so is it 1:0 or just 1?
#help-23
remote kernel
hazy elbow
Write just 1
opaque geyser
i'm trying to find the equation for this function, it can't be cotangent as that is not covered in this course, i initially thought it was a transformation of -x^3 but not with those asymptotes. i'd really appreciate some help.
safe radishBOT
i'm trying to find the equation for this function, it can't be cotangent as that...
abstract dust
by the looks of it it is a rational function
i.e. y=P(x)/Q(x) where P and Q are polynomials
do you know how to identify P and Q?
opaque geyser
i do not
opaque geyser
right
abstract dust
that means Q must have factors (x+3)(x-4)
opaque geyser
i can see how that might help finding the long run pieces, what about the bit in the middle?
abstract dust
What do you mean "bit in the middle"
there is still a lot of information we haven't used
opaque geyser
that means Q must have factors (x+3)(x-4)
ignore me. i see this though.
abstract dust
do u follow
opaque geyser
so far i think
abstract dust
Good
to not overcomplicate things we can say that Q(x) = (x+3)(x-4), (we could introduce higher odd powers to (x+3) for example but that wouldn't really match the shape as it would make it flatter)
Now we have y = P(x)/((x+3)(x-4))
observe that we have an x-intercept at x = 3
that means, at y=0, x=3 is a solution
but when y=0 notice P(x) must be 0
Therefore we can say P(x) has a factor of (x-3), and since it is the only x-intercept, we can write it as some constant times (x-3) I.e. k(x-3)
opaque geyser
ok
abstract dust
we now have y = k(x-3)/((x+3)(x-4))
one thing left to consider: y-intercept
the y intercept is at (0, 1)
abstract dust
we now have y = k(x-3)/((x+3)(x-4))
and plugging it into this gives us k = 4
therefore
y = 4(x-3)/((x+3)(x-4)) is what we are looking for
opaque geyser
incredible, thank you
abstract dust
👍
loud osprey
What single transformation could I use?
safe radishBOT
What single transformation could I use?
loud osprey
I was thinking maybe a rotation 90 degrees counterclockwise over some point but im not sure how to find that point
safe radishBOT
@loud osprey Has your question been resolved?
loud osprey
<@&286206848099549185>
raw grail
Are you sure ABC and A'B'C' are in the right spots?
loud osprey
Yeah there weren’t any labels so I asked my teacher.
I was told to do so, but will it make more sense to switch them?
raw grail
switching them won't solve the issue here
the rigid transformations of the plane are rotations, reflections, and translations
loud osprey
Yup
raw grail
since the two triangles aren't even in the same orientation then translations are clearly out of the question when you're trying to find the one transformation that will do it
loud osprey
ok
raw grail
so we're only allows rotations or reflections really
no matter which point you pick with the way these triangles are placed you won't be able to rotate from one to the other, at least not all in one go
one way you can think about rotations is that the distance from every point to the center of rotation stays the same
loud osprey
Yeah
raw grail
so you have to find a point that is equidistant to
A' and A, C' and C, B' and B
but just staring at it for a bit you'll see that's not really possible
loud osprey
That’s what I’m confused about :/
raw grail
so the only option here is reflections
there's no symmetry happening here
that you can do a reflection on either
my only conclusion is, while the triangles are clearly congruent, they're only congruent with composite transformations as shown
if you want a single transformation to represent this, there isn't one
so they're probably not drawn correctly
loud osprey
Interesting
Yeah I already found a composite transformation involving a rotation and then a translation
Alright I’ll ask my teacher about that, thanks 🙏
raw grail
no problem, it could just be that I'm not seeing it
but I really don't think there is one
safe radishBOT
safe radishBOT
Available help channel!
mortal fractal
safe radishBOT
mortal fractal
I'm only getting two eigen vectors despite having a 3x3 matrix
for part b
wait nvm
i got it
..
.close
lean otter
Did i draw this synthetic division table correctly?
safe radishBOT
@lean otter Has your question been resolved?
safe radishBOT
@lean otter Has your question been resolved?
safe radishBOT
@lean otter Has your question been resolved?
lean otter
help
help
help
hel
help
help
help
help
help
help
helpa
help
help
help
lean otter
Did i draw this synthetic division table correctly?
