the sides of the triangle, and then you can use Pythagoras theorem
normal goblet
Which sides
brazen plume
The ones I drew
brazen plume
Let the point where there is the right angle be K
normal goblet
25-8-7= 10
brazen plume
Yeah
normal goblet
What’s after that?
brazen plume
Find KE
normal goblet
Sorry I’m struggling
normal goblet
BC + KE = AF
K? You mean D?
brazen plume
No K, the point where I made the right angle
normal goblet
Oh rightt
brazen plume
brazen plume
DK is 10cm, we just found, and DKE is 90°
normal goblet
Yes
brazen plume
You understand this diagram?
normal goblet
You understand this diagram?
Yesyes
brazen plume
Yeah so if you see, BC + KE = AF
brazen plume
Yeah so put in the values of bc and af, and find KE
normal goblet
Wait so I’ll minus AF by BC then?
brazen plume
Yep
normal goblet
So 4
brazen plume
But if you are trying to find x then you won’t really need to find DE, only need DK and KE
normal goblet
So I just ignore that DE line?
brazen plume
Oh it’s ok now, I was saying it before you calculated it