A 'nice' function would have f'(x)=0 at critical points
#help-10
timid silo
Ok, let's talk about continuous (at least twice) differentiable functions here
the first derivative is positive when the function increass
and negative when it decreases
trim island
yep
timid silo
0 when it is flat
so if you know that your function is, say, quadratic
then by finding f'(x)=0 you find the tip of the parabola for example
which is the minimum if x^2 coefficient is positive
and maximum if it's negative
can you see that?
trim island
this is for the 2nd derivative no ?
timid silo
for the first
trim island
the first is always = 0
timid silo
no
bro
please talk to your math teacher
But for now
what does a 0 derivative mean?
when it's 0 for all inputs?
.
tell me
trim island
what does a 0 derivative mean?
the rate of change at a specific point is 0
trim island
for a quadratic
timid silo
ok
forget about quadratics
for a sec
think in the abstract
what does a der = 0 on the entire domain mean ?
trim island
okok
trim island
what does a der = 0 on the entire domain mean ?
the rate of change at every point is 0 ?
trim island
linear
timid silo
ok
trim island
no ?
timid silo
but more specifically constant
slope = 0
it's not quadratic
well, aside from the degenerate case where all coefficients are 0
with the constant being anything
so 0x^2+0x+c
but nobody means that when they say quadratic in general
trim island
right
trim island
yep
timid silo
what about x^2 ?
trim island
2x
timid silo
great
so as you can see the derivative of a quadratic is nowhere near 0 for all values
trim island
i just remember the dy/dx of x^2 = 0 is something that we put in to find the minimum/maximum point
dy/dx is not = 0
whoops
trim island
so as you can see the derivative of a quadratic is nowhere near 0 for all values
yh okay
trim island
bc the rate of change at that point is 0
timid silo
graphically
trim island
it can increase or decrease
trim island
if u go slightly up or slightly back
timid silo
and then the other
so if we know this property of the parabola
and the graphical definition of der
we can deduce that when der = 0, it's the max/min of the parabola
which is not necessarily true for other functions
trim island
so e^2x has no parabola so therefore this does not apply to it
so what is the derivative of e^2x showing then
trim island
the derivative of e^2x is never 0
yh that makes sense now
timid silo
it approaches 0 for -inf
trim island
right, its an exponential
timid silo
the derivative of this function is itself times 2. and graphically it's exactly what we see
it just shows that the rate at which it grows is related to the input
timid silo
but more simply it just means that the function decreases fast to the left and increases fast to the right
ask
but then I leave to other questions :))
trim island
a function can only give u 1 answer
trim island
so in the sinx and cosx graph
timid silo
per 1 input
timid silo
huh
I am not sure I understand
The inverses of sin and cos will have infinite solutions for each input (or no real solutions at all)
timid silo
correct
obtuse pebbleBOT
timid silo
bro wait
just a sec
I highly recommend reading this slowly
a function is necessarily injective by definition
meaning each input has exactly ONE output
obtuse pebbleBOT
Available help channel!
timid silo
but not necessarily surjective
obtuse pebbleBOT
but not necessarily surjective
timid silo
.close
obtuse pebbleBOT
timid silo
shall read
good luck bro
trim island
its not really even something i need to learn for school more out of interest
thanks
timid silo
its not really even something i need to learn for school more out of interest
proud of ya. Godspeed
obtuse pebbleBOT
Available help channel!
tardy abyss
How can I graph sum of these two vectors without them touching each other? I thought that I could just add the components but if I do that how could I know the initial point of the vector (since the question didn't specify from the origin of the plane or not)?
obtuse pebbleBOT
How can I graph sum of these two vectors without them touching each other? I tho...
spiral maple
How can I graph sum of these two vectors without them touching each other? I tho...
You move the vectors so they're tip to tail
long sinew
I remember this from the beginning of the year (In physics)
You just translate them over
tardy abyss
So, I could use the triangle law of vector addition, and get something like this?