Do you have access to a pencil and piece of paper
lean otter
final halo
A is for A/(x+1), not A/x
lean otter
lean otter
A is for A/(x+1), not A/x
oh wait
final halo
That is correct
lean otter
i shared wrong problem
lean otter
That is correct
My work is correct?
final halo
Check yourself, add the fractions you got and see if you get 1/(x(x+1))
lean otter
no?
It doesn't work
oh wiat
it does
It did it in my head like five times
and it didn't work out
the sixth time works
😭
😭 I forgot the -1 in front of x^-1
Did i mess up?
How did i mess up
I don't understand why its imaginary
oh wait
idk
fast gazelle
...how did you get those values?
lean otter
$$12x+4=A(x^2+1)+B(x-3)$$
$$ x = 3$$
$$12(3) + 4 = A(3^2+1) +B(3-3)$$
$$40 = 10A$$
flat frigateBOT
Brandon H
lean otter
$$12x+4=A(x^2+1)+B(x-3)$$
$$x=i$$
$$12(i)+4 = A(i^2+1)+B(i-3)$$
$$12(i) +4 = A(-1+1)+B(i-3)$$
$$\frac{12i +4 }{i-3} = B$$
flat frigateBOT
Brandon H
safe radishBOT
@lean otter Has your question been resolved?
lean otter
<@&286206848099549185> Did i do B right?
why does wolfgram show 4x.
How do i make b 4X
Hello
Hello
What is b?
Could I get a diagram
or Image
of the question
Okay..
So first you simplify and cancel where it is possible
but in this scenario don't
Give me a sec.
The whole question?/
What are you trying to ask?
How do i get the correct B value
Wolfgram says B = 4x
yes... I don't get the question though
what do u need help
what do u need help in
I need help with partical fraction decomposition 
oh alr
I have no idea what i did wrong here
kind patio
y=tan^2(sec(2x^4)), does anyone know how to solve this
safe radishBOT
y=tan^2(sec(2x^4)), does anyone know how to solve this
uneven veldt
What is the exact question
quasi bison
,w tan^2(sec(2*42069^4))
flat frigateBOT
kind patio
our topic right know is chain rule, Constant multiple, constant power, product quotient, so I guess a combination of that that or sumthn
jade magnet
so you are asking for the derivative
quasi bison
derivative yes
could have and should have said that!
kind patio
my bad
jade magnet
have you tried anything
kind patio
yeah
jade magnet
can you send
jade magnet
from first glance it doesnt look right but i can tell for sure if you show the work
you split it into 3 functions no?
kind patio
jade magnet
and used the chain rule
kind patio
i tried again
jade magnet
derivative of 2x^4 is?
oh nvm i got confused since you used
x as multiplication
you put 2 * 4x^3 which is correct
is correct though i didnt check your last simplification
kind patio
so its correct?
jade magnet
yes your last line simplifying also looks correct
using x as multiplcation made it a lot harder for me to read 💀
kind patio
my bad i got used to using x haha
safe radishBOT
Available help channel!
keen mural
If I know through Bolzano's theorem that a function in a given interval has at least one root, can I prove there's only one root by verifying Δy/Δx>0?
safe radishBOT
If I know through Bolzano's theorem that a function in a given interval has at l...
keen mural
the function is x^5 + x^3 + x - 8
safe radishBOT
@keen mural Has your question been resolved?
keen mural
.close
safe radishBOT
@keen mural Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
gleaming blaze
.help
safe radishBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
gleaming blaze
.open
solid dragon
What is the easiest way to solve this integral? What rules can be applied?
light shoal
What is the easiest way to solve this integral? What rules can be applied?
try multiplying the num and denom by the sum of the square roots?
queen parcel
Rationalize denom
light shoal
that's a standard trick when you have a difference of square roots
solid dragon
The integral I got after rationalizing the integral is: integral(sqrt(x+2)+sqrt(x+1))
Is this correct?
stoic dune
I like how that works out
bleak scroll
safe radishBOT
bleak scroll
Does any German want to discuss this with me?
