i changed 2 to 2/1
#help-10
glossy basalt
worthy peak
if here
glossy basalt
yea?
worthy peak
how did it get the 3rd power
glossy basalt
1/3 * 3 = 3?
1
worthy peak
1
oh nvm
so if there an fractional exponnet multply both sides of it by the reciprocal
tysm
worthy peak
o
obtuse pebbleBOT
@worthy peak Has your question been resolved?
timid silo
Can somebody explain the generality written at the bottom of this screenshot and give examples by the already done results above the generality?
obtuse pebbleBOT
Can somebody explain the generality written at the bottom of this screenshot and...
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
:(
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
frigid prism
Can somebody explain the generality written at the bottom of this screenshot and...
It’s just for consistency
There’s no real meaning to it, it’s just an attempt at standardizing notation
The probability for a continuous distribution is basically the same whether or not you include the equal sign
Since the area under a point is zero
devout parcel
The angles opposite the two congruent sides of an isosceles triangle are congruent.
(This was a part of my homework, and the only question I got confused on.)
True or False
obtuse pebbleBOT
The angles opposite the two congruent sides of an isosceles triangle are congrue...
spice chasm
yo
spice chasm
What does it mean by “Solve each system by using the inverse of the coefficient matrix”
.close
obtuse pebbleBOT
spice chasm
.reopen
obtuse pebbleBOT
✅
spice chasm
What does it mean by “Solve each system by using the inverse of the coefficient matrix”
static beacon
What does it mean by “Solve each system by using the inverse of the coefficient ...
Put the coefficients in a matrix
And find the inverse of that matrix
azure anchor
$\sqrt{x}+\sqrt{y}=1$
obtuse pebbleBOT
$\sqrt{x}+\sqrt{y}=1$
warm shaleBOT
b0ngl0rd
warm shaleBOT
b0ngl0rd
azure anchor
then what
empty hull
square it
azure anchor
$\left(\sqrt{y}\right)^{2}=\left(1-\sqrt{x}\right)^{2}$
warm shaleBOT
b0ngl0rd
azure anchor
?
wooden cipher
indeed
empty hull
what is the square root of a number squared
azure anchor
right that makes sense, i was stuck multiplying both sides by y instead of applying a square to the terms themselves
but now im trying to find the derivative
$y'=2\left(1-\sqrt{x}\right)\left(-\frac{1}{2\sqrt{x}}\right)$
warm shaleBOT
b0ngl0rd
warm shaleBOT
b0ngl0rd
azure anchor
that doesnt look right did i mess up the s igns
$-2\left(\frac{1-\sqrt{x}}{2\sqrt{x}}\right)$
warm shaleBOT
b0ngl0rd
azure anchor
$y'=-\frac{1-\sqrt{x}}{\sqrt{x}}=\frac{\sqrt{x}-1}{\sqrt{x}}$
warm shaleBOT
b0ngl0rd
azure anchor
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
smoky zenith
I just need a confirmation here, does the x-2 represent the axis of revolution?
daring rock
Yeah, sort of
It's more accurate to say that (2-x) is the radius of rotation
2-x is the distance from a given x value to the axis of rotation x=2
round dune
??
empty hull
factorise sqrt(44)
round dune
uh like √2^2 * 11?
empty hull
yes
round dune
so the answer would be 8√11?
nocturne minnow
uh like √2^2 * 11?
I suggest that if you use that sqrt symbol, use parentheses to denote what's under the root
wooden helm
not really math but can anyone help me with this annoying logic symbolization
ionic hawk
hi can someone look at my multiple choice answers and tell me if its right. the question involves relations on the set of integers. theyre 8 questions.
obtuse pebbleBOT
hi can someone look at my multiple choice answers and tell me if its right. the ...
nocturne minnow
No one can help if you don't post any of the questions
nocturne minnow
idk if it violates the server rules
Is it a test/quiz?
nocturne minnow
Elaborate
nocturne minnow
If it's suppose to test knowledge from reading, then you should read and do it to the best of your abilities
ionic hawk
ye i tried but i like 30% guessed it
ive done the readings and everything
just want to make sure im on the right path
nocturne minnow
In my opinion, pre reading stuff, is just to make sure you did the reading, and you answer to the best of your abilities
Then in class your teacher will discuss it
So it doesn't matter if you're right or wrong because it'll be talked over in class
ionic hawk
dont go to lectures 💀
nocturne minnow
That's not my fault then
ionic hawk
so no help?
timid silo
We are only here to guide you through only after you have attempted the problem, we are not here to do your work after you guessing
nocturne minnow
so no help?
