the line
#help-27
minor silo
flint spire
when slope is positive at a point, say A
minor silo
the line is going straight at the top of B and C?
flint spire
it means the distance will increase
pale bear
It’s over 0 if it’s going up 💯
minor silo
could u possibly dumb it down even more? my freshman year i went bus. ad. teehee
pale bear
could u possibly dumb it down even more? my freshman year i went bus. ad. teehee
Think abt walking up that part of the line or like biking
pale bear
If it’s hard to bike up it’s over 0 if you just cruise down it’s negative
pale bear
Yes
flint spire
minor silo
again, i just wanted to apologize of my ignorance
its crazy how i forget all of this stuff after 1 year of taking accounting
minor silo
is it because F is already at the top starting to go down?
flint spire
youre at the top of the hill
minor silo
negative would be C D F
flint spire
is it because F is already at the top starting to go down?
yes
minor silo
and when its at zero it is
flint spire
negative would be C D F
CD only
minor silo
F
minor silo
ah i see
flint spire
neither going upward nor downward
flint spire
minor silo
what is it really asking from smallest to largest. as in how steep the hill is?
and how much u can cruise down
formal quarry
and how much u can cruise down
I believe in this scenario it is asking for you to rank it from easiest to go down, to hardest to go up
minor silo
easiest to go down would be C D E A B F
C D E A B F? bc F is at 0?
smallest is F?
im just thinking out loud atp
formal quarry
C D E A B F? bc F is at 0?
not quite. F would be in the center of the list. Since F is not easy to go down, or hard to go up. it is simply moving normally.
minor silo
C D is definitely easy becacuse you are going down. E is going up something small. A and B is a hugeee hill
formal quarry
as for B, you are still going up. so it should be higher in the list
minor silo
okay yeah that makes sense
formal quarry
dont mind what i said, i just misread something
formal quarry
C D is definitely easy becacuse you are going down. E is going up something smal...
this seems correct