safe radishBOT
@bleak scroll Has your question been resolved?
safe radishBOT
@bleak scroll Has your question been resolved?
safe radishBOT
@bleak scroll Has your question been resolved?
safe radishBOT
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Available help channel!
magic river
convert 5i---> trig form
safe radishBOT
convert 5i---> trig form
magic river
r is 5 cus
root 25 is 5
then
tanx=0
cus a is 0
and i got
2pi
but is wrong
safe radishBOT
@magic river Has your question been resolved?
plush parrot
convert 5i---> trig form
tanx=0
cus a is 0
what?
magic river
?
plush parrot
idk what you mean
plush parrot
why is tanx = 0
dark cargo
direct division by 0 is always undefined
hoary nimbus
Im doing question b if the angle is greater than 90 degrees but less than 180 shouldnt i be using the formula with a negative in front? Why is the answer key using the formula with no negative sign when it says thats only used for less than 90 degrees
safe radishBOT
Im doing question b if the angle is greater than 90 degrees but less than 180 sh...
stray socket
It wanted the magnitude of the projection
Not sure why they had -2.4
Oh no
Uh
Okay this is notation stuff
The -2.4 is what I was taught was the "projection scalar"
So |proj| is that
hoary nimbus
So |proj| is that
wait but why do they use |v|costheta instead of -|v|costheta
since the angle is 110 degrees
stray socket
|v| is magnitude of v
|proj| can be negative
It's a notation thing, vertical bars can have multiple meanings
|proj| is the scalar
abs(|proj|) is the magnitude of the scalar
So it can get confusing
|v| is just the magnitude of v
hoary nimbus
|v| is just the magnitude of v
i understand that part what im confused about is where it shows me 4 formulas and what needs to happen for me to use each one, so then where it says 90 < theta < 180 wouldnt i be using that one since the angle is 110
hoary nimbus
but the answer uses the other formula without the negative in front
stray socket
I think it's telling you that the projection scalar can be negative if the angle is between those two values
hoary nimbus
oh ok
stray socket
I mean it's poorly written is what I'll say
cinder creek
A sphere of d = 6cm is dropped in a right circular Cylindrical vessel partly filled with water The diameter of cylindrical vessel is 12cm. If the sphere is completely submerged in water then the level of the water raise in the Cylindrical vessel is
safe radishBOT
A sphere of d = 6cm is dropped in a right circular Cylindrical vessel partly fil...
cinder creek
.close
safe radishBOT
cinder creek
.reopen
safe radishBOT
✅
cinder creek
!status
safe radishBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
why close immediately after opening lmao
quasi bison
ok well
- .close is for when you're done with your question
- .reopen is for when you've closed the channel but realize you have more to say
- !status is a command to get progress info out of uncooperative helpees
so now that you've invoked !status on yourself (which is kind of an odd thing to do) you have to share with us your progress thus far.
cinder creek
on the prblm right?
cinder creek
so now that you've invoked !status on yourself (which is kind of an odd thing to...
on the prblm
cinder creek
ls wld y lk t by ' vwl
what
quasi bison
"also would you like to buy a vowel"
but with all the vowels removed, like you did with the word "problem" for no reason
cinder creek
but with all the vowels removed, like you did with the word "problem" for no rea...
ic 
quasi bison
and idk what to do next
now that you know the volume of the sphere, how high would that same volume of water go if poured into the cylindrical vessel?
cinder creek
now that you know the volume of the sphere, how high would that same volume of w...
equal to the volume of the sphere
quasi bison
this does not answer my question...
cinder creek
the sphere is submereged into the cylindrical vessel which already has some water in it
quasi bison
ok let me rephrase this
you found that the volume of the sphere is 37.71 cm^3. i'll take your word for that.
if you poured 37.71 cm^3 of water into an otherwise empty cylindrical vessel of the same diameter as yours,
how high would the water level be?
cinder creek
if you poured 37.71 cm^3 of water into an otherwise empty cylindrical vessel of ...
correction the volume is 113.14 cc sorry about that
cinder creek
if you poured 37.71 cm^3 of water into an otherwise empty cylindrical vessel of ...