I suggest to just do it, submit and then go to class tbh
And ask questions there
ionic hawk
We are only here to guide you through only after you have attempted the problem,...
lol
ive attempted the problem
and im asking for guidance
have you been reading?
but yes ill follolw ur advice dl
.close
odd rampart
Can I get help
obtuse pebbleBOT
Can I get help
odd rampart
I have no idea what to do with part b
I've tried whatever I can and it doesnt make sense
odd rampart
what I did before was $\int_0^6 \int_2^6 (x-y)\frac{-1}{x+y} dy dx$
warm shaleBOT
Brotractor
odd rampart
and idk if thats right cause im not 100% sure about the change of variable stuff
yeah i tried.
fathom flicker
that is not right
those are the bounds for the uv plane
what the question there is saying
is
changing variables from x, y using u=xy and v=x-y maps the original region D
which is given above
to the rectangle
the rectangle makes it much easier to integrate, so that's the reason for making the change of variables
but you can't just swap the bounds and leave the integral in terms of the normal variables
if I have an integral like this
warm shaleBOT
AustinU
warm shaleBOT
AustinU
odd rampart
the bounds are in the "u"-world
yes
but i dont know exactly how to change the bounds in this case
fathom flicker
that is the nice part for you
they tell you how the bounds change
first you have this complicated bounds
they say the region D is
blah blah blah
and then they say
making the change of variables u=xy and v=x-y
maps D to the rectangle....
so your new bounds after the change of variables
is whatever the region D is in the uv world
well and they tell you what it is
its the rectangle
fathom flicker
you don't ?
odd rampart
basically they tell us that in the xy world the bounds are 2 to 6 in x and 0 to 6 in y
odd rampart
okay so then
fathom flicker
changing variables to u and v, changes the bounds to just the bounds of the rectangle
odd rampart
so then... the new bounds are [2,6] x [0,6]
fathom flicker
the new bounds are 2 to 6 in u and 0 to 6 in v
odd rampart
yes yea i understand that now
so then i have to solve for the integral in terms of u and v right?
odd rampart
with the formula being $\iint_\mathcal{R} v\frac{-1}{x+y} dv du$?
warm shaleBOT
Brotractor
odd rampart
okay then
i assumed the jacobian was the most wrong
cause i have the jacobian in terms of xy
fathom flicker
you need to slow down
odd rampart
ok
fathom flicker
let me help you okay
odd rampart
ok
odd rampart
yes
fathom flicker
this region is complicated
who knows what to make the bounds in xy
its gonna be hard
so, if we wanted to do this integral
we might want to substitute variables
this will make our bounds easier
odd rampart
so basically u sub but uv sub
fathom flicker
and the questions tells us what swap to make
so that is nice
but the nicer part is
it tells us what the swap will be
so let me explain what the question actually wants from you
odd rampart
it tells us what the swap *will be*
it tells us that the bounds go from whatever the complicated mess is gonna be to [2,6] x [0,6]
fathom flicker
- it wants you to manually make the swap of variables, and find the new integral, and evaluate it. 2. it wants you to compare what you find the integral as, to what the real integral is
and it tells you what the real integral will be!!
it says
verify that once you swap variables
it is equal to the integral of v
dudv
and!!! it tells you the bounds
it says in u-v world
the bounds will be this nice rectangle
odd rampart
so then all i literally need to do is just the jacobian
and plug it into the formula
oh
warm shaleBOT
AustinU
fathom flicker
but what the question truly wants you to do
is arrive at that integral on your own
although it gives you a lot of tips about what the end result should be
fathom flicker
so then all i literally need to do is just the jacobian
to figure out that this will be the integral, it is necessary to do the jacobian and make all the subs
but it does also just tell you straight up what it will be
odd rampart
wait so i dont care about the jacobian in the final integral because its in terms of uv?
