the second integral is not correct
#help-42
vivid idol
vivid idol
mhm
strange lichen
wow its made super clear there lol
vivid idol
its a different problem tho
vivid idol
kkkk
strange lichen
tag me when u done
strange lichen
ya
strange lichen
be careful with ur use of arrows and equals signs, it gets confusing in some places
strange lichen
no
strange lichen
close tho
so ur second to last integral is correct, its just -6
now leave that -6 off to the side
dont touch it for now
strange lichen
this, keep this to the side for now
its correct
this part is correct
but we dont evaluate it with the -2x
vivid idol
what do we evaluate it with
strange lichen
its an integral that has alrdy been completed
once u evaluate the -2x, the answer to that will add to -6 for the final answer
strange lichen
show ur work
vivid idol
strange lichen
ye u good
strange lichen
i think and hope so
strange lichen
np
calm coralBOT
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olive canyon
Can I have help converting something to the standard form of an ellipse
wanton wave
Go ahead and post your specific problem
And any work or any ideas you've tried so far
olive canyon
Z^2=(8-4z)^2+y^2
humble oyster
$$Z^2=(8-4z)^2+y^2$$
potent lotusBOT
Bestower
olive canyon
Ik im supposed to complete the square and stuff but I keep getting stuck
It’s supposed to convert into the standard form of an ellipse
wanton wave
Okay, do you know what the standard form of an ellipse looks like?
humble oyster
$$\frac{X^2}{a^2} +\frac {y^2}{b^2 }= 1$$
wanton wave
Yeah, only that x^2 and y^2 might be (x-h)^2 and (y-k)^2
potent lotusBOT
Bestower
wanton wave
You said you got stuck, can you show what you did so far?
olive canyon
Basically speaking I expanded 8-4z squared
And then I fooled around a bit with it and got some really awful numbers
wanton wave
Yeah it's not gonna be pretty
But that's the right move
We want the constant term on one side, and everything else on the other side
So after expanding the binomial and moving somethings around, you should end up with something like
$15z^2-64z+y^2 = -64$
olive canyon
Ooo Ty
potent lotusBOT
tatpoj
olive canyon
Would I divide by -64 at this point or after complete the square
wanton wave
I'd do that last
olive canyon
K
wanton wave
Factor 15 out of the z terms
And complete the square inside the parentheses
y^2 is already a perfect square so just leave that alone
wanton wave
,rccw
potent lotusBOT
wanton wave
You're almost done
Simplify the LHS
And finish completing the square in the parentheses
I mean, literally write it as (z - something)^2
olive canyon
Don’t I need to get rid of the 15?
wanton wave
Not really
We're going to divide by the LHS to get 1 there
And then whatever coefficients remain on the RHS, we can re-express by putting their inverse in the denominator
Do you see what I mean? @olive canyon
wanton wave
,rccw
potent lotusBOT
wanton wave
Exactly the right idea, but the 64 under the (z-32/15) part isn't quite right (it shouldn't just be a 64)
Check again, that 15 doesn't really cancel out
The 15s actually multiply together so you end up with 64/225 in the denominator there
calm coralBOT
@olive canyon Has your question been resolved?
sweet hill
Hi
sweet hill
This is a simple econ question, but i messed up somewhere on my maths
sweet hill
I am following this to calculate for Opportunity Cost
But when i try to calculate for this problem, im getting backwards result
This is my calculation
But for example im getting for every 1 wheat = 20 cameras
when it should be other way around
I dont know if im calculating wrong or this formula just doesn't work in this case
rotund olive
So whenever China produces on camera it takes 100hrs
And with 100hr you can produce 20 wheat
So 1 camera= 20wheat
calm coralBOT
sweet hill
So whenever China produces on camera it takes 100hrs
actually wait hold up
rotund olive
np
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calm coralBOT
in my calculation
sweet hill
I am following this to calculate for Opportunity Cost
so is this way of calculating invalid for this problem then?