idk
quasi bison
do you know how to find the volume of a cylinder in general?
cinder creek
yes
quasi bison
the water poured into a cylindrical vessel itself forms a cylinder
quasi bison
if you poured 113.14 cm^3 of water into an otherwise empty cylindrical vessel of the same diameter as yours,
how high would the water level be?
the water level is the height of said cylinder
cinder creek
ok ic wat ur trying to tell
quasi bison
so now i am asking you to find the height of the cylinder knowing its radius (or rather the diameter) and volume
cinder creek
so now i am asking you to find the height of the cylinder knowing its radius (or...
so I took 113.14 as 36π and i got the ans as 1 cm
so is it correct
quasi bison
seems like it.
lost timber
I need help on this thing
safe radishBOT
I need help on this thing
lost timber
I got m = 2
so what I did was do mx=(x-2)^2+4 and substitute number into x
and find m
I got 2 from this
am I doing it correctly ? or I need to change the way I solve this
lost timber
oh
spice grove
Even x values like -sqrt{65}
lost timber
I see
spice grove
Not so easy to put those and check, is it?
lost timber
so I can't usethat method
spice grove
Yeah.
lost timber
yeah
spice grove
you have mx = (x-2)^2 + 4
lost timber
mhm
spice grove
Rewrite this as,
x^2-(4+m)x+4=0
This is now a quadratic in x.
Are you able to tell, when or when not a quadratic will have roots?
Real roots that is.
hot thistle
Real roots that is.
pfp moment
lost timber
Rewrite this as,
x^2-(4+m)x+4=0
how did it transform to this?
lost timber
yep
spice grove
Do it.
lost timber
x^2 -4x +4
lost timber
x^2 -4x + 8 -mx
spice grove
Yes.
Might as well rewrite that as, x^2-(4+m)x +8
Now, do you know when or when not a quadratic has REAL roots?
lost timber
ohhh
spice grove
That's a question, ohh doesn't help.
lost timber
square root b^2 - 4ac > 0
spice grove
=
spice grove
Yeah, that's what you have to do.
supple monolith
Hi great math fellows, sorry got a stupid algebra question.
So I was trying to solve following
safe radishBOT
Hi great math fellows, sorry got a stupid algebra question.
So I was trying to s...
supple monolith
I came up with
still charm
Lol
supple monolith
But textbook stated the correct solution should be
supple monolith
Yes, factorization, and graph transformation. my solution won't help much about transformation
still charm
None of these forms are factorized forms
You cant add constant terms
It has to be just multiplication
Try factoring out an x from the original polynomial
supple monolith
The expected solution actually added +1-1, then factor out the x^3-3x^2+3x-1
supple monolith
Try factoring out an x from the original polynomial
Yes I see, but it won't help with graph transformation.
Figured it out, got the pattern
Thank you for your time
.close
safe radishBOT
safe radishBOT
Available help channel!
brisk siren
safe radishBOT
brisk siren
Hi, is this limit correct? Many calculators say it should give 0 but I don’t think the computing takes into account the x
cosmic grove
the limit of a function isnt equivalent to a function
but the function is
sin(x) is equivalent to x for x ≈ 0
brisk siren
Sure, and here we have x/2n ≈ 0 for n going to infinity
cosmic grove
yes
brisk siren
Then could this change be applied for computing the limit?
cosmic grove
its correct but sometimes its better to use bigger order for the Taylor expansion
brisk siren
the limit of a function isnt equivalent to a function
I didn’t write the limit notation after the equivalence (but it should be there)
Sure I’ll try Taylor
cosmic grove
f(x) is equivalent to g(x)
not lim f(x)
brisk siren
But it is possible to compute limits using infinitesimal equivalents, right? How couldn’t it be in this case
cosmic grove
now its good
wise nova
safe radishBOT
wise nova
I don't know where to start
A condition when doing this question applies and that is to not use the cosine or sine rule to find a solution
upper kite
Look up the properties of a 30 60 90 triangle.