if it was in xy then i wouldve?
odd rampart
OH
fathom flicker
when we swap from x-y
odd rampart
so
odd rampart
when you actually do the math and solve it to find the integral
fathom flicker
and that was the result
odd rampart
they just straight up are telling you
solve the integral
with bounds [2,6]x[0,6]
and integrand v
with dv du
fathom flicker
yes
fathom flicker
but
the goal of the question is for you to find that integral on your own
they are giving you lots of tips so you don't get stuck
but you learn nothing from being handed the answer like that
odd rampart
yeah, like im doing other questions rn and im stuck on exactly this stuff
mind if i show you that too?
fathom flicker
you can send another one
fathom flicker
here's my recommendations ( this will apply to a and b, but only do it one at time)
first sketch the region
odd rampart
i did
fathom flicker
ignore the integrand
once you have the region sketched
write down what it is
in terms of the lines enclosing it
because these are the lines that make the bounds complicated
odd rampart
so like a parallelogram and triangle, as the question tells us?
fathom flicker
draw the specific parallelogram with those points as its vertices
then find the equations of the lines that make its boundaries
these lines are what make the boundary of the region in x-y coordinates complicated
odd rampart
well yeah
fathom flicker
so these are the lines that you will want to choose for your substitution of variables to make it simpler
please don't interrupt
once you have chosen the substitutions, compute the jacobian for those substitutions using the formula. And then you can also solve for x and y in your substitutions to substitute out the integrand. This will give you 1. easier bounds which you can find in the u-v world from looking back to your original substitutions 2. a jacobian to input into the new integral in order to allow the substitution 3. a way to replace the original integrand in x-y into u-v. At that point, you will have an easily solvable integral in u and v coordinates, and you will be done because the question states you do not need to evaluate
really just try that out for a bit
if you get stuck, try it again in a new way
you can DM me if you are stuck on those in an hour
odd rampart
I'll probably just take this and work on it for a bit and then sleep on it if i dont get it as I have to be up early in the morning, so are you okay if I DM if you tomorrow morning? Approx. 9.5 hrs from now if it's not night-time for you?
fathom flicker
sure, you can DM me, I'll just expect that you show me some work/effort of what you tried and we can go from there if you need!
odd rampart
Okay, I'll do what I can, thanks!
hot dawn
obtuse pebbleBOT
hot dawn
"Why" are x,y,z all of order 2?
Also, why are we allowed to simply "assume" that G is cyclic?
obtuse pebbleBOT
@hot dawn Has your question been resolved?
obtuse pebbleBOT
@hot dawn Has your question been resolved?
past walrus
obtuse pebbleBOT
thick gyro
!15m
obtuse pebbleBOT
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.
obtuse pebbleBOT
thick gyro
.reopen
obtuse pebbleBOT
✅
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
boreal spade
obtuse pebbleBOT
severe reef
for the function to be defined, the denominator has to be non zero
you get your domain from that
boreal spade
you get your domain from that
can you explain through an example as above
severe reef
when is the denominator becoming 0?
in your circled example
for what value of x
is your denominator 0
severe reef
yes so that means at x=2 the expression will become not defined
so your domain can not have 2
other than 2 there is no value of x which makes the function undefined
therefore your domain is all real values of x except 2
now for the range
i like to equate this thing to some constant k, and see what k can not be for x to be defined
boreal spade
how would i graph that though
like i mean
cause we use the denominator to find the x value shift
if there is one
but in this example we seem to be getting rid of the bottom x
(which from my examples, i need in order to be able to get the graph points)
severe reef
oh mb i didnt see you also have to graph it
i thought we just need the range and domain
boreal spade
yeah this is graphing rational functions
basically like
an easy example similar to this is
this
in this example we would take that 7 and itd mean shifting the graph left by 7
and the 5 would mean its going down by 7
and the 10/x is what we use for finding the graph points
basically we make up the x value to use for the 10/x and use that for graphing
and then use the 5 and the 7 to shift that graph in the end
but in this example, the x value isnt singular its 4x which makes me wonder what to do in that situation
<@&286206848099549185>
obtuse pebbleBOT
@boreal spade Has your question been resolved?