Now that im looking at it, could be that it's invalid since the unit is quantity whereas the problem uses hours
dark osprey
calm coralBOT
remote mural
the horizontal line across which the graph (parabola) is symmetrical 😂 ?
that emoji because I realised that I just rephrased the same thing lol
remote mural
i need help with 13 questions
you might wanna learn about function transformations to be able to answer that question
if y -> y + a (read as y transformed to y + a, which means that all that occurances of y in the equation is replaced by y + a)
where a < 0,
the graph shifts upwards,
and vice verse
calm coralBOT
@dark osprey Has your question been resolved?
south plover
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tall spruce
why is this function undefined in desmos despite having a fixed value? is it because it crosses the maximum limit of desmos?
oblique current
,w e^(709.783)-709.783
potent lotusBOT
zealous hawk
Too big
oblique current
Desmos just can't handle that big of a number yeah
tall spruce
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runic tiger
what does 3x/x^2 evaluate to?
calm coralBOT
what does 3x/x^2 evaluate to?
runic tiger
does 3x^-1 work?
sterile seal
Yes
runic tiger
so to expand the numerator
x^3-2x^2+3x-1
then seperate them with x^2 each
x-3+3x+3x^-1+x^-2
then integrate
(1/2x^2)-(3x)+(3/2x^2)-(3/2x^-2)-(1/3x^-3)
multiply all that by 3
then evaluate for f(2)-f(1)
is that right?
calm coralBOT
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@runic tiger Has your question been resolved?
violet willow
am I dumb lioke
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violet willow
help
leaden thunder
what's your question
wanton wave
@violet willow Are you confused because you got the same result as your friend?
violet willow
Yes
wanton wave
You didn't find the entire surface area, you're missing a surface
wanton wave
Right, you just forgot the flat circle
wanton wave
But be careful on this one. Here you're looking for volume, not surface area
wanton wave
No, this is good
The volume is just the 3-dimensional space that it occupies
Like if you cut an orange in half
The volume is just, half an orange
But you've created new surfaces
that you need to count for surface area
wanton wave
if that makes sense lol
violet willow
yea
wanton wave
👍
wanton wave
Hm
Looks like that 11 is referring to the edge of the pyramid
So you might have to do some pythag to find the height of the triangles
violet willow
ah ok
calm coralBOT
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jolly basalt
halp
civic dirge
You can!
jolly basalt
i tried but it got me a diff answer
civic dirge
Note if you multiply everything by 12, you have to divide everything by 12 to cancel that out
jolly basalt
oh wait
if i had an equal sign and multiply that side by 12 too would i still have to divide everything by 12?
civic dirge
No not in that case. You're allowed to multiply both sides by 12.
civic dirge
Lol glad it clicked. Feel free to ask if you have anything else
eternal mason
x+3/2=4/3
eternal mason
why 6
icy fable
no
icy fable
yk how to multiply fractions
icy fable
yeah
eternal mason
@icy fable
icy fable
yeah im multiplying by 6
eternal mason
o alr
oh nvm i see my mistake
alr 3x+9=8
sub 9 both sides
-1
-1/3
ohhh
alr i see
.close
twin ocean
calm coralBOT
twin ocean
How in the world
calm coralBOT
@twin ocean Has your question been resolved?
leaden thunder
,rotate
potent lotusBOT
calm coralBOT
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fathom pecan
Having an issue with statistic frequencies.
calm coralBOT
Having an issue with statistic frequencies.
fathom pecan
This is what I get.
This is the data.
And these are the class limits.
I know it's probably me just overlooking something, but I keep getting the same exact frequency distribution.
