from nothing?
#help-10
royal basin
timid silo
yes?
royal basin
the lengths of some of the arcs pictured here might help
that's the only thing i can think of other than the angle itself
or maybe the areas of some of these regions
timid silo
hmmm
solar trellis
just use a protractor lol
royal basin
if this diagram came from nothing then this angle is of no relevance to anything
royal basin
there is nothing in my message to "hmmm" about.
timid silo
how do you calculate an angle regularly? like do you have an example?
royal basin
it depends heavily on what else is known and what the diagram is like
there are numerous theorems that relate angles in certain configurations to each other or to lengths. there are too many to give an exhaustive list.
timid silo
there are numerous theorems that relate angles in certain configurations to each...
hmmm ok thx anyways
.close
plucky patio
how do I do b?
obtuse pebbleBOT
how do I do b?
knotty crow
I guess you've already done (a) part?
you can use the sketch from (a) to show that or just find inverse and then do that
plucky patio
you can use the sketch from (a) to show that or just find inverse and then do th...
uhh question b? to find k?
knotty crow
oh
sr
you can also use a graph to determine solution to the b)
imagine function y = k (line parallel to the x-axis) for some k's
determine 'k' such that line y = k crosses your f(x) in two point whose x-coords are negative
grizzled shore
you could just do -(x+1)^2+4-k where the you check the sign of this
so u know a is negative and the top has -b±∆
so for it to be negative the top cant also be negative
so -b±∆ > 0
±∆ > b and u just see what kind of k's give u this inequality
at least that's how i'd think about this question algebraically
this is actually similar to thinking about it as, look at your vertex point, ∆/(2a) as how far this is from the vertex and saying the + of this from the vertex is negative
cos if the vertex + |∆/(2a)| is negative then the vertex - |∆/(2a)| is definitely also gonna be negative
plucky patio
so -b±∆ > 0
oh nice thanks this makes sense
feral island
How do I write a equation for this graph?
obtuse pebbleBOT
How do I write a equation for this graph?
royal basin
do these measurements say 19^2 m and 1ab m?
grizzled shore
is that supposed to be a parabola?
obtuse pebbleBOT
@feral island Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
slender fjord
This is just a hypothetical to help me understand something.
obtuse pebbleBOT
This is just a hypothetical to help me understand something.
urban patrol
No way is that technoblade
slender fjord
lol
urban patrol
ok so sin(theta)=1/2
slender fjord
yeah
urban patrol
the expanded double angle formula for cosine can be 3 things if I remember correctly
You can just plug in the 1/2 into any of them
then solve for cosine(theta)
urban patrol
Or maybe you can use the value of arcsin 1/2
urban patrol
okay cool
slender fjord
Or maybe you can use the value of arcsin 1/2
thanks for the help
urban patrol
no problem
azure hollow
Hello, I need help with finding 75% of 110. I tried what my teachers try to teach me is to make 75 into 0.75 and then multiply it with 110. But I still do not understand why we make 75% into 0.75.
obtuse pebbleBOT
Hello, I need help with finding 75% of 110. I tried what my teachers try to teac...
gleaming burrow
75% is another way of saying 75/100
gleaming burrow
And 75/100 when expressed using decimal notation is 0.75
azure hollow
oh bec ause .75 means 75 hundreths
gleaming burrow
% percent -> per one hundred
azure hollow
oh ok
gleaming burrow
per -> / (division)
obtuse pebbleBOT
@azure hollow Has your question been resolved?
wooden cipher
They left :l
spring frost
In this problem how do i find the vertical stretch
obtuse pebbleBOT
In this problem how do i find the vertical stretch
spring frost
I initially thought it was 8 but it doesnt seem to be that way
haughty coyote
What do you call vertical stretch ? The length of the interval of value reached ? If so remember sin has a stretch of 2, not 1
spring frost
oh sorry it was 2
I accidently changed it to 3 when I typed it the new one is below
ok so it is that
that also doesn't have a vertical stretch of 8 thought as well
how do I find it again?
haughty coyote
What do you call vertical stretch ? The length of the interval of value reached ...
What's the definition of vertical stretch ?