royal shard
You could also just get some points and then extrapolate
obtuse pebbleBOT
thick gyro
i think it just has to be bigger than 0
royal shard
,w log-1(1)
warm shaleBOT
thick gyro
,w log-2(5)
warm shaleBOT
thick gyro
guess there is no restrictions
royal shard
log_a(b)=c means a^c=b
So in this case
(-1)^0=1
Notice that 0 is not the only solution though
thick gyro
aslong as you only want to stay in real numbers
other way round
aslong as you dont care about staying in real numbers
royal shard
So i would say if we stay above 0, we will get a well defined function. Otherwise we have to choose one solution
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
I found the tangent of a point on a function, im being asked to find a parallel tangent somewhere else on the function but i have no idea how to find the paralell.
The function is x^3+x^2-5x+3 and function of one of the tangents is 3x+15 at (-2,f(-2))
obtuse pebbleBOT
I found the tangent of a point on a function, im being asked to find a parallel ...
timid silo
I suppose the parallel tangent is 3x + some constant
royal basin
warm shaleBOT
MathIsAlwaysRight
trim portal
also use parenthesis next time
yep, can you now solve it?
keep in mind log(5) and log(4) are just numbers
Okay, try to expand parenthesis
(x-2)*6 = 6x-12
e.g.
it would be (x)log(5) - 2log(5) but yeah
yep
now move everything with x on one side and everything without x on other side
Now factor out x
from left side
ab+ac=a(b+c)
yep
oh I meant divide both sides by (log(5) - log(4))
but this is also good, now divide both sides by log(5/4)
And that will give you x on one side and everything else on other side
so just plug that in calculator
or you could also simplify it
Oh okay
So just simplify the other side
$x=\frac{\log\left(4\right)+2\log\left(5\right)}{\log\left(\frac{5}{4}\right)}$
warm shaleBOT
MathIsAlwaysRight
sage dagger
Hi, im trying to complete the square and i think i did something wrong
obtuse pebbleBOT
Hi, im trying to complete the square and i think i did something wrong
sage dagger
can anyone check for me?
sage geode
(7/2)^2 is not 7^2/2
sage dagger
huh
oh i know i just wrote it incorrect
ignore that for now
pretend its (7/2)^2, but aside from that what else
wanton hull
i dont think completing the square works for this question
sage dagger
completing the square works for any quadratic equation
sage geode
You should have -2.75 under the sqrt
sage dagger
You should have -2.75 under the sqrt
where did you get that number?
sage geode
That's -15 + (7/2)^2
sage dagger
oh i thought because it was under the square root that we could remove the square
sage dagger
but it doesnt make sense to operate the square root on only one term of an equation and not the other i guess
makes sense
wanton hull
completing the square works for any quadratic equation
i tried to mean that it is too complicated
sage dagger
i tried to mean that it is too complicated
eh not really
sage dagger
That's -15 + (7/2)^2
oh right -15 + 12.25
thick gyro
@sage dagger discriminant of b^2 - 4ac = 49 - 60 = -11
sage dagger
uh is the discriminant part of completing the square
sage dagger
it is?
wanton hull
eh not really
comparing to the formula?
sage dagger
comparing to the formula?
are you talking about the quadratic formula
wanton hull
are you talking about the quadratic formula
yep
sage dagger
is this correct now btw
thick gyro
a(x+b/2a)^2 = a(b/2a)^2 - c
a(x+b/2a)^2 = b^2/4a - c
wait i feel like im missing something
nvm
sage dagger
what were the three cases
thick gyro
that is the point
if delta > 0
there are 2 real roots
if delta = 0
there is 1 equal root
if delta < 0
there are no real roots
wanton hull
imaginary roots:)
thick gyro
just like your friends
wanton hull
thick gyro
a(x+b/2a)^2 = b^2/4a - c
sage dagger
is this correct now btw
btw this is correct right 
thick gyro
,w roots of x^2 - 7x + 15
warm shaleBOT
thick gyro
not really
thick gyro
plus youll end up realising that, x^3 = 1, doesnt just have x = 1. there is also x = -1/2 + sqrt(3)/2 i and x = -1/2 - sqrt(3)/2 i
sage dagger
so far ive only been introduced to the sets of; N,Z,R,Q,Q'
by the way when writing the domain and range of functions
are we allowed to use subset notations
(im just assuming its possible)
idk if you can actually do that
thick gyro
personally i dislike set notation, so i cant really answer that
sage dagger
alright thanks, was just wondering
wise talon
its totally fine lmao
sage dagger
so the set of Q refers to fractions like -2/3 right or integers in p/q
so would Q' refer to fractions such as sqrt(3)/2
or for Q' would the denominator and numerator not be a whole number
.close
faint prism
Third line, (x+4)(x+3)
(x+4)(x+3)=?