If I'm missing something or not explaining it correctly, I can mention more.
calm coralBOT
@fathom pecan Has your question been resolved?
calm coralBOT
@fathom pecan Has your question been resolved?
calm coralBOT
@fathom pecan Has your question been resolved?
wild marten
hi
swift marsh
Well u can sketch the circles
A = pi *r^2
and $dA = pi * (r+ \bigtriangledown r)^2$
potent lotusBOT
Mortta
wild marten
I already finished that part
think I did it right
im lost on number 2 now
.close
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regal plinth
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regal plinth
Can anyone just explain what the NOTE say in simpler terms im having a hard time understanding it
severe tundra
for sure
so
the function doesn't have to be defined at a point in order for it's limit to exist
that's actually like the whole point of why we use limits, to evaluate something where it would otherwise be undefined
regal plinth
Maybe I’m just not getting it but why does it say at x = 0 is undefined but then say the limit is 2
severe tundra
both of those are true
regal plinth
Oh god this is confusing
severe tundra
the function is undefined at x = 0 because the function will have a zero in the denominator
when x = 0
sqrt(0 + 1) - 1
regal plinth
Oh yeha right
severe tundra
but
limits allow us to see what the function approaches at that point
which in this case is 2
the table they have there is kinda a good visual
we're taking the function and evaluating it at values closer and closer to the point, but not on it
regal plinth
So what does the 0 represent?
Sorry
But i understand the 2
Is there a difference between what the limit equals and if the limit is defined or not
severe tundra
this reads in english as "The limit of (the function) as x approaches 0"
the limit is defined because on either side of x=0, the function does have a value
look to the table, they start with small numbers on both the positive and negative sides of 0
because they are BOTH getting closer to 2, you can conclude the limit does exist and is 2
you CAN split up a limit into two "one sided limits"
when both of those exist, and approach the same value, the main limit itself exists
regal plinth
So even if the limit is still undefined I can still know what limit it is?
severe tundra
well no
if its undefined its nothing
but, if a function is undefined you can know its limit
at a point
the function is undefined here at x=0
but its limit exists because the function is defined on either side
calm coralBOT
@regal plinth Has your question been resolved?
regal plinth
How do I find the limit
calm coralBOT
How do I find the limit
regal plinth
inner zealot
How do I find the limit
The limit of f(x) as x->a is not the same thing as f(a). Where does the graph appear to go to, ignoring the hole in the line?
regal plinth
2?
inner zealot
Yes.
inner zealot
In this context, no. If the question were to ask if the function were continuous at x=2, how would you answer that question and how would you prove that?
regal plinth
set the equations equal to each other..?
inner zealot
No. You would need to use limits to prove that it is continuous at x=2.
inner zealot
Yes.
regal plinth
Why wouldn’t it be 1?
regal plinth
Ohhh right
inner zealot
It concerned about the value of f(a ± n) where n is an infinitesimally small number.
inner zealot
yw
regal plinth
One more thing ik this is dne bc Ik the left side isn’t approaching 5
Is that an appropriate answer
inner zealot
No.
fallen dragon
inner zealot
There are three questions you need to ask about a point on a function to determine if it is continuous.
For #16, the second condition is not met. The limit as x->a^- does not equal the limit as x->a^+.
Because of that, the limit as x->a is DNE.
inner zealot
Correct.
regal plinth
Sorry a few more questions
Would I just it’s dne bc it’s an asymptotoe ?
At 3
3
inner zealot
No, if the curves were both going up, the limit from either side would both go to +infinity and therefore the limit would be +infinity.
It is DNE because the limit from the left does not equal the limit from the right.
inner zealot
What do you think the answer is? Apply what I've explained earlier.
inner zealot
Fair statement. The lines should have arrows indicating that they continue upwards and downwards.
regal plinth
bc the limit from the left doesn’t equal the limit coming from the right?
Bc of this
regal plinth
Positive infinity
inner zealot
And from the right?
regal plinth
Negative Infinity
inner zealot
Correct.
regal plinth
wb this one
What does this even mean
I would say DNE
but both sides of the limit equal each other
dull wagon
if both one sided limits are equal why would you say dne
dull wagon
whatever one sided limits you found to be equal
inner zealot
,calc sec(0.00001)
potent lotusBOT
Result:
1.00000000005
,calc sec(-0.00001)
potent lotusBOT
Result:
1.00000000005
What are both values approaching?
regal plinth
0
inner zealot
What does the result say?
regal plinth
1
inner zealot
You have these two limits.