Because I actually don't know how you've defined that
spring frost
in a function that is af(x)
its the a
so its the amount you multiply the y-coordinates by
haughty coyote
And what is f here ? The stretch is relative to something
spring frost
idk but I think d is the vertical shift in this function
srry
I was using notes from a different chapter on accident
alr thanks for the help
I think I just figured it out
.close
long phoenix
How would I take the function from this graph?
obtuse pebbleBOT
How would I take the function from this graph?
long phoenix
i dont know if i should take sin or cos
brave bramble
Either can work. cos looks easier, though
wanton violet
if it passes through (0, 0) then sin otherwise use cos (but technically both will work)
brave bramble
Do you?
long phoenix
or 3cos[b(x-d)]
wanton violet
so i got 3cos(x)
almost, 3cos(x) has a period of 2pi but the graph only has a period of pi
long phoenix
yea so i could do 3cos(1/2x)
wanton violet
2x not 1/2 x
for horizontal stretches you do 1/the factor you want to stretch by so in this case 1/(1/2) = 2
wanton violet
yep
long phoenix
tytyty!
wanton violet
np
timid junco
migght be a stupid question but I was wondering why he didn't solve for f''(x) on this problem
obtuse pebbleBOT
migght be a stupid question but I was wondering why he didn't solve for f''(x) o...
knotty crow
migght be a stupid question but I was wondering why he didn't solve for f''(x) o...
why should we do in your opinion?
timid junco
So it seems like all we have to do is solve when f'(x)=0 and plug it back into the original equation
timid junco
why should we do in your opinion?
I just thought f''(x) was the way to find which values are max and min
knotty crow
I just thought f''(x) was the way to find which values are max and min
it is, but there is also a way using first derivative
timid junco
Well first derivative only shows if it's going up or down right?
Only rate of change of f(x)
knotty crow
yeah, it's about monotonicity of f(x)
timid junco
I don't follow
knotty crow
if you want to use f''(x) to determine them, then u should try this:
f'(x) = 0 and f''(x) < 0 --> max
f'(x) = 0 and f''(x) > 0 --> min
knotty crow
for example
for max
it follows
If the function $f$ has a derivative on the interval $(a,b)$ and $f'(x)>0$ for $x \in (a,x_{0})$ and $f'(x)<0$ for $x \in (x_{0},b)$, then $f$ has a maximum at $x_{0}$.
timid junco
Oh I think I understand now
warm shaleBOT
Modus
knotty crow
like in other words
if function increases to some point
and then decreases from this point
on some interval
then it's maximum
shortcut is to determine change of the sign of f'(x) at the point we investigate
if it changes from "+" into "-" then it's max
if it changes from "-" into "+" then it's min
timid junco
if it changes from "+" into "-" then it's max
if it changes from "-" into "+" th...
You're saying if I enter positive number in f'(x) and the output is negative then it's max? And negative and get positive then min?
For example f'(4)=-2 then this is max
f'(-4)=2 then min
knotty crow
not really
it's not about the only one value
let's say you investigate x = 4
for some function
you can take for example f'(-3.9) and f'(4.1), if f'(-3.9) < 0 and f'(4.1) > 0 then it's max
but this method rather works with graph of f'(x), because we can't be always sure that we take interval which is small enough
obtuse pebbleBOT
@timid junco Has your question been resolved?
timid junco
seems a bit complicated
slim cove
migght be a stupid question but I was wondering why he didn't solve for f''(x) o...
When you're trying to maximize a function in an interval, you have to check the boundaries of the interval
Because it's possible that the derivative is not zero there, but they could still be the absolute min/max
That's why they plug 0 and pi in
timid junco
I thought they plug 0 and pi because the question asks for the value at those points
slim cove
no the question doesn't ask for the value at those points, it asks for the maximum and minimum value of f
when 0 ≤ x ≤ pi
timid junco
yeah the max and min in that interval of f(x)
slim cove
right
lemme give an example
so let's say we're trying to find the max and min of this function in the interval [0, pi]
you could set the derivative equal to zero
and try to find maxes/mins that way
but that doesn't give you all the possibilities
it only gives you these two points
because you need to check the endpoints at all
aka these purple points
does that make sense?
timid junco
setting to 0 doesn't find all endpoints got it
obtuse pebbleBOT
@timid junco Has your question been resolved?