Perhaps that gives you a better starting point =]
Then you know the lefthand triangle is 45 45 90
wise nova
Apparently it needs to be solved by SOHCAHTOA
upper kite
Ok, so then use SOH CAH TOA. Do you know how to apply it?
wise nova
yh but there are too many unknown sides
upper kite
The problem does not seem to restrict you using standard properties of triangles.
Why can't you just use 30 60 90?
wise nova
our teacher said so
upper kite
You can then use soh cah toa to find the segment of the left triangle
Solve for the line between the triangles using B's angle and x
Then you have the angle a
So you can use tangent to solve for the bottom left segment
Try to get as much as you can and then feel free to ask about what parts you're struggling with.
upper kite
You can use soh cah toa to find that line as well since you have 30 degrees and the hypotenuse
But yes
safe radishBOT
safe radishBOT
Available help channel!
ruby stirrup
For any two sets of A and B, prove that A ′ ∪B=U⇒A⊂B.
safe radishBOT
For any two sets of A and B, prove that A ′ ∪B=U⇒A⊂B.
Show your work, and if possible, explain where you are stuck.
ruby stirrup
i havent really done anything
im stuck at whether to take an arbitrary variable
or with venn
granite idol
do you know how to prove subsets?
ruby stirrup
i do
lean otter
For any two sets of A and B, prove that A ′ ∪B=U⇒A⊂B.
are you telling that
A' union B = A intersection B ?
ruby stirrup
nono
lean otter
oh nvm
granite idol
no, A' is probably the complement of A
lean otter
I misunderstood
ruby stirrup
A' union B is equal to uni
ruby stirrup
then we have to prove a is a subset of B
i google this but random stuff starting popping up
started*
what do i do
ruby stirrup
ok
granite idol
certainly x must be in U as well
granite idol
but you're given an "alternate definition" for U in the antecedent, right
that is, U = A' u B
so x must be in A' u B as well
but x is in A, so it cannot be in A'. so it must be in B.
i.e., A is a subset of B
granite idol
that might be enough actually
ruby stirrup
thanks a lot man
jade gust
How do I show that either equals exp(θi)
safe radishBOT
How do I show that either equals exp(θi)
jade gust
RHS is the binom expansion of LHS (obv)
dull sequoia
can you use the limit definition of e?
jade gust
that a question to me? or a question to the question, as in are there any restrictions to how i'd be solving it
dull sequoia
that a question to me? or a question to the question, as in are there any restri...
2nd one
do you not see why it's true or do you have to prove it a certain way
jade gust
Doesn't specify but let's say we don't use the limit def of e
dull sequoia
then i dont know either haha
jade gust
otherwise that would js be straight forward
unless it goes too deep into the maths lore
dull sequoia
i mean it is straightforward
dull sequoia
chatgpt isn't particularly good and reasoning and maths
so it might confidently do an illegal step
jade gust
it says that equals 1
dull sequoia
not even surprised
dull sequoia
otherwise that would js be straight forward
what do you mean here then
do you know why it is e^itheta?
final halo
this looks like you just asked it the wrong question
jade gust
this looks like you just asked it the wrong question
idk i js wrote what does lim as n tends to infinity of (1+(theta i)/n)^n equal to
final halo
thats the exact thing you wrote? bc it looks like you asked it what the limit of 1 + ((theta i)/n)^n is
jade gust
do you know why it *is* e^itheta?
cause lim n to infity (1+blah/n)^n = exp(blah)
jade gust
thats the *exact* thing you wrote? bc it looks like you asked it what the limit ...
ye js checked i did infact do that
Okay maybe a better question would be how would i prove the RHS is exp(theta i) or possibly instead of theta i let's say a in place of theta i in the summand
final halo
You would first have to say what your definition of exp(a) is
jade gust
as in exp(a) def= lim n to infty (1+a/n)^n or lim n to 0 (1+n)^(a/n) or the sum def?
lean otter
How did you do this on chat GPT tell me!
jade gust
it understands latex
it understands most to a certain extent
it's quite iffy sometimes
i mean idk my q has no purpose was js curious
.close
ashen swan
safe radishBOT
safe radishBOT
@ashen swan Has your question been resolved?