To be more specific.
long sinew
One sec
Or it might be the other way
Whatever
This is how I always did it
OK yeah I did it right
@tardy abyss
tardy abyss
So does it matter which tip I put to which tail?
long sinew
Yes
@tardy abyss I haven't done this in a while forgive me, but I think it somewhat matters which one you put to which
@spiral maple Help me out here lol physics minor
obtuse pebbleBOT
@tardy abyss Has your question been resolved?
obtuse pebbleBOT
@tardy abyss Has your question been resolved?
tardy abyss
I figured I'd just ask my teacher and she said that either tip to either tail would work just fine for solving these. Thanks.
stable sedge
obtuse pebbleBOT
stable sedge
is the angle A bisected when we draw median
from A to BC
hmm i think no we can not prove ABD ADC congruent
long sinew
I think not, but it is possible if its like an isosceles triangle where its the angle created by the congruent sides (Also for equilateral triangles)
worthy comet
in general no: AD is a bisector if AB:AC=BD:DC
raven spire
in general no: AD is a bisector if AB:AC=BD:DC
which implies AB = AC is a necessary condition :o
which means BC = 0
which means, your right triangle is a ... uhmm
stable sedge
in general no: AD is a bisector if AB:AC=BD:DC
oh right
sides bisected ratio = sides containing the angle ratio
i almost forgor
thanks all
wanton kraken
help
wanton kraken
In triangle ABC, symmetrical bisector of AC crosses AB at point Q
Find perimeter of triangle ABC, if triangle QBC = 22 cm and AC = 9
wanton kraken
ugh I don't have discord on my phone
and I use a touchpad
for drawing
so it's hell rn
pls help xD
I can do a scuffed
af
one
through paint
wanton kraken
AC=9
P(QBC)=22
ABC=AC+AB+BC
AC=9
ABC=9+AB+BC
AB=AQ+BQ
AQ=QC
ABC=9+AQ+BQ+BC=9+QC+BQ+BC
PQBC=QC+BQ+BC
9+22
ffs
.close
trail hemlock
Hi, can someone explain how this is solved?
obtuse pebbleBOT
Hi, can someone explain how this is solved?
trail hemlock
I tried this for a while now and I just couldn't get it done
tardy epoch
use trig identity for $\sin^2(x)$ and then use the quadratic formula
warm shaleBOT
riemann
trail hemlock
use trig identity for $\sin^2(x)$ and then use the quadratic formula
What's trig identity
tardy epoch
look in your notes or textbook
trail hemlock
I'm not studying maths in english
unique solstice
sin(x)=cos(x-pi/2) would be a trig identity for example
Not the one you use
But a trig identity
Just a rule ig
trail hemlock
I think ik what you mean, thanks
i'll try that
I tried to mess around with it but I got nowhere
pine sail
No man he meant cosx= sin(π/2-x) is an example but he even said you don't use this one here.
timid silo
I tried to mess around with it but I got nowhere
Do you know about the identity sin^2(x) + cos^2(x) = 1?
royal solar
Hi, can someone explain how this is solved?
sin2(x) + cos2(x) = 1
royal solar
sin2(x) + cos2(x) = 1
basically what @timid silo said
trail hemlock
Do you know about the identity sin^2(x) + cos^2(x) = 1?
Yes
pine sail
$sin²x+cosx-sin²x-cos²x=0$
warm shaleBOT
Sakata Yaksha
pine sail
I hope you will solve this now by yourself now.
timid silo
that works, you could have also substituted sin^2(x) = 1 - cos^2(x)
pine sail
Yes, what I did was more simple Ig but anything works.
trail hemlock
I hope you will solve this now by yourself now.
Yeah I think I got this
pine sail
Nice.
obtuse pebbleBOT
Available help channel!
kindred nacelle
I don't know how to do these
obtuse pebbleBOT
I don't know how to do these
short spruce
factor and use zero product property
jade eagle
obtuse pebbleBOT
tardy epoch
how'd you get from the top line to the bottom? there should be a summation of $i^2$ term. did you already substitute that formula?
warm shaleBOT
riemann
obtuse pebbleBOT
@jade eagle Has your question been resolved?
jade eagle
how'd you get from the top line to the bottom? there should be a summation of $i...
yeah i did the summation for i
ohhhh was i supposed to do the summation for i^2?
tardy epoch
what is (-1 + 6i/n)^2
jade eagle
that’s when you plug it into f(xi)
tardy epoch
expand it
main halo
Hi how do y'all start practicing maths
like how is the discipline brought
and what are your study habits
raven spire
Hey sanao
sorry I keep forgetting the limit definition for definite integral, could you write it for me please?