jagged edge
obtuse pebbleBOT
jagged edge
i kind of dont understand this one
white urchin
i kind of dont understand this one
you don't understand how to answer it or you don't understand about how to read the given information?
jagged edge
i do understand the givern information
but like i dont quite get what the question is
white urchin
it is like :
A={1,2,3,4}
B={2,3}
then {1,4} = A-B
You have to create an equation involving the sets A, B, and C that gives {-7,-7,-5,-3,-1,1,3,5,7,9}
you can add a '-', '+', '∩', '∪', etc in your equation
obtuse pebbleBOT
@jagged edge Has your question been resolved?
sleek cosmos
obtuse pebbleBOT
sleek cosmos
I don’t know how to do this equation
What I mean is that I don’t know what to do on how to plot the four points other than vertex
On 4x
4c*
high lily
to get additional points, choose some values of x, plug into the equation to get the respective y values to get your points
high lily
yes
sleek cosmos
What does ax^2+bx+c have to equal as seen in my thing which equals 3
high lily
your question is unclear
high lily
where exactly
sleek cosmos
on the parabola equation
high lily
they're all about parabolas
sleek cosmos
like the section where it says plot 4 points other than vertex you see -3
sleek cosmos
oh ok
high lily
thats what you get from plugging in those values
f(0) = f(4) and f(1) =f(3)
since x=2 is the axis of symmetry
sleek cosmos
ohhhhhhh
I get it now. I will try another question
on the page and check if I did it right
@coral groveov#0921 did I do it right?
Sorry for the ping of wrong person
@high lily
obtuse pebbleBOT
@sleek cosmos Has your question been resolved?
gray hill
obtuse pebbleBOT
gray hill
I need help solving this. I found the point of intersection, but not really sure how to integrate this
hybrid gull
Given that you’re integrating about the y-axis, you’ll be integrating with respect to y
So you’ll need bounds in terms of y
This may help you get started
gray hill
so my bounds are 8 & 0 for limits?
I'm not really sure what steps to take except just knowing how the formula is
because what to plug in for r (radius)
hybrid gull
If you have the formula, then you’re good to go. You just need the setup
You’re trying to make the integral describe the volume
gray hill
If you have the formula, then you’re good to go. You just need the setup
right but I've seen some examples and I'm not sure how they get that number
hybrid gull
Which number? The limits? The radius?
gray hill
like this example:
i'm sure I have to do the same thing with this problem
oh wait
I see it now
so basically make x=y
so y^3/2=8
so y=4
so my limit is 4 0 and I just plug in my x, which is pi(y^3/2)^2 dy right?
hybrid gull
It helps to draw a picture
gray hill
how come then in that example they used what y was as the limit then?
so i just change it to 8 0 pi(y^3/2)^2 dy then?
hybrid gull
how come then in that example they used what y was as the limit then?
Hmm, not sure
I’m gonna look at a picture
gray hill
im stuck lol
tried to follow what was in the example above but not sure if im doing that step right
hybrid gull
I think what they’ve done is wrong
Get a picture of specifically the region you’re revolving
hybrid gull
Get a picture of specifically the region you’re revolving
.
gray hill
That is bounded by what the problem tells yo
not good at the revolving thing 
hybrid gull
You can use a graphing calculator to get a picture
hybrid gull
This, but a picture that includes the bounded region
wooden cipher
They have the rotate arrow
gray hill
You can use a graphing calculator to get a picture
what should I put in the desmos graph calc?
hybrid gull
Right
So revolving this about x = 0 means the horizontal layers of your solid will start at y = 0, end at y = 8, and radius will be equal to x = y^(3/2)
gray hill
oh the green line?
gray hill
By the way, do you have desmos link?
whatg's that
gleaming burrow
I thought you used it to make the graph
gray hill
gleaming burrow
Anyway, the bounded region is between them all
gray hill
so shade all of it in the space within all 3
gray hill
gleaming burrow
Kind of ambiguous the way you draw it, but it's rotating around the vertical y axis
gleaming burrow
So consider drawing a single cylinder / disk on the line for an example
Based on the question, it revolves all the way around.
gray hill
so draw a cylinder from 0?
gleaming burrow
I will draw it
gray hill
@next reef I see you lurkin' 
im so bad at this 
next reef
gray hill
nice reactions 
gleaming burrow
gleaming burrow
gray hill
so what do I do now?