Which is what the limit as x->0 is actually saying.
From the left side, sec(-0.00001) ≈ 1, and from the right side, sec(+0.00001) ≈ 1.
As that difference gets smaller and smaller, it becomes so close to the value of 1 that it is essentially 1.
inner zealot
Well, you should either know what sec(x) equals at x=0 or just evaluate sec(x) for some small number from x=0 as I did earlier.
,calc sec(0.0000001)
potent lotusBOT
Result:
1
yw
regal plinth
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drifting inlet
calm coralBOT
drifting inlet
I have no clue how to do this T-T
right now we're learning about limits am I supposed to make a limit out of this?
teal coral
I assume the limit of the average velocity as the interval squeezes to 9
i.e. the instantaneous velocity?
teal coral
well yeah, but that's why the first part
coral osprey
It would be dumb if it wanted the average velocity at a singular point 💀 but its possible given that they're forced to use a limit of some kind
teal coral
obviously it's related to the instantaneous velocity, but it's asking for the difference quotient at some finite difference I think
because that ties in neatly with part (b)
coral osprey
obviously it's related to the instantaneous velocity, but it's asking for the di...
This
teal coral
do you know what "velocity" means?
drifting inlet
yeah
teal coral
so could you write an expression for the average velocity of the thing from time t = 9 to time t = 10?
scenic eagle
Can someone help me find the height and length of this
calm coralBOT
Can someone help me find the height and length of this
scenic eagle
?
scenic eagle
Sorry
everyone just says like 1 thing then ignores me
ill close it and wait
.close
calm coralBOT
calm coralBOT
✅
coral osprey
Just leave this open.
coral osprey
The bottom is 1 foot?
scenic eagle
yes
coral osprey
The sides next to it are both 6 inches long?
Okay for consistently please use 12 inches
scenic eagle
Ok
coral osprey
Are you given any other information
potent igloo
someone else drew it for me
?? Is this like an actual assignment you need to go?
scenic eagle
Kind of
its for a project
A model of a animal enclosure
and if its too big we automatically fail
potent igloo
What's going on here?
potent igloo
I suggest scrapping this and start over on graph paper
scenic eagle
ok
potent igloo
You're not going to get anything reliable out of this drawing, sorry.
calm coralBOT
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random stratus
f(x) = x*exp(x^2)
i don't get why lim f(x) when x tend -infinite = -infinite
for me exp(x^2) tend more quickly to 0 than x tend to -infinite
shy iron
Can someone explain to my why when Z= 2i-3 z* isn’t 2i+3
calm coralBOT
Can someone explain to my why when Z= 2i-3 z* isn’t 2i+3
wanton wave
complex conjugate negates the imaginary part, not the real part
Complex numbers are typically written in the form a+bi, not bi+a
So in your example z = -3+2i
and z* = -3-2i
wanton wave
I mean, probably yeah
It's just a convention that the real part comes first
The more important thing is that z* means you negate the imaginary part
wanton wave
Can someone explain to my why when Z= 2i-3 z* isn’t 2i+3
what you did here was negate the real part
shy iron
Ok
shy iron
It's just a convention that the real part comes first
So let’s say there was a surds question. Would I make the denominator a+bi before then time top and bottom by a-bi
wanton wave
yeah
trail heart
Trying to understand this proof:
calm coralBOT
Trying to understand this proof:
trail heart
Specifically, how do we know that P must have defeated all the players that W defeated?
remote mural
W does not list P
so P is neither one of the ones W defeated, or one of the ones defeated by those defeated by W
trail heart
Ah, okay I completely misunderstood. I'll take another shot at it, thank you very much.