warm shaleBOT
Ansh
raven spire
tyvm. you might want to redo the whole conversion thing because the expression you've arrived to at the second step itself looks incorrect
jade eagle
yeah i figured it was wrong but idk what im doing wrong 😬
raven spire
that's when you try it again. not already start looking for help
can you spot the mistake in 2nd step?
jade eagle
the sigma 2?
jade eagle
i distributed the 2 wrong in f(x)
raven spire
function in consideration here is: 2(x²) + 1 I suppose
kay
next mistake is 3rd step
the sum was computed incorrectly, plus you didn't even expand (-1 + 6i/n)² correctly
jade eagle
yeah i see where i went wrong
for some reason idk why i distributed wrong 🤔
i was following a video to help with a similar problem and they distributed the 2 to the whole thing
ty for your help tho
i think i can figure it out if i spend 2 hours on it 💀
.close
rocky cosmos
obtuse pebbleBOT
rocky cosmos
How do I determine the constants A and B?
tired shell
think of what numbers sin^2(x) on its own goes between
rocky cosmos
We know that sin(x) has the amplitude 1, so the minimum value is -1, and the maximum value is one.
tired shell
A stretches that and B changes the height
raven spire
A scales the min, max value of your function accordingly while B shifts the entire graph upwards by B.
rocky cosmos
Okay
so, to find b, we only put X equals zero, and then isolate the variable b
y(0) = A sin^2(0) + B
Sin(0) = 0
y(0) = A*0+B => B.
Okay so what does this tell us? that -3 = B?
So the vertical shift is -3.
Now how do we find the amplitude?
Is it ((max+min)/2)?
In which case we have 1+(-3)/2 = -2
The way someone else explained it was:
We know that sin (x) will vary between -1 and 1. If we square it, we can think that sin² (x) will vary between 0 and 1, because it can no longer be negative (real squares are never negative) but the maximum can be 1² = 1.
The curve y = sin² (x) thus has the height 1. If we want to influence this, we adjust the function with A. This tells how high your function can be in total. In your case, you want the curve to be 1 - (- 3) = 4 units high, so how much should A be to transform from a function with height 1 to one with height 4?
Then you can very accurately calculate B in the way you tried to do in your comment.
Anyone could give Give me any advice?
I didn’t get the part where he says “… you want the curve to be 1- (-3) = 4 units high.”
Where is that formula from?
obtuse pebbleBOT
@rocky cosmos Has your question been resolved?
obtuse pebbleBOT
@rocky cosmos Has your question been resolved?
obtuse pebbleBOT
@rocky cosmos Has your question been resolved?
mystic saffron
woop#3112
crimson berry
What is the question
mystic saffron
find variables
i'm trying to use special triangle rules but not working
do i have to draw some auxillary line?
keen cave
im confused on what to do here
The first thing I thought of was try solving a system of equation. We have x^2 + y^2 = 15^2 and (18-x)^2 + y^2 = 12^2.
Looking at it to see if there a faster way.
mystic saffron
i thought that but i don't think we have done systems with exponents.. or does that even matter?
keen cave
nope.
mystic saffron
i dont think system of equations is the way to do this
mystic saffron
i cant find any other way
keen cave
nvm it system of equation but it just algebra. We have x^2 + y^2 = 15^2, that implies y^2 = 15^2 - x^2. Also notice we also have (18-x)^2 + y^2 = 12^2. The rest follows from that.
mystic saffron
i got x=11.25
keen cave
yep.
inland spoke
Hi
inland spoke
So for b I got sin (5pi/12)
Idk if that's right
and I dont understand what it means by exact form
onyx moss
if it’s asking for exact values it wants an answer in radians
so in terms of pi
with no trigonometric function
inland spoke
crude cloud
By 12*
crude cloud
Yeah that also work .
inland spoke
with no trigonometric function
wait so do you mean 5pi/12 not sin(5pi/12)
crude cloud
It's sine (pi-theta) so in the XY plane it means that it'll lie in the 2bd quadrant
Where sin is +
In the second quadrant sin is + so if u do pi - thetha there will be no changes but if u do sin pi + theta ull get a minus sign.