gleaming burrow
Now you need to start with the volume of a single cylinder
gray hill
but same formula right
gleaming burrow
For our sample cylinder, we would do pi * dx^2 * dy since the height is dy and the radius is dx
Yeah, you will use same formula
The only problem is it is easy to get confused on this type of problem
gray hill
so I do pi*y^(3/2)dy?
gleaming burrow
That gives you the value of a single cylinder, and to add them all up you turn it to an integral
gray hill
gleaming burrow
Is that wolfram?
gleaming burrow
Wait, did we remember to square it?
gray hill
just the y^3/2 part yeah?
gleaming burrow
since y^(3/2) is radius and it needs to be squared
gray hill
since y^(3/2) is radius and it needs to be squared
yeah that's the answer, thanks for showing me how to work the problem out
.close
feral island
I am given a question to determine a quadratic equation with these characteristics
Minimum value is 12
X=-4
Y intercept of 60
obtuse pebbleBOT
I am given a question to determine a quadratic equation with these characteristi...
quaint glen
When you write "x=-4" what does that mean? Is that its axis of symmetry? It's x-axis intercepts? Something else?
royal basin
@feral island do you have the exact problem statement?
feral island
<@798366001829642241> do you have the exact problem statement?
That’s the exacte problem statement
Determine a quadratic function step by step:
minimum value of 12 at x=-4 and y intercept of 60
feral island
Does it make a difference?
royal basin
i think this answers your question of "where is the minimum"
and tells you exactly what the coords of the vertex are
feral island
Thanks
feral island
(-4,12), yes
May I ask than is the equation 60=a(0+4)^2+12?
since Y-int=(0,60)
Vertex=(-4,12)
royal basin
when you say "the equation" do you mean "the equation of the curve" or "the equation that gives the value of a"
royal basin
then yes
feral island
But I kept on getting the wrong answer for some reason
royal basin
were you putting your answer into your homework system that kept rejecting it?
show the work that led to your wrong answer.
royal basin
how did a(0+4)^2 + 12 become 28a?
devout solar
no
royal basin
no, 4^2 is not 12
feral island
Oooh
royal basin
16a + 12 ≠ (16+12)a
devout solar
16a+12a is 28a
feral island
Thanks I got it now
obtuse pebbleBOT
Available help channel!
zenith dagger
I forgot all the percentage stuff, some one help me
obtuse pebbleBOT
I forgot all the percentage stuff, some one help me
devout solar
no
royal basin
you havent yet converted that into a percentage
the wording "2% out of 100" is kinda sus tho
devout solar
it is
zenith dagger
the wording "2% out of 100" is kinda sus tho
Imma come clean. this aint some worksheet problem, I was shiny hunting a pokemon and I wanted to calculate the chances but my mind became blank
gleaming burrow
So just 2% of 1/8192?
obtuse pebbleBOT
@zenith dagger Has your question been resolved?
flat apex
Please help. Why it says that R\(closure of Q) is an open set? I'm sure that I've read before that R\Q isn't open set.
obtuse pebbleBOT
Please help. Why it says that R\\(closure of Q) is an open set? I'm sure that I'...
warm canopy
timid silo
So for n = 123, i got either p = 9, 3. p = 3, 10, however I don't understand how 2n = 66, wouldn't 2n = 246 if its multipied by 2?
obtuse pebbleBOT
So for n = 123, i got either p = 9, 3. p = 3, 10, however I don't understand how...
high lily
consider rounding
e.g take 5 as an example
sum of its digit is 5,
but 2*5 = 10
which has a digit sum of 1+0 = 1
timid silo
so 5 have a digit sum of 5 and 10 has a digit sum of 1?
vestal rose
Is there a difference between the two statements? Or is the first one a more compact way of saying the other one?
obtuse pebbleBOT
Is there a difference between the two statements? Or is the first one a more com...
royal basin
there is no difference
vestal rose
Yeah I figured, just making sure, I'm learning about math notation
Thank you :)
.close
narrow brook
Is a tangency point also a point of intersection?
I've always thought of a tangent line as one that 'touches but does not intersect' a curve (or circle, etc.) because for me, 'intersect' seems to imply 'cutting through' or 'crossing'.