Look at your fourth line.
Ops, my bad.
Looks fine to me.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
river axle
quick question how do you put sin^2 in calc?
obtuse pebbleBOT
quick question how do you put sin^2 in calc?
tropic leaf
sin x * sin x ?
river axle
wont that change the final answer?
river axle
sin x * sin x ?
and its error 💔
tropic leaf
,w sin x * sin x
warm shaleBOT
tropic leaf
It works for me
kind hawk
lets not forget that some calculators need brackets
sin(x)^2 or (sin(x))^2 might also work
tropic leaf
What is your calculator model
river axle
What is your calculator model
casio
kind hawk
just checking, your calculator can handle putting in x. or you are putting in a number instead of x, right?
river axle
just checking, your calculator can handle putting in x. or you are putting in a ...
n o i dont think so
this is what were supposed to sovle using calc
tropic leaf
It's stated that you need the calculator?
river axle
It's stated that you need the calculator?
yes
tropic leaf
Calculate cos 30
wanton hull
what is $\cos 30$?
tropic leaf
then square the result
warm shaleBOT
bettim
river axle
ohh you can do that?
wanton hull
you dont even need a calc to be fair
obtuse pebbleBOT
@river axle Has your question been resolved?
green glade
How do I solve part (b) ?
obtuse pebbleBOT
How do I solve part (b) ?
trim portal
start with $y=\arctan\left(x\right)$
green glade
I got $\frac{dy}{dx} = cos(y)^2$
trim portal
Show your work
green glade
x = tany
d/dx x = d/dx tany
1 = sec^2 y * dy/dx
dy/dx = 1/sec^2 y = cos^2 y
Wait mb, it should be y above
trim portal
Well so you got cos^2(y)
warm shaleBOT
FireÞeLost🔥
trim portal
Okay thats correct
now recall that y=arctan(x)
so it will be $\frac{dy}{dx}=\cos^2(\arctan(x))$
warm shaleBOT
MathIsAlwaysRight
trim portal
arctan will map that length on unit circle to angle theta, and from theta it then gets mapped to the cos
trim portal
So using geometry you will have to find something that relates the tan length and cos length
warm shaleBOT
FireÞeLost🔥
green glade
$\frac{dy}{dx} = \frac{1}{1 + x^2}$
warm shaleBOT
FireÞeLost🔥
graceful wind
obtuse pebbleBOT
obtuse pebbleBOT
@graceful wind Has your question been resolved?
obtuse pebbleBOT
@graceful wind Has your question been resolved?
obtuse pebbleBOT
@graceful wind Has your question been resolved?
lone bolt
why is this true
obtuse pebbleBOT
why is this true
median dome
You can use implicit differentiation to prove this
lone bolt
how so
abstract flame
isn't that the definition of ln
median dome
Let y = ln x, then e^y = x
frosty spoke
isn't that the definition of ln
interesting choice of definition LOL
median dome
Differentiate both sides wrt x and solve for dy/dx
abstract flame
interesting choice of definition LOL
im pretty sure that ln is defined as integral from 1 to x of 1/t dt
and then this is trivial by ftc
median dome
im pretty sure that ln is defined as integral from 1 to x of 1/t dt
No it isn’t
frosty spoke
well you certainly can define it that way
but you can also define it as some sort of inverse of e^x
abstract flame
idk that's the way it's defined in calc usually
median dome
The natural log is defined as the inverse function of e^x
abstract flame
but you can also define it as some sort of inverse of e^x
this is ususally how it's defined in precalc
median dome
idk that's the way it's defined in calc usually
That isn’t a definition, it’s a result
frosty spoke
you can pick your definitions and results
median dome
It’s not what ln represents
abstract flame
well not really the two definitions are equivalent
so which one you pick is arbitrary
frosty spoke
just like how we usually don't define x^n as e^(n ln x), but it's common later on
never heard of log x being defined like that though
abstract flame
that's how my calc book did it
frosty spoke
I guess it does really help with showing the log rules
abstract flame
that's how my calc book did it
and then it showed that it also happened to be inverse of e^x
frosty spoke
that seems like an annoying proof with Riemann sums lol
lone bolt
should i just
try to do y'
of ln x
im new to math man, not trying to do rocket science
or is it impossible
and should i just say it ='s 1/x
like e^x = e^e
median dome
and should i just say it ='s 1/x
You can assume that for now
You don’t really need to prove it
median dome
like e^x = e^e
What??