Here u need to find the valur of sin(105,°)
inland spoke
long sinew
inland spoke
so basically it's the same thing as adding pi/2 to pi/4 to get 3pi/4
where the sin functions are the same?
but instead of adding we're subtracting
doing it in reverse?
crude cloud
I got it....u just need to simplify see ...u can write 7 pi/12 as 4pi/12+3pi/12
Now just appl sin(a+b)
onyx moss
so basically it's the same thing as adding pi/2 to pi/4 to get 3pi/4
Draw the graph $\sin(x)$ and you will see why $\sin(x) = \sin(\pi-x)$
crude cloud
Root3-1 /root 8
short spruce
why use the bot if you're just making your text a picture lmao
onyx moss
my bad
short spruce
\sin 
inland spoke
so
warm shaleBOT
lgargaro
onyx moss
😂
inland spoke
sin(5pi/12)=sin(7pi/12)
flat anvil
if you wanted to show it you could use the additive identity
of sin(x)
sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
obtuse pebbleBOT
@inland spoke Has your question been resolved?
brisk arrow
I have a question
obtuse pebbleBOT
I have a question
brisk arrow
The formula that the math teacher using to calculate students grade is: usual test has the proportion of 30% then test A and test B is 20% and 30% respectively
It’s solved
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
red lark
How are irrational numbers not integers?
obtuse pebbleBOT
How are irrational numbers not integers?
obtuse pebbleBOT
@red lark Has your question been resolved?
red lark
Well no, actually I was watching this video on proving an irrational number, and there they said that irrational numbers are not actually integers.
That's what got me thinking
<@&286206848099549185>
sudden fox
How are irrational numbers not integers?
irrational numbers cannot be defined as a/b where a, b are integers
but all integers could
red lark
so to frame it in other words, because a and b are not integers, the number is irrational?
is that what it is?
@sudden fox
sudden fox
hmmm wait a minute
A real number that can NOT be made by dividing two integers (an integer has no fractional part).
well its not because a and b are not integers, but its because there doesn't exist an a and b that are integers to express the number
timid silo
How to prove that the areas of the small triangles inside the big triangle are equal to each other?
obtuse pebbleBOT
How to prove that the areas of the small triangles inside the big triangle are e...
@timid silo Has your question been resolved?
novel elm
Hello, can anyone help me here <@&286206848099549185>
obtuse pebbleBOT
Hello, can anyone help me here <@&286206848099549185>
novel elm
Oh sorry
raven spire
Lol isn't it a marked quiz or something?
novel elm
It is a homework
raven spire
Anyways,
My hint is to convert it to a form where you'll have an expression in negative x exponents of "5" so that their individual limits all turn 0
plain basin
hello
plain basin
If 2x + y = 5, then 4x + 2y is equal to _______.
pls help me
im a highschool student
<@&286206848099549185>
worthy drum
15 min flew by
flat anvil
compare the left hand side first off
do you notice any relationship between
2x + y and 4x + 2y?
warm shaleBOT
M.E.G. Yottachad
plain basin
uhh
flat anvil
do you add something? multiply by something?
flat anvil
no
plain basin
since x is 1
flat anvil
can you see how 2(2x+y) = 4x + 2y
stable gale
If 2x + y = 5, then 4x + 2y is equal to _______.
No
flat anvil
can you see how 2(2x+y) = 4x + 2y
read this closely
plain basin
WOAH
plain basin
can you see how 2(2x+y) = 4x + 2y
how is it thx bro
i understood
this is linear algebra right
stable gale
If 2x + y = 5, then 4x + 2y is equal to _______.
Ur second equation was simply multiplied by 2
stable gale
If we multiply that by 2
plain basin
4
stable gale
U get 4x +2y = 10
obtuse pebbleBOT
tardy epoch
what's the first order definition?