But some looking around suggests that tangent lines are said to intersect at one point (the tangency point). Something about that seems very unsatisfying.
obtuse pebbleBOT
Is a tangency point also a point of intersection?
I've always thought of a tange...
severe dune
Is a tangency point also a point of intersection?
I've always thought of a tange...
Yes
A point of intersection that intersects a circle only once is known as a tangent
So all tangents must be intersection
narrow brook
So all tangents must be intersection
That seems to work for circles, but what about curves? The tangent line could easily intersect a curve more than once
severe dune
Yes
But the point where it's tangent at is still an intersection
As a definition intersection is just the points where 2 functions are equal
narrow brook
So I'm wondering, how best to define the tangent line at a point in the case of the curve of a function?
severe dune
If you visualise it like this the tangent is cutting through the curve and then cutting back out between a and b as a-> b
Point of intersection
Because it is
Just infinitly small
narrow brook
sure, but it seems we can't define the tangent line of a curve at a point as one that intersects the curve at that point (and only that point)
We could specify that the gradient of the tangent line and the curve at the tangency point are equal, but then I'm trying to define the derivative in terms of the tangent line. And at the moment the definitions seem circular.
obtuse pebbleBOT
@narrow brook Has your question been resolved?
flint sundial
obtuse pebbleBOT
@narrow brook Has your question been resolved?
high lily
I mean that's more or less the limit definition of the derivative
steep harness
Is a tangency point also a point of intersection?
I've always thought of a tange...
two functions f(x), g(x) intersect iff f(x)=g(x) for some valid x. a line is tangent to a function if it is on the outside of the concavity of the function on either side of an intersection.
i.e. if the function is ccu at a particular point, then the tangent line will be less than the value of the function (at least locally) around that point of tangency
narrow brook
Thanks, that helps
steep harness
this is important especially for things like the tangent line to f(x)=x^3 at x=0, the tangent line graphically is above the function on the left side, but below the function on the right, and so it "crosses" the function, but it stays on the outside of the concavity at all times.
obtuse pebbleBOT
@narrow brook Has your question been resolved?
trail haven
obtuse pebbleBOT
trail haven
how would i find x and y
harsh remnant
English
trail haven
sure
The box diagram shows the result from a sample. The sample indicates the number
hours one person slept per night for a period of 15 nights
the values in the sample below are given in order of magnitude. Two values have
replaced by x and y, respectively.
harsh remnant
Is it related to mean, median, and mode?
trail haven
yh think so
harsh remnant
So what's the question?
harsh remnant
the values in the sample below are given in order of magnitude. Two values h...
These are given
harsh remnant
The numbers listed are the possible/recorded values
trail haven
oh nvm yh that makes sense
harsh remnant
Yes, nice
trail haven
and the y?
trail haven
x should be 3
what about the y?
harsh remnant
Not...sure...
trail haven
alrighty
obtuse pebbleBOT
@trail haven Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hearty thunder
Hey
hearty thunder
Im working on long division of polynomials
How do i approach a problem like
(x^5+1)/x+1
kind hawk
well like you would approach any other division of polynomials
it may help to write x^5+1 = x^5+0x^4+0x^3+0x^2+0x+1
but apart from that just your usual algorithm
hearty thunder
This is the first time im dealing with these kinds of problems
Can you solve it
And maybe a step by step process if you wouldnt mind
I just learn better that way
Oh my
Nvm
obtuse pebbleBOT
@hearty thunder Has your question been resolved?
timid silo
Determine where the given function is a linear transformation. If it is, find it’s standard matrix A.
obtuse pebbleBOT
Determine where the given function is a linear transformation. If it is, find it...
timid silo
what is the definition of a linear transformation?
I’m not sure…
timid silo
look up the definition in your book/class notes
It says a linear transformation is a function from one vector space to another that respects the underlying linear structure of each vector space.
timid silo
does it get more specific?
No, that’s all it provides.
kind hawk
what a shitty book
a map $T:\bR^3 \to \bR^3$ is called linear if for all constants $a,b\in\bR$ and all vectors $x,y\in\bR^3$ we have $T(ax+by)=aT(x)+bT(y)$
warm shaleBOT
Denascite
kind hawk
there is nothing specific about R^3 here, this also works for R^n or in general any vector space
sometimes this definition is also seperated into the two conditions that T(x+y)=T(x)+T(y) and T(ax)=aT(x)
timid silo
there is nothing specific about R^3 here, this also works for R^n or in general ...