.close
orchid karma
We have A = {-2, -1 , 0 , 1 ,2}. Find the number k of relations in A that are symmetric and transitive. Find the number m of equivalence relations in A.
calm coralBOT
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orchid karma
<@&286206848099549185> '
I have found the number of equivalence relations with bell number which is 52
orchid karma
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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
Did you try (A^2 - B^2) = (A+B)(A-B)
right
A+B will give you the full binomial expansion, the other is similar, but put the minus sign on y
cosmic totem
calm coralBOT
hollow totem
left side is a factor of w^m-1
cosmic totem
left side is a factor of w^m-1
the summation?
hollow totem
yes
cosmic totem
how are u sure
oblique current
you can use geometric series formula
hollow totem
zero product property and we know w-1 =/= 0
cosmic totem
left side is a factor of w^m-1
and then why its equal to 0?
hollow totem
because w^m = 1
cosmic totem
ok
cosmic totem
calm coralBOT
rose haven
Time to solve the Riemann hypothesis
robust oar
seems like willan's formula?
idk how they expect you to come up with something like that though
also not a very elegant solution to add to that :P
cosmic totem
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@cosmic totem Has your question been resolved?
calm coralBOT
@cosmic totem Has your question been resolved?
viscid silo
maybe they want a recursive def?
gaunt drum
Willan's formula
It works by essentially encoding an algorithm for computing the n'th prime using only basic arithmetic and trigonometric functions
gentle grove
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lyric pollen
Can someone explain P(Xi=1)=1-P(Xi=0)=p
so many equal signs im confused, it seems like a typo?
lyric pollen
kind prawn
A bernoulli R.V. has two outcomes, if one has probability p the other has probability 1-p. i.e., P(Xi = 0) has probability 1 - p
lyric pollen
A bernoulli R.V. has two outcomes, if one has probability p the other has probab...
Exactly so if P(Xi=1)=p, then P(Xi=0)=1-p, but is this really a correct way of typing it "P(Xi=1)=1-P(Xi=0)=p"
something is missing right?
velvet osprey
no, nothing is missing
kind prawn
no
velvet osprey
this says that three quantities:
P(X_i = 1)
1 - P(X_i = 0)
p
are all equal to each other
lyric pollen
so the outcomes have equal probabilities?
ripe spade
the outcome that Xi = 1 has probability p
the outcome that Xi = 1 also has the same probability as the outcome of Xi not being 0
lyric pollen
oh okay
calm coralBOT
@lyric pollen Has your question been resolved?
remote mural
Is the product of a differentiable (continuous) function with a test function also happens to be a test function perchance?
remote mural
i assume if it has compact support, then so does the product
glass heart
if the test function has compact support then clearly any product of it with anything else has
but I doubt the product is in C^infty in general.
but I don't wanna come up with a counterexample rn
remote mural
well instead of generalising
I am basically dealing with $\phi (x) \sin(nx)$ where $\phi (x)$ is a test function
potent lotusBOT
Lixera
smoky fulcrum
Is it possible to find angle x
calm coralBOT
@smoky fulcrum Has your question been resolved?
dry pecan
Is it possible to find angle x
shouldnt it be 60 degrees ...
faint nimbus
calm coralBOT
@smoky fulcrum Has your question been resolved?
uneven saffron
calm coralBOT
uneven saffron
No clue where to start
velvet osprey
how about working out the surface areas themselves
you are given all relevant formulas and all the data required for them
uneven saffron
i believe we can remove pi
velvet osprey
also how come you said you had "no clue where to start" yet you clearly had worked this much out already
velvet osprey
uneven saffron
i saw my friends homework its so much easier compared to mine
but do we simplify pi
so (4x^2) : 9 *x^2 + x^2)
velvet osprey
yes exactly
uneven saffron
so 10x squared to 4x squared
wait
so 10 to four??