lone bolt
i know
median dome
Ok
median dome
its a rule
It’s more so a definition than a rule
lone bolt
but not proven
median dome
It’s what defines e
graceful quail
I am using this formula to graph the velocity of an object in projectile motion. After the first 10 seconds, gravity is inverted, the object than has a positive value for gravity and should start accelerating upwards. The only issue is that my graph doesn't seem to start where the top one leaves off (in reference to the y values).
Does anyone know what's wrong?
obtuse pebbleBOT
I am using this formula to graph the velocity of an object in projectile motion....
@graceful quail Has your question been resolved?
frosty spoke
I assume you write v = -gt or something?
then the equation of your next thing should be v = g(t-10) + v(10)
obtuse pebbleBOT
@graceful quail Has your question been resolved?
graceful quail
then the equation of your next thing should be v = g(t-10) + v(10)
What do you mean with this, sorry just getting familiar with the terminology.
frosty spoke
it's tax szn
a similar thing happens with marginal tax rates
oh wait they calculate things differently now LOL
but honestly same thing
actually it's pretty neat so let's go with it
you know that the slope of your velocity vs time graph after you flip the world upside down is +g
see if you can find a point on that one
and then use point-slope form
graceful quail
see if you can find a point on that one
With the following formula it computes the following for velocity:
(initialVelocity * sind(angle) - gravity * 10) = 79.66
frosty spoke
yeah but that's not a point on this line
well it is
but you said yourself that this line starts at the wrong place
graceful quail
Somehow my algorithm is not correct.
frosty spoke
where should it start? that's a point on the line
frosty spoke
Somehow my algorithm is not correct.
I'm very well aware of that
graceful quail
It should start at -18.3957
graceful quail
see if you can find a point on that one
Set this value equal to point slope form equation?
graceful quail
yeah sure go for it
What would I use as the x and y values?
frosty spoke
a point on that line would be (10, -18.3957) wouldn't it
graceful quail
a point on that line would be (10, -18.3957) wouldn't it
Okay so I would also want to calculate the slope as well?
graceful quail
isn't the slope just g
How do you know this is the slope?
frosty spoke
kinematics? constant acceleration gives a linearly increasing velocity
graceful quail
kinematics? constant acceleration gives a linearly increasing velocity
Sorry I don't know what kinematics is but I did do the calculation I'm not sure how helpful it is.
obtuse pebbleBOT
@graceful quail Has your question been resolved?
frosty spoke
this reminds me far too much of doing my taxes
obtuse pebbleBOT
@graceful quail Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
rough anvil
Work so far: 1+2=3, 1-1/3=2/3, 1-1/(2/3)=1/2, 1-1/(1/2)=-1, 1+1=2, 1-1/2=1/2. I don't know where I went wrong
obtuse pebbleBOT
Work so far: 1+2=3, 1-1/3=2/3, 1-1/(2/3)=1/2, 1-1/(1/2)=-1, 1+1=2, 1-1/2=1/2. I ...
sand forum
It is talking about function composition, right? Though when I see that they put parentheses around the power
sand forum
your mistake is the third composition I think
1 - 1 / [ 2/3 ] should be 1 - 3 / 2 = -1/2
Also uou should get -1/2 instead of 1/2 as a final answer. It should be 3, 2/3, -1/2, 3, 2/3, -1/2. You have 3, 2/3, 1/2, ...