Isn’t there also the commutative property of scalar multiplication?
kind hawk
that's included in the vector space axioms
timid silo
that's included in the vector space axioms
I’m not sure what that means.
kind hawk
do you know what a vector space is?
timid silo
do you know what a vector space is?
It’s a space consisting vectors, together with the associative and commutative operation of addition of vectors, and the associative and distributive operation of multiplication of vectors by scalars.
kind hawk
and scalar multiplication is also commutative
timid silo
and scalar multiplication is also commutative
How do I find standard matrix A?
kind hawk
well how about you first determine whether T is actually linear
timid silo
well how about you first determine whether T is actually linear
I don’t think T is linear.
kind hawk
and why do you think that
timid silo
and why do you think that
I don’t think distributive property works?
timid silo
which distributive property
I’m just lost..
kind hawk
let $x=(x_1, x_2, x_3), y=(y_1, y_2, y_3)\in\bR^3$ be two vectors. can you calculate $T(x+y)$ and $T(x)+T(y)$ ?
warm shaleBOT
Denascite
timid silo
let $x=(x_1, x_2, x_3), y=(y_1, y_2, y_3)\in\bR^3$ be two vectors. can you calcu...
T(x^1+y^1), T(x^2+y^2), T(x^3+y^3)?
warm shaleBOT
Denascite
timid silo
can you tell me what $T(x)=T(x_1, x_2, x_3)$ is?
Between 3 x spaces that are inside the vector.
kind hawk
what? I don't understand what you mean
timid silo
I want you to apply this definition to T(x_1, x_2, x_3)
X, 0, -y
timid silo
I asked for T(x_1, x_2, x_3)
I’m just not sure.
kind hawk
instead of x you now have x_1, instead of y you now have x_2 and instead of z you now have x_3. that's just renamed. nothing else changed
timid silo
instead of x you now have x_1, instead of y you now have x_2 and instead of z yo...
Oh I get it
timid silo
instead of x you now have x_1, instead of y you now have x_2 and instead of z yo...
What do I do next
kind hawk
you haven't yet done what I asked for
timid silo
X,y,Z
kind hawk
no
kind hawk
T(x_1, x_2, x_3) is not equal to X,y,Z
also I don't know why you wrote X and Z in capital letters
timid silo
Sorry
timid silo
T(x_1, x_2, x_3) is not equal to X,y,Z
Yea idk I’m sorry
timid silo
T(x,y,z)=(x,0, -y)
T(x_1, x_2, x_3) = (x_1, 0, -x_2)
Oh I was stupid sorry
kind hawk
**Denascite**
can you now do this?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dreamy forge
obtuse pebbleBOT
obtuse pebbleBOT
@dreamy forge Has your question been resolved?
dreamy forge
<@&286206848099549185>
obtuse pebbleBOT
@dreamy forge Has your question been resolved?
obtuse pebbleBOT
@dreamy forge Has your question been resolved?
slim cove
How do I find the traces of these?
do you know what trace means
obtuse pebbleBOT
@dreamy forge Has your question been resolved?
dreamy forge
do you know what trace means
Not really
slim cove
I looked it up and it seems to just mean the shape of the cross section in this context
can you describe what shape z = 2x^2 + y^2 is?
slim cove
@rugged bobcat check #❓how-to-get-help
rugged bobcat
ok
dreamy forge
can you describe what shape z = 2x^2 + y^2 is?
Yeah
How would I find the trace
I set y=0
Then I got z = 2x^2
dreamy forge
Quadratic
dreamy forge
so what shape is thay
Why do we need know shape
dreamy forge
I got z = 2x^2
slim cove
yea
slim cove
where
slim cove
try z = 2x^2 maybe
timid silo
obtuse pebbleBOT
timid silo
Answer is B right?
restive ridge
no, why?
restive ridge
ah
timid silo
cuz look
restive ridge
I didn't read the every seven years part lol
restive ridge
yes B is correct
somber sierra
How does g(t+h) = 3(t+h)
obtuse pebbleBOT
How does g(t+h) = 3(t+h)
main cedar
its hard to tell without the full context
can you post the original question as well?