Can you write down $f(x_1, x_2)$? and $\nabla f(x_1, x_2)$ ?
warm shaleBOT
riemann
tardy epoch
let $X_0 = (a_1, a_2)$. can you write down $f(X_0) + \nabla f(X_0) \cdot (X-X_0)$?
warm shaleBOT
riemann
tardy epoch
why
tardy epoch
**riemann**
what did you end up for this then?
and why can't you show it's bounded above by $f(X)$ ?
warm shaleBOT
riemann
tardy epoch
expand this
tardy epoch
,w plot x^2 + xy
warm shaleBOT
obtuse pebbleBOT
@lavish zinc Has your question been resolved?
obtuse pebbleBOT
@lavish zinc Has your question been resolved?
obtuse pebbleBOT
@lavish zinc Has your question been resolved?
night igloo
what's D
night vault
hhey
bleak nest
Because the line falls by 6, and since it is falling it becomes negative
night vault
ok so if the line for example... starts att +8 and then ends at -5
oh wait i got that wrong...
bleak nest
The calculation would look like this: -5-8=-13
night vault
ah
bleak nest
You always start with the end value and minus the start value
night vault
like for exampple, what they did here?
bleak nest
They started on a 4 and ended on a -2: -2-4=-6
bleak nest
Yes, and after that you do the same with the x-values and divede them
bleak nest
When you subtract the end value with the start value you usually note it with a Δ
bleak nest
alright
night vault
here on the graph i showed, y= (0,4)
bleak nest
Wdym?
bleak nest
Yea it can be Any two points on the graph
night vault
will it change the answer?
any 2 point's who are going to meet together when gone in a rise/run direction
i heard that if the upper one is in an order, then the lower one should be in the same order?
bleak nest
Give me some time, i need to walk a short distance
night vault
oh sorry
bleak nest
I didn't mean it to sound harsh, i just needed to get to my destination, before i could get my pc out
What do you mean by order? English isn't my first langauge, so i dont know all math terms.
obtuse pebbleBOT
@night vault Has your question been resolved?
snow pewter
greetings
snow pewter
i have a problem: i am given the equation for a line in the cartesian plane, the x coord of a point A, and the x coord of a point B
i need to find the length of the line segment AB without using the distance theorem
i cannot use sqrt(Δx^2 + Δy^2)
royal solar
can i see the question please
snow pewter
it's in italian but here it is
sage geode
They already stated the question
royal solar
ouch, might need translation
royal solar
They already stated the question
they might have missed something
sage geode
You sure there's a way without using Pythagorean theorem?
snow pewter
royal solar
You sure there's a way without using Pythagorean theorem?
perhaps so,
or not
what if i found the vector a
that travels from one point to another
and found the magnitude of the vector
sage geode
Yeah, and magnitude is sqrt of sum of squares
royal solar
still pythagorean theorem
snow pewter
"given the line r of equation y = 2x + sqrt5 and given points A and B such that x_A = 1 and x_B = -3, calculate the length of the line segment of AB without using the formula for the distance between two points"
royal solar
but still not using the distance formula
sage geode
Yeah I mean if you consider Pythagorean theorem to be different from the distance formula then do that
You could show that visually
royal solar
Yeah I mean if you consider Pythagorean theorem to be different from the distanc...
yeahh,
snow pewter
what if i found the vector a
yeah i strongly doubt that is the solution
we never used vectors in math
royal solar
y = 2x +c
so delta y = 2 delta x, right?
so what if i found…
oh
can i still use pythagorean theorem?
royal solar
and squares?
high lily
distance formula is pretty much an application of pythag
royal solar
y = 2x +c
so delta y = 2 delta x, right?