sand forum
this is tedious work X_X. Are you using a calculator to do this?
rough anvil
No-
sand forum
Rough
nocturne minnow
,rotate
warm shaleBOT
thick gyro
@timid silo summation formula
acc
hmm
yh summation formula
remember though
that after the first drop of 5 meters
the vertical distance is double
the height it reaches
since it goes up and then back down
its best
if you dont start with 5 meters
keep 5 meters on the side
and start with the first bounce
and then do the sum formula
and double the answer
then add 5 ontop
think about it
you started from 5 meters
how can the next bounce
be higher
read it again
properly
well you have read it, but youre getting a different
idea
from what its saying
yh
and then
multiply that
by 4/5
to get the next bounce
its a geometric sequence
thick gyro
well its not 8th bounce
its best if you start the series with
5 *4/5
and then go up to the 7th term
yh
$h_n = ar^{n-1}$
warm shaleBOT
doctor99268
thick gyro
you know what a and r should be
you want to find the sum
of the first 7 terms
double it
and then add on the 5 we started with
you can see that from after the first time the ball touches to the ground
to the 8th time it does
there are 7 heights
inbetween
which is why we do 7 terms
yh
you dont need to do this manually
you can use the geomertric sum formula
we do
7 terms
n = 7
yh
yh that seems fine
the bottom one
wwill be negative aswell
and itll cancel out
@timid silo it askes fort he vertical distance travelled
for a single bounce
the vertical distance travelled
is twice
the height of the bounce itself
because it goes up then goes down
also not sure
why you rounded that
to 16
yh
its because
the first bounce
not first bounce
but the first height
of 5 meters
isnt doubled
oh you mean
8 to 7
its because you can draw it out
7 heights
from the first time it touches the ground
to the 8th time it touches the ground
quartz basin
Hi, i have a question its too simple but time based,
Chris saw a vase in a museum he visited in 2020.
When reading the information about the vase, he discovered year the vase was found and his birt date same. He learned that vase was 300 years old when vase was found. In addition, during this visit, his age multiplied 39 is equal to year the vase was made. Accordingly, how old is Chris in 2020?
Here my aproach: Chris birt year and vase discovering year = "X", the year vase made = "x-300", chris age = "2020-x" equation == 39(2020-x) = (x-300) its true but it takes too long to solve. but instead of doing (2020-x), giving his age = y, and x+y = 2020 makes too much simple and time saver. but how do i know i have to do 2 variable?
obtuse pebbleBOT
Hi, i have a question its too simple but time based,
Chris saw a vase in a museu...
quartz basin
edit: but how do i know i have to do 2 unknown?
dark stirrup
Time based?
quartz basin
in exam, i have solve less than 3 minute
i have to solve*
i hope its understanding if not please ask, i translated question. both way are true, but the second way is time friendly. but how can i know i have to do second way. @dark stirrup
nocturne minnow
in exam, i have solve less than 3 minute
Are you saying you are taking an exam?
quartz basin
no. im going to take an exam,
questions will be like this and there will be time limit.
my question, how can i learn different approaches the math questions.
both are them true, but second one is fast, and simple. how can i see this?
tardy epoch
The fastest one is the one you practice more
So spend less time thinking which one is simpler and just do more problems
quartz basin
thanks for answering. the one im familiar with is still takes too long. because its big numbers. and i want to improve my aproach the problems.
even if i do solve lot more, its like memorizing the solutions. no change in aproach.
obtuse pebbleBOT
@quartz basin Has your question been resolved?
quartz basin
.close
obtuse pebbleBOT
frank horizon
So you know how if you factor an equation that is in the form x^2+nx+a it gives you two answers or zeros
cerulean grail
Yes
frank horizon
It would be something like (x+a)(x+b)
So try doing the opposite since you already have the zeros
cerulean grail
Is this what you mean?
frank horizon
There needs to be x terms in there since it’s a function
timid silo
can someone help me please?
obtuse pebbleBOT
can someone help me please?
timid silo
i dont know how to solve this with my calculator
fathom flicker
I would recommend using the formula binom.dist in excel
fathom flicker
google sheets
timid silo
how would i plug it into google sheets n solve it?