(also, i think you are asking why g(t+h) = 3(t+h)+6)
fierce lagoon
^
It states that g(t+h) = 3(t+h)+6
That easily means that g(t) = 3t+6
And it even states that
somber sierra
Oh yeah it does shit.
sorry, Im thinking Of other stuff not paying attention looks like
Thanks .close
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
graceful quail
Is the period in -3sinx+4 equal to 2pi?
obtuse pebbleBOT
Is the period in -3sinx+4 equal to 2pi?
compact shadow
Minimal period, yeah
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
How do i find the roots
obtuse pebbleBOT
How do i find the roots
obtuse pebbleBOT
obtuse pebbleBOT
✅
royal basin
rational root theorem sounds like it might help
timid silo
factorize
group first
it will be (-3x³ - 2x²)+ (- 6x - 4)
find the common factor in each group
Ohh okay
then factorize again
How do i factor again?
compact shadow
Factorize the remaining quadratic of it if it can be factorized
timid silo
Okay
royal basin
may i suggest
multiplying the whole thing by -1
just to get rid of all the minus signs
obtuse pebbleBOT
@timid silo Has your question been resolved?
leaden shoal
idk what to do
obtuse pebbleBOT
idk what to do
leaden shoal
royal basin
you are wrong about the events' mutual exclusivity and also your abbreviation of the events to "true" and "false" made you mislead yourself
these events are NOT mutually exclusive, as the problem clearly states
royal basin
90% ≠ 80% so what?
royal basin
whether or not the probabilities of two events are equal has NOTHING to do with their mutual exclusivity
leaden shoal
ok lets make this clear
mutually exclusive means that both events happen simultaneously right?
royal basin
no
leaden shoal
what?
royal basin
mutually exclusive means the events exclude each other
mutually exclusive means that if one event happens then the other cannot
leaden shoal
oh yes ur right
royal basin
mutually exclusive means that the events CANNOT happen simultaneously
leaden shoal
i mean non mutually exclusive
leaden shoal
no?
mutually exclusive means both cannot happen simultaneously
non mutually exclusive means both can happen simualtaneously
royal basin
mutually exclusive means both cannot happen simultaneously
non mutually exclusive means both can happen simualtaneously
yes sure
leaden shoal
is that sarcasm
i cant tell!
so for this its mutually exclusive?
u cant pick true and false at the same time
actually i think its non mutually exclusive
how about the second part
royal basin
is that sarcasm
it is not
were it sarcasm i would've marked it as such
and also your abbreviation of the events to "true" and "false" made you mislead yourself
leaden shoal
ok
just to clarify
the answer is non mutually exclusive
both can happen the same time
idk what to do
royal basin
languid vapor
Hey
languid vapor
If i had an exponential in the form of $a\cdot b^x$
warm shaleBOT
PixelWolf
languid vapor
What was the name of b and x?
tranquil heart
B is base and x is power are u asking this?
obtuse pebbleBOT
@languid vapor Has your question been resolved?
elfin tangle
obtuse pebbleBOT
elfin tangle
Im having trouble with this one,
clever nacelle
you just do
elfin tangle
I did (300,000(1.07))(12)
clever nacelle
its 1.07^12
compound interest
since every year it appreciates 7% so it will be based on the new appreciated value every year
so after 1 year it will be 300,000*1.07
elfin tangle
so its the 2nd one right
clever nacelle
2nd year
elfin tangle
the only one that makes sense is the second one
true but still
clever nacelle
2nd year (300,000)*1.07*1.07
elfin tangle
just to make sure
clever nacelle
use a calculator
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
spring frost
obtuse pebbleBOT
spring frost
is what I did at the bottom correct?
tardy epoch
call this w. do you know how to find the equation for w?
spring frost
so
is it 3, -3
or something?
I know I need to get one of these as the final answers
tardy epoch
is it 3, -3
close. you need one more negative sign
spring frost
close. you need one more negative sign
how do I know which was in negative or not, I cant find a good source online
tardy epoch
vector points to the right/up -> positive sign
vector points left/down -> negative sign
spring frost
yeah
tardy epoch
v points left and up so the first coordinate should be negative and second coordinate positive
tardy epoch
right
spring frost
ok can you come back in like 5 minutes or something, I think I can figure the rest out
tardy epoch
maybe. ping helpers if not
elfin tangle
obtuse pebbleBOT
elfin tangle
How would I do this?
proven zephyr
expand first and then simplify 🙂
cerulean tulip
use distributive property
you can also notice that this is a difference of squares
kindred oasis
@timid silo come here you closed the channel
obtuse pebbleBOT
<@456226577798135808> come here you closed the channel
kindred oasis
Basically we know that the sum of their ages is 45
And Jim's age is twice Jane's age right?