Show your work, and if possible, explain where you are stuck.
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@ashen swan Has your question been resolved?
pulsar pecan
how do I solve this qs on the calculator
what have you tried?
reef grail
how to do part iv?
safe radishBOT
how to do part iv?
reef grail
Ik that x = rcos(theta)
y = rsin(theta)
1 + 2cos(theta) = cos^2(theta) - sin^2(theta)
r^3 = x^2 - y^2
but I still have r
and I assume that's not allowed in cartesian
safe radishBOT
@reef grail Has your question been resolved?
desert inlet
1 + 2cos(theta) = cos^2(theta) - sin^2(theta)
are you saying that 1+cos(2theta)= cos²(theta)-sin²(theta)?
because that's not the case
reef grail
are you saying that 1+cos(2theta)= cos²(theta)-sin²(theta)?
ohh mb
I still have no clue how to solve it
<@&286206848099549185>
desert inlet
you know you can just replace the r with y
we're just trying to figure out what the maximum value is of r
which sounds same if you're trying to find out the maximum value of the function f(x)=1+cos(2theta)
@reef grail
safe radishBOT
@reef grail Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
slim grove
I need to find the radius of this circle, pls help
safe radishBOT
I need to find the radius of this circle, pls help
@slim grove Has your question been resolved?
slim grove
I need to find the radius of this circle, pls help
safe radishBOT
I need to find the radius of this circle, pls help
rich tree
Anything come out at you with AOB?
slim grove
Anything come out at you with AOB?
isosceles triangle but how do i count 'r' from that
rich tree
Split it in half and you have two right angles triangles
You need another piece of information still though
slim grove
yeah and idk how to figure it out
rich tree
Okay well we are probably going to be looking for an angle within the triangle or the height of O
safe radishBOT
@slim grove Has your question been resolved?
jade gust
Just looking at your diagram you can possibly use power of a point and tangent-secant theorem
Possibly intersecting chords theorem too
safe radishBOT
@slim grove Has your question been resolved?
safe radishBOT
@slim grove Has your question been resolved?
safe radishBOT
@slim grove Has your question been resolved?
charred sable
PC^2 = PA. PB = 24 so PC = 2sqrt(6) = x
S = sqrt((x+2+3)(x+2-3)(x+3-2)(3+2-x))/4 = sqrt(23)/4
Draw AH perpendicular to CP. We get AH = S/2sqrt(6) . 2 = sqrt(138)/24
Call M the midpoint of AC. AM = 1
Using sin law you know AM/r = AH/AC
So r = 8sqrt(138)/23 or 4.09
You could easily do this using tasman suggestion but you don't even try to think a little more. How could this simple question make a secondary student waste 9 hours!
jade gust
Damn this been up for 12hs
safe radishBOT
@slim grove Has your question been resolved?
safe radishBOT
earnest wagon
Can v=(3,1) not be written (3,1,0)?
zinc token
just apply a linear transformation on u_2 (what transfomation?)
,w 90 deg rotation matrix
zinc token
just pick a 3d rotation matrix
safe radishBOT
echo wadi
youre meant to open a channel after you have a question ready
slim grove
PC^2 = PA. PB = 24 so PC = 2sqrt(6) = x
S = sqrt((x+2+3)(x+2-3)(x+3-2)(3+2-x))/4...
i usually solve harder exercises, im just not good in geometry that's all, thx for help tho
safe radishBOT
safe radishBOT
Available help channel!
crisp mica
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lean otter
do you know where to start at least
you are given two sides, its a right angled triangle, what could you do
lean otter
just use sohcahtoa
coarse anvil
First label the sides,
So 52 will be h, 38 will be a
use soh cah toa to find the trig equation which has h and a
then substitute in
crisp mica
just use sohcahtoa
so like sin(x) = 6sqrt35/52 ?????
crisp mica
true ig
lean otter
do you think that even makes sense
crisp mica
nah but I got that in the online calculator
crisp mica
cos-1 thing?
lean otter
yeah
crisp mica
I forgot so its cos -1 = what?
lean otter
x = cos^-1 (38/52)
blissful locust
How do you get rid of a numerator by chance?
safe radishBOT
How do you get rid of a numerator by chance?
blissful locust
0.89 = 343/(343+x)
Im aware of how to remove denominator, but what would you do when you need to get rid of the top?
lean otter
ok so
candid inlet
||I|| ||Dont|| ||Know||
lean otter
||I|| ||Dont|| ||Know||
...
blissful locust
Should i times both sides by the denom & move the 0.89 over?
lean otter
0.89 = 343/(343+x)
you would times brackets and all
blissful locust
lean otter
wait a sec
blissful locust
Okay
severe spoke
So then itd be 343 + x = 343/0.89?