so what if i found…
^^ yeah cuz
royal solar
yeah
snow pewter
but only for the sake of not typing out the whole thing
royal solar
but idk how to on mine
snow pewter
we do not work with changes
royal solar
that’s the only way to find the length of a line,
snow pewter
this channel is taken
royal solar
use another help channel my friend
snow pewter
but if i do it your way
raven spire
👀 Hey Hugger
snow pewter
how'd i do it
royal solar
also, add equation 1 and 2 to 3
royal solar
how'd i do it
delta y = 2 delta x
find delta x
and use pythagorean theorem
royal solar
delta x is literally x1-x2
raven spire
mhmm
snow pewter
oh i get it
royal solar
yeah
royal solar
yep
snow pewter
and then take the root
royal solar
and pythagorean theorem
royal solar
and then take the root
YEP
royal solar
no, i’ve not used the theorem at all here. i’ve done it all myself
i didn’t need to calculate a single y value
snow pewter
first off, look at the solution in the photo
royal solar
in distance theorem, you have to individually calculate the y value
snow pewter
secondly, it's just as if you calculated the difference of y values
royal solar
which one
snow pewter
the distance theorem is both the difference and the delta
the one that has two dots on ti
royal solar
yeah, difference is delta
snow pewter
yeah
which is why we had both forms
under the name of distance theorem
so no, it won't work
again, seeing the solution i could just say "factor out x_B - x_A"
royal solar
ahh, they’ve done unit vectors. well. same idea
royal solar
yeah, unit vector is like doing Pythagoras to the slope
2 and 1 in this case
and multiplying that to delta x
royal solar
2 and 1 in this case
this works because for every unit you move across this line, you move the hypotenuse value on the slope
yeah
royal solar
no worries mate
that’s still the same idea
but you will come across that again when you get unit vectors
@snow pewter close the page if you’re done :))
oblique sage
If I have the function f(x)=sqrt(x) and g(x)=x^2 + 4, and h(x) = f(g(x)), is h(x)’s domain XER or no
obtuse pebbleBOT
If I have the function f(x)=sqrt(x) and g(x)=x^2 + 4, and h(x) = f(g(x)), is h(x...
spiral maple
x^2+4>0 so yes
reef grotto
yeah but x^2+4 is always positive
drifting jay
Wait hold on my bad
reef grotto
so the domain is all real numbers
drifting jay
I was looking at it like independently but they're linked
spiral maple
yeah but x^2+4 is always positive
Only true cause x in R
drifting jay
Yeah it is XER
night vault
I didn't mean it to sound harsh, i just needed to get to my destination, before ...
oh sorry for the wait, i mean like; y1-y2/x1-x2. NOT y2-y1/x1-x2
obtuse pebbleBOT
@oblique sage Has your question been resolved?
true kraken
60% of cookies is made sugarfree, 40% is cookies saltfree. 5% of sugarfree is broken and 3% of saltfree is broken
obtuse pebbleBOT
60% of cookies is made sugarfree, 40% is cookies saltfree. 5% of sugarfree is br...
spiral maple
it's either broken and sugarfree or broken and saltfree
true kraken
I mean what are the odds the cookie is broken in percentages
spiral maple
Yeah
true kraken
I thought it was 8% but incorrect
spiral maple
it's either broken and sugarfree or broken and saltfree
.
P(Broken and Sugarfree)=P(Broken|Sugarfree)P(Sugarfree)
true kraken
Sugar has a 5% of breaking, Salt has a 3% of breaking
Why is it not 8
I dontgtet it
spiral maple
P(Broken and Sugarfree)=P(Broken|Sugarfree)P(Sugarfree)
.
true kraken
Whats p
spiral maple
probability
You pick a cookie and want to know the probability it's broken and sugar free
therefore it needs to be a sugarfree cookie, and be broken
ie probability you get a sugarfree cookie (60%) times the probability it's broken (5%)
so 3%
spiral maple
Literally just said.
spiral maple
ie probability you get a sugarfree cookie (60%) times the probability it's broke...
.
true kraken
P(60|5)P(60)
true kraken
So broken and saltfree is 0.4*0.03
spiral maple
yes.
true kraken
Which is 0.012
spiral maple
yes.
true kraken
But how do i calculate if 1 cookie is randomly picked whata the odd of it being broken
spiral maple
sum them together.
true kraken
0.042
true kraken
How
I see
Thanks tho
Yeah that makes sense
Thx
I nearly thought it would be 0.042%
So the broken cookie for saltfree is 1.2% right
Not 0.012
Cuz have to times 100
Right
Yea
Okie
.closed
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
crimson charm
obtuse pebbleBOT
crimson charm
hey guys can anyone point me in the right direction for this proof?
tardy epoch
what's RLM?
Does that follow from matrix multiplication?
First write down the definition of $\bf{X}$ and then calculate $\bf{X^T}\bf{X}$.
warm shaleBOT
riemann
obtuse pebbleBOT
@crimson charm Has your question been resolved?
tardy epoch
**riemann**
actually it's probably easier to calculate $\bf{Xw}$ first, then multiply on the left by $\bf{X^T}$
warm shaleBOT
riemann
crimson charm
@tardy epoch hey just wondering
Does a matrix transposed * itself give something special?