@timid silo
Ok. Knowing that you can already find both of their ages. Do you have any ideas on how to do that or I should give you a hint?
Correct
Yw
.close
elfin tangle
obtuse pebbleBOT
cedar lichen
What have you tried?
elfin tangle
i tried solving for x and it didnt make any sense
and i truly don't know where to start lol
cedar lichen
What is a horizontal asymptote?
elfin tangle
no clue LOL
cedar lichen
You don't know what a horizontal asymptote is? Because that's kind've a prerequisite
cedar lichen
A horizontal asymotote is what the y value approaches when you go infinitely far to the left or right
1/x has a horizontal asymptote at 0, for instance, because the function approaches 0 as you go infinitely far in one of the directions
cedar lichen
Well, what does the function approach, if anything, as x gets more and more positive?
elfin tangle
i dunno 😭
cedar lichen
Plug in values
Plug in 10, 100, 1000
What does the function look like it does?
Does it approach a value?
Does it blow up?
elfin tangle
when i plug in 1000 i get a math error lol
cedar lichen
Is the math error overflow?
elfin tangle
wdym?
cedar lichen
The number is really fuckin big when you put in 1000, right?
You should be able to see that without a calculator
elfin tangle
i dont even get a number lol
cedar lichen
Because it's too big for the calc to handle
elfin tangle
but yes
cedar lichen
So clearly, there's no asymptote to the right. It just gets bigger
What about to the left?
-10, -100, -1000?
elfin tangle
im still so confused LOl
oblique sage
What number does the graph approach as x app - infinity?
elfin tangle
What number does the graph approach as x app - infinity?
i dont know
cedar lichen
Maybe we can try something else
oblique sage
Plug it into Desmos my guy and see
elfin tangle
idkk 😭
what steps
do i need to do to get an answer
bc these examples arent working for me
heavy beacon
@elfin tangle ok look at the graph of e^x-1
what part of that graph shows that the graph is approaching a certain value
heavy beacon
elfin tangle
yes its approaching 1,-1
elfin tangle
ok wtf im rlly confused now
cedar lichen
I would highly suggest reviewing asymptotes. I'm sure you can find plenty of sources online
heavy beacon
u see the part of the function where its flat lining but not ever reaching that y value
yh y=-7
autumn atlas
what is the growth rate of V(t) = 50(1.006)^t in percent?
obtuse pebbleBOT
what is the growth rate of V(t) = 50(1.006)^t in percent?
warm shaleBOT
The following error occured while calculating:
Error: Undefined function ln
proven zephyr
is this exponential growth?
proven zephyr
no
hexed agate
I mean technically yes?
heavy beacon
.6%
autumn atlas
ok so its 0.6%?
hexed agate
Yes
proven zephyr
if it was exponential decay would it be -%?
this is compound growth and decay if im not wrong
proven zephyr
like 0.950 would be -5%?
yes
autumn atlas
well its an exponential function
proven zephyr
ok idk what's the difference, i give up
autumn atlas
.close
static cargo
How woudlI go about this problem?
obtuse pebbleBOT
How woudlI go about this problem?
thick trail
hello
static cargo
and i got -4sinx
thick trail
can anyone help me
static cargo
meaning that -4sinx = -8pi
thick trail
if x-y=7, xy=39, find x^3-y^3
thick trail
ok
static cargo
and ask it
main cedar
But then i got like x = sin^-1(2/pi)
That looks correct
static cargo
That looks correct
what would i do next?
static cargo
That looks correct
so i got csc(2/pi)
main cedar
Do you have access to a calculator?
knotty crow
That's it basically, you've found x-coord
static cargo
oh what
main cedar
Csc is 1/sin while arcsin is the inverse of sin
obtuse pebbleBOT
@static cargo Has your question been resolved?
obtuse pebbleBOT