got it right
im too cold with it
Am I an idiot
junior fern
so divide
uneven saffron
cool story but yeah i was right
but help with this one cause
i must be a bozo
so
(4 x pi x (x)^2) = (2 x pi x (x+3)^2)
4 * pi * x^2 = 2 * pi * (x^2+6x+9)
get pi outta here
so 4x^2 = 2(x^2+6x+9)
expand brackets
so 4x^2 = 2x^2 +12x + 18
make equal to zero
so -2x^2 - 12x - 18 = 0
bro what the FUCK man
whats the point man
@velvet ospreyassistance pls
i forgot the area of base
velvet osprey
the base of a hemisphere is a circle
uneven saffron
fml man
im such a failure
lowkey been feeling like if i died no one would miss me recently man
(4 * pi * (x)^2) = (2 x pi x (x+3)^2) + (pi * (x+3)^2)
velvet osprey
oh my god please do not use the letter x for multiplication
uneven saffron
im sorry
better
is what i put above right?
No sorry mayne
(4 * pi * (x)^2) = (2 x pi x (x+3)^2) + (pi * (x+3)^2) would simplify to
4 * pi * x ^ 2 = 2 * pi (x^2+6x+9) + pi * (x^2+6x+9)
simplify
4 * x^2 = 2x^2 +12x + 18 + x^2+6x+9
so
4x^2 = 3x^2 +18x + 27
so -x^2 + 18x + 27 = 0
so x is 19.4
Im tired of existing in this plane man
I wake up
eat
workout
study
sleep
no one checking on me
no one seeing if im good
no hoes
just a void of thoughts
is something wrong with me man? why was I made this way
so many questions, so few answers
someone help me
so
Its a long question
first
4/3 * pi * r = 7 x 10^23
x by 3
divide by 4
divide by pi
square root
use the found radios in the formula 2 * pi x r
bobs your uncle?
is this process correct
@velvet osprey
sorry for excessive pinging btw
just need to get this homework done
.close
calm coralBOT
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quasi hare
help pls idk what to do
calm coralBOT
help pls idk what to do
royal salmon
how old are you
quasi hare
13
severe tundra
help pls idk what to do
A trick for fractions, when you divide by a fraction, you can instead multiply by the reciprocal of it
Reciprocal meaning quite literally flip it upside down
ie reciprocal of x/y = y/x
quasi hare
???
severe tundra
switch it to 7/10 * 2/1
amber basin
that's correct
quasi hare
switch it to 7/10 * 2/1
then what
amber basin
multiply
quasi hare
so it’s 14/10
amber basin
yeah, and that can be simplified
amber basin
yep
any time you are multiplying/dividing mixed numbers, you should change to improper
quasi hare
umm it’s 144/15?
potent lotusBOT
Result:
1.9444444444444
it can’t be simplified it can be a mixed fraction tho?
amber basin
ignore all that
quasi hare
amber basin
yeah 168/15 is correct
amber basin
it can’t be simplified it can be a mixed fraction tho?
and yes
quasi hare
so 11 3/15
smoky prairie
probably they are both divisible by 3 so 56/5 = 11 1/5
quasi hare
how do i find if they’re divisible ?
amber basin
dividing by 3
amber basin
well 168 is not a common one to "know"
but 15 is, presumably
so you can just quickly divide 168/3 and see if it is
quasi hare
ok i have a word question problem
fourteen friends share 8 3/4 bags of trail mix equally. what fraction of a bag does each friend receive
8 3/4 divided by 1/14?
quasi hare
so you can just quickly divide 168/3 and see if it is
yea idk what you mean but ok
amber basin
8 3/4 divided by 1/14?
well you're dividing it among 14 friends, so 8 3/4 divided by 14
amber basin
yea idk what you mean but ok
well what exactly is your question? I'm just explaining how to know if 168 is divisible by 3 (hint: dividing it 
)
quasi hare
i’m usin a multiplication chart and that number isn’t there is there a way on a calculator that you could find if they’re divisible ?
or what idk.
amber basin
yeah you could divide 168/3 and if it's a whole number, it's divisible
quasi hare
well you're dividing it among 14 friends, so 8 3/4 divided by 14
yea 1/14 is the same as 14?