A^TA for example
obtuse pebbleBOT
obtuse pebbleBOT
✅
tardy epoch
Does a matrix transposed * itself give something special?
it gives a symmetric matrix
obtuse pebbleBOT
@crimson charm Has your question been resolved?
tardy epoch
Don't ping until 15 minutes after posting question
tardy epoch
Read
noble berry
how do i factor this?
obtuse pebbleBOT
how do i factor this?
noble berry
I can factor like
6x+30 and stuff but htisi s just kinda confusing me
noble berry
6(x+5)?
noble berry
y(1+5x)
raven spire
and.. p - 7p?
noble berry
p(1-7)??
raven spire
which is -6p (@_@;) but yes
so, when you replace p with (3x - 2z), you get: \ $(3x - 2z) - 7(3x-2z)$
warm shaleBOT
Ansh
raven spire
just slightly more intimidating, but you can obviously factorize p - 7p right?
noble berry
yesh but now I'm lie confused but not exactly sure what in confused on which makes it harder
raven spire
:c firstly, were you able to successfully replace p with 3x - 2z in the factorization of p - 7p?
$(3x - 2z) - 7(3x - 2z) \equiv p - 7p$
warm shaleBOT
Ansh
noble berry
wait what-
raven spire
hmm? 👀
noble berry
what dies replacing have to do with it
nocturne minnow
Ansh was showing an equivalent expression
noble berry
hows it equivalent?
nocturne minnow
I would have said, distribute the 7, combine like terms, then factor
nocturne minnow
hows it equivalent?
Because it is
noble berry
I would have said, distribute the 7, combine like terms, then factor
you can do that?
nocturne minnow
Yes
nocturne minnow
It's honestly better to simplify, in my opinion
noble berry
so it'd become
-6(3x+2z)?
nocturne minnow
Looks like it
raven spire
so it'd become
-6(3x+2z)?
wow (@_@;) perfect
noble berry
says its wrong
raven spire
=_=
balmy mortar
why are there congruences here
noble berry
We were learning like factoring by grouping so is that lie another solutoint hats different
raven spire
ofc it'd be wrong 🤦♂️ you replace "p" with the wrong thingyy
balmy mortar
oh nvm
raven spire
you were meant to replace "p" with "3x - 2z" and not "3x + 2z"
nocturne minnow
so it'd become
-6(3x+2z)?
Did you math something wrong? How is there a +2z?
nocturne minnow
you were meant to replace "p" with "3x - 2z" and not "3x + 2z"
They didn't understand that, so I stated to simplify then factor
noble berry
nocturne minnow
You realize that -7 * -2z isn't -14z
noble berry
wait typo
nocturne minnow
Second, factor out -6 instead
noble berry
-6(3x+2z)?
nocturne minnow
No
noble berry
-6(3x-2z)?
nocturne minnow
Yes but also notice the similarity that Ansh was demonstrating about
noble berry
I'm still kidna confused about that
nocturne minnow
p = (3x - 2x)
So then p - 7p
Which was then -6p
And because p = 3x - 2z, replace that back in
noble berry
Oh that makes more sense
nocturne minnow
That's why they were equivalent looking
obtuse pebbleBOT
noble berry
.reopen
obtuse pebbleBOT
✅
noble berry
just relized I have this, is there a msarter way than multiplying and adding/subtracting
spiral maple
factoring probably
noble berry
like facorte the 2.7*6.2 or the 6.2-9.3 ones?
nocturne minnow
Multiplication takes priority
So you can't do 6.2 - 9.3
You can move terms around because addition is commutative
noble berry
so should I factor the multiplication sets first?
nocturne minnow
Move the terms around so you can them factor the common term
noble berry
I got it to here but I don’t know any common factors for the second parentheses
nocturne minnow
You realize that the common factor is 1.2
That makes it easier
Because then that becomes a 1
Also, why did you factor it per number?