fathom flicker
using the formula binom.dist and following the instructions it should give you for how to input it
drifting wraith
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
.close
obtuse pebbleBOT
fervent tusk
Make x the subject for both the inequalities
obtuse pebbleBOT
@spiral pollen Has your question been resolved?
torpid bane
how do i show this works ∣A ∪ B ∪ C∣ = ∣A∣ + ∣B∣ + ∣C∣ − ∣A ∩ B∣ − ∣A ∩ C∣ − ∣B ∩ C∣ + ∣A ∩ B ∩ C∣
obtuse pebbleBOT
how do i show this works ∣A ∪ B ∪ C∣ = ∣A∣ + ∣B∣ + ∣C∣ − ∣A ∩ B∣ − ∣A ∩ C∣ − ∣B ...
torpid bane
∣A ∪ B ∪ C∣ = ∣A∣ + ∣B∣ + ∣C∣ − ∣A ∩ B∣ − ∣A ∩ C∣ − ∣B ∩ C∣ + ∣A ∩ B ∩ C∣
torpid bane
how
torpid bane
ok
obtuse pebbleBOT
@torpid bane Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
haughty blaze
hii wondering where i went wrong
obtuse pebbleBOT
hii wondering where i went wrong
haughty blaze
i think it has to do with the first part of the question but i'm not sure where i went wrong
fervent tusk
could you send the actual question
haughty blaze
yupppp
fervent tusk
okay so you want to use product rule
your u would be 2x
and your v would be ln(2/3x)
haughty blaze
did i just divide fractions wrong LOOOOL
fervent tusk
i think you did
fervent tusk
no worries
timid silo
How would I find ‘h’?
obtuse pebbleBOT
How would I find ‘h’?
timid silo
<@&286206848099549185>
Do I just sub in 30 to T and 7 hours to t
and then solve for h
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
<@&286206848099549185>
obtuse pebbleBOT
@timid silo Has your question been resolved?
wild forge
how do i get the points?
obtuse pebbleBOT
how do i get the points?
wild forge
timid silo
probably recognising that the first equation is an ellipse and the second is a hyperbola is helpful
you don't need to find the points themselves
just how many there are
wild forge
yeah but how do i get them
timid silo
you want to get them?
wild forge
yeah
timid silo
like the values?
wild forge
yeah
timid silo
will thats not what your question is asking but you still can
it is a system of equations
timid silo
[
\begin{cases}
2(x+1)^2 + (y-2)^2 &= 25 \
4(x+1)^2 - 3(y-2)^2 &=15
\end{cases}
]
find the suitable $x$'s and $y$'s by whatever method you solve a system of equations with (substitution, elimination)
warm shaleBOT
timid silo
i got x=+/- 3 square root of 2 - 1
no thats wrong seemingly
wild forge
i did this
2a^2+b^2=25 got multiplied by 3
ohh wait its supposed to be 10a^2=90
nvm x is 2 or -4
wild forge
nvm x is 2 or -4
then what do i do with these?
do i just substitute them with the given equations?
timid silo
well actually
you have four values of x
you have
\begin{align*}
x&= -4 \
x &=2
\end{align*}
from the first equation, and
\begin{align*}
x&= -4 \
x &=2
\end{align*}
from the second equation
warm shaleBOT
wild forge
ohh i see
timid silo
so you need to plug in those 4 values of x in the corresponding equations to get 4 values of y too
timid silo
yeah
wild forge
i remember now lol
timid silo
you have 4 intersection points
wild forge
oh btw you said earlier that i dont need to find the points to get the answer
timid silo
yeah
wild forge
or did i misinterpret it?
timid silo
u dont
because reread ur question
it doesnt ask u to find them
it asks u to find how many there are
wild forge
yeah i see that but how do i know that its 4
timid silo
like i said
recognise that the first equation is a vertical ellipse
and the second equation is a horizontal hyperbola
wild forge
ahhh i see
wild forge
i just tried it on desmos
timid silo
,w graph
2(x+1)^2 + (y-2)^2 = 25
4(x+1)^2 - 3(y-2)^2 =15
wild forge
its only possible for them to intersect 4 times
warm shaleBOT
Requested by ♡Lixera♡#5050
timid silo
well okay