????
quasi hare
how do i do 8 3/4 divided by 14
amber basin
multiply by the reciprocal
amber basin
nah this is just like before, where you want to flip the second number
so reciprocal of 14 is 1/14
so 35/4 x 1/14
quasi hare
35/56 and it’s 5/8?
amber basin
yup
quasi hare
each of them get 5/8 of trail mix oh ok
i have another word question problem
you put tires on a car assembly line. you earn $5 for each set of tires that you install it takes 4 1/4 of an hour to install each set of tires. if you work 8 1/2 hours, how much will you earn
it’s multiplication ?
idk what to do
8 1/2 x 5?
amber basin
well let's look at our info
it takes 4 1/4 hours for every set of tires
and we're working for 8 1/2 hours
so how can we find how many sets of tires we can install?
in that time
calm coralBOT
@quasi hare Has your question been resolved?
golden tulip
calm coralBOT
golden hearth
have yoy tried simplifying it>
the coefficient of iota on the left hand side would be the same as that on the right (y)
golden tulip
ya i get a polynomial of third degree
golden hearth
can you send the whole question?
golden tulip
sorry its on a paper irl and i cant take a pic of it im on pc
soo just wrote down the equation
golden hearth
oh thats the whole thing?
calm coralBOT
@golden tulip Has your question been resolved?
remote mural
Prove that for all x, y ∈ R, if x is irrational then either x + y is irrational or x − y is irrational, could i just do like x = a/b and y = c/d and then just do x + y + x - y and sub in
carmine sorrel
so you're assuming both terms are rational?
remote mural
yes
carmine sorrel
you could assume x+y is rational, and then show that x-y must be irrational
remote mural
is that proof by contradiction
carmine sorrel
no
remote mural
uh whats that proof method called
carmine sorrel
direct proof?
carmine sorrel
what would it mean if x+y is rational?
carmine sorrel
ok, so what does y = then?
remote mural
so have a rational number and subtract it by something that will make it irrational
carmine sorrel
no, not something
you have a specific equation here.
if x+y is rational, x+y = a/b
so what is y?
remote mural
a/b times x
carmine sorrel
times?
carmine sorrel
and howd you get that? from x + y?
remote mural
isolating for y
carmine sorrel
so you multiplied by x to get it out of x + y?
carmine sorrel
yes
great, now you know what y is, plug it into the other thing and see what you get
remote mural
so plug in y = a/b - x into x + y?
carmine sorrel
x - (a/b -x)?
carmine sorrel
yes
there's no equality here. So you can't get that x = anything
2x - a/b, is that rational or irrational?
given that x is irrational
remote mural
it still is rational yes
carmine sorrel
irrational + rational = ?
remote mural
irrational and 2x-a/b is irrational
carmine sorrel
yes
barren quiver
calm coralBOT
warm warren
I can’t really tell what your thought process is for i
barren quiver
Omg sorry, i meant ii
barren quiver
I can’t really tell what your thought process is for i
Sorry
noble cedar
calm coralBOT
noble cedar
Why is the domain for this question only [0,8] ?
cosmic totem
what function
dull wagon
can't cut out more than you have
noble cedar
can't cut out more than you have
So the domain must satisfy length and width and height separately
I can’t have a negative output on any of them
This is a somewhat trickier question because normally I use a number line to see what works based on the factors
And the zero product property
median roost
. 0 ≤ 16-2x ≤ 16
and
0 ≤ 30-2x ≤ 30
noble cedar
But here I can’t have negative outputs
noble cedar
. 0 ≤ 16-2x ≤ 16
and
0 ≤ 30-2x ≤ 30
Wait how did you get less than or equal to 30 for the second line?
median roost
0 ≤ 30-2x ≤ 30 <= this for the length
0 ≤ 16-2x ≤ 16 <= this for the width
noble cedar
Oh OK
median roost
30-2x can't pass 30
hallow stirrup
for a function, is it necessary for each value in its domain to have an image?
viscid silo
yes
hallow stirrup
in case of surjective functions, every value of domain has an image in the co domain, and every value in the co domain is the image of a value in the domain. right?