That looks right
blissful locust
blissful locust
severe spoke
I don't get it
blissful locust
Ahh yes, i was wondering how to isolate the denom
severe spoke
Hm
severe spoke
So then itd be 343 + x = 343/0.89?
That's it to isolate the denom
lean otter
are we solving for x?
blissful locust
That's it to isolate the denom
Ohh whew!
Yes
I ended up getting 42.39
Thank you two for the help
lean otter
np
blissful locust
.close
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Available help channel!
rare cedar
When solving for x intercepts on quadratic equations you set y = zero , and solve , if its ax^2+bx+c you will have to factor, usually you'll get 2 factors for 2 x-intercepts, but what if you get a quadratic equation with a GCF so like 2(x-6) (x+4)
safe radishBOT
When solving for x intercepts on quadratic equations you set y = zero , and solv...
unreal kindle
what's the problem?
rare cedar
There is no problem (yet at least) its a concern for what to do when encountering 3 factors or 2 factors with a gcf
Im pretty sure you distribute the factor the gcf is attached to but I saw a weird video where this guy ignored it
and then 3 factors what do u even do because your solving for 2 x-intercepts for a parabola
unreal kindle
you just want to solve the equation?
unreal kindle
When solving for x intercepts on quadratic equations you set y = zero , and solv...
here you just solve x-6=0 and x+4=0
rare cedar
how do I know your right
unreal kindle
what part of this don't you understand?
rare cedar
ok but what if
it was 2x(x-6) (x+4)
then you have 3 factors what do you do then, cause there can only be 2 x-intercepts
unreal kindle
then you have 3 factors what do you do then, cause there can only be 2 x-interce...
if you have 3 factors, it's not a quadratic equation anymore
there is no way you can factor a quadratic equation into something like that, only 2 x intercepts
rare cedar
so if its a cubic quadratic equationm and you end up with 3 factors like 2x(x-6) (x+4) or (x+1) (2x^2-3) (2x^2+3)
you'll never be asked to plot/solve x-intercepts for a parabola
?
no?
it stemmed from a perfect square
(4x^2-9)
thats why
its like that
what do you call it then
unreal kindle
yeah but you wrote (2x^2) in your first message
rare cedar
I didnt provide the other math mb
unreal kindle
I didnt provide the other math mb
ok but anyway, cubic or quadratic, you should have no problem finding the equations
unreal kindle
would f(x) = x^2 be wider or narrower than g(x)= 1/3x^2
x² is narrower
the graph would be narrower
hidden quartz
can someone explain how he got from these 3 equations to this 4th degree polynomial?
safe radishBOT
can someone explain how he got from these 3 equations to this 4th degree polynom...
whole forge
i mean i havent tried, its too messy
but perharps you take the last equation - the first equation to get 0
Then you square this equation
you should something with a^4 inside, and we know we can express a^4 can be expressed as b^4+ something
could be wrong tho, i havent tried. and you might get a b^3 term but it should cancel out to 0, if it doesnt then im defintiely wrong
@hidden quartz makes sense?
willow rain
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polar knot
i dont understand what this means?
safe radishBOT
i dont understand what this means?
polar knot
what A means
lean otter
it wants you to find the number of students who play hockey AND tennis, and NOT football
what zone on the venn diagram corresponds to that
polar knot
i know but
what does the in terms of x mean
i mean obviously is
F prime n (H n T)
lean otter
you wont get an explicit answer
polar knot
but when i wrote it my teacher said im wrong
lean otter
just use x as a variable
lean otter
no that is not what your answer should look like
your answer should be a number with x as well
polar knot
how is x both
lean otter
when calculating how many people there are
polar knot
the term to express
all three sports
and at the same time
the people who only lpay
tennis and hockey
lean otter
because you want to subtract
lean otter
no
i'll give you an example
this isnt the correct answer
you should write something like
polar knot
ok
lean otter
30 - x
polar knot
ok
hazy elbow
i dont understand what this means?