It's similar to a * b - d * a = a(1 * b - d * 1) = a(b - d)
obtuse pebbleBOT
@noble berry Has your question been resolved?
noble berry
You realize that the common factor is 1.2
1.2 is a factor of 6.2?
nocturne minnow
Yes
noble berry
I’m just going to do it the longer way since factoring it is making brain go brrr and confuse itself rn… welp
nocturne minnow
It's just factoring the common term
If you can factor p - 7p or -9.3p - 2.7p, it's the same process
obtuse pebbleBOT
@noble berry Has your question been resolved?
magic cairn
how can i determine slope of tangent to curve y=x^2 - x, x = 3
obtuse pebbleBOT
how can i determine slope of tangent to curve y=x^2 - x, x = 3
magic cairn
point is (3, 6)
short spruce
what have you tried
magic cairn
i dont know what to try
short spruce
have you learned derivatives?
short spruce
so you know the limit definition of a derivative?
magic cairn
this is the hw
short spruce
well that might be a problem
burnt jungle
L'hopital?
short spruce
no?
magic cairn
idk what a derivative is
burnt jungle
Which are you talking about then
short spruce
$\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$
warm shaleBOT
a disappointing son
burnt jungle
This is it
burnt jungle
What
magic cairn
i thought u need two points for that
bright plinth
How can I find the reference angle for 20pi/3?
obtuse pebbleBOT
How can I find the reference angle for 20pi/3?
short spruce
determine quadrant
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dark orchid
E
stiff halo
Can you make a table?
stiff halo
Solve or graph?
stiff halo
You know what graphed equations do when they are equal?
dark orchid
No.
stiff halo
Did you try to graph them?
stiff halo
The top graph?
dark orchid
Yes
stiff halo
How do you solve for -(0-2)^2-1?
dark orchid
stiff halo
You need more than the vertex
dark orchid
Teacher just showed me that, didnt have time to clarify thro
stiff halo
The easiest way is to plug in values. Like, y=-(0-2)^2-1 at x=0 and y=-(1-2)^2-1 at x=1
Since it is quadratic, you need more than the slope and the vertex to graph
Equations with exponents on x are not straight lines
dark orchid
🤔
Hm.
So y= -(2-2)^2-1
Would be x = 2
?
Then i plug it, 2 into y = x - 5
To get y ?
Yes? Or no?
stiff halo
Would be x = 2
How did you get that number?
stiff halo
But what steps do you take to get 2?
dark orchid
I just insert a random number into x
Seems to work, work better if i stick close to 0
stiff halo
I mean how do you get 0^2-1=2?
dark orchid
Whut
dark orchid
Ye. : )
stiff halo
You need to solve for y
dark orchid
Yes
timid silo
dont you find x first and then plug it back in to find y? sorry if im wrong
dark orchid
Ur right
timid silo
Need help on 4 too
here, you divided it by 50, dont
subtract 50x from left, so you end up with x^2 - 50x + 616
then, you can factor
stiff halo
Also, y=-(1-2)^2-1=x=1 is supposed to be y=-(1-2)^2-1 when x=1
dark orchid
🤔
timid silo
here, this is what i did
I'm not sure if this is the best way though...
it's quite annoying to factor
stiff halo
Looks good to me, except for the missing =0
timid silo
oh right, i should include that
obtuse pebbleBOT
@dark orchid Has your question been resolved?
lone shore
I need help guys been studying for my exams and we were given a practice sheet(not graded) and I just cant find the answer
The length of a rectangle is 12 m more than thrice its width. The perimeter of the rectangle is 200 m. Find the length of the rectangle.
its been almost an hour
obtuse pebbleBOT
I need help guys been studying for my exams and we were given a practice sheet(n...
short spruce
what have you tried
lone shore
lone shore
tried finding the formula
nocturne minnow
The question was what you tried, not repost the question
short spruce
so... what did you do in that attempt
if it's been almost an hour i assume you have a paper somewhere
lone shore
no I dont use paper I'm trying to solve it mentally
astral ivy
@lone shore do u know what perimeter is
lone shore
since the time limit for the exam is very limited
astral ivy
Yeah don’t clog your mind with formulas to memorize
nocturne minnow
no I dont use paper I'm trying to solve it mentally
It helps to write the process down
short spruce
<@&268886789983436800>
hot hazel
they say they're studying.
short spruce
since the time limit for the exam is very limited
did i misinterpret this
hot hazel
astral ivy
They’re studying for it