Write respective values inside the bubbles
hazy elbow
Yess
lean otter
yeah
polar knot
i thought it was gonna be harder
ok then i have another question
nevermind
thanks guys
lean otter
its only one point so it couldnt be that hard. you can generally assume the difficulty of a question given how many points you get. just a tip for future reference
modest holly
help?
modest holly
is the f(x) given in the photo the original equation which we have to sollve?
yea that is thr f(x) given
proud pewter
yea that is thr f(x) given
you have two methods to solve this
1- graphical , 2- diffrentiation
which one have you tried?
modest holly
you have two methods to solve this
1- graphical , 2- diffrentiation
which o...
i dont know what diffrentiation is
proud pewter
i dont know what diffrentiation is
ok then
modest holly
can u explain?
proud pewter
here we can see that D>0 for the eqn
modest holly
here we can see that D>0 for the eqn
why D?
proud pewter
therefore it must have 2 roots
modest holly
therefore it must have 2 roots
so factoring?
modest holly
did you find them?
should i factor?
polar knot
yes
proud pewter
should i factor?
yes
polar knot
what
modest holly
-2 is not >1
ohh yea
polar knot
though
proud pewter
also you should know for a fact that if a<0 then the eqn is downward parabola
proud pewter
take -2 common if youre having trouble
modest holly
now factor
even more?
polar knot
okay ill exaplin
proud pewter
which std are you in?
modest holly
so you factored first by dividing -2
polar knot
modest holly
which std are you in?
std?
polar knot
heres the equation right?
proud pewter
go ahead
polar knot
so a = -2
polar knot
and because a is a negative, we know the parabola opens down
no wait
and because the c = 32
modest holly
and because a is a negative, we know the parabola opens down
what if the constant was 35?
then what
modest holly
35x^2 + 12x + 36
no -2x^2+12x+35
modest holly
u can do that?
polar knot
yes...
modest holly
i thought we had to find common
polar knot
why not?
modest holly
numbers
modest holly
is there any easier way?
modest holly
because i heard if a>1 then we need to divide by a
polar knot
but thats harder
modest holly
but thats harder
but that wont help me in this case
polar knot
if a != 0
modest holly
because i dont need roots
polar knot
why dont you need roots
modest holly
wait i still dont get the answer
its asking where it will inc
where does it inc?
hello?
modest holly
ur good
polar knot
let me explan
modest holly
k
polar knot
okay its kinda hard to explain give me some time to think
how to explain the best way
modest holly
k
polar knot
okay r u here?
modest holly
ye
polar knot
heres what it looks like
modest holly
yea
polar knot
now your question asks
what form can you see to answer teh question most efficiently
and the question is to find
all the intervals where f of x is increasing
increasing
modest holly
yes
polar knot
does this ever increase?
polar knot
yup
modest holly
so we are basically finding the vertex?
modest holly
what box
modest holly
ohh it has standard form, vertex form, and factored form
modest holly
wdym?
modest holly
not the form
polar knot
this is null right
modest holly
idk
polar knot
im still confused as to why it asks for the form, if your answer doenst include it
polar knot
so it cant be null
what
modest holly
no
polar knot
what does the question want
modest holly
it asks for form so we can find where the interval increases
modest holly
the vertex is the inc
modest holly
because its the maximum point
polar knot
but the parabola opens DOWN
polar knot
are you sure its because you didnt choose the form correctly
im pretty sure its a 2 part qustion
modest holly
no
just 1 part
the form is just to help
you
find the interval
of where it increases
polar knot
choose vertex form and put null
polar knot
no
modest holly
ok
polar knot
choose vertex and put null
modest holly
vertex form
polar knot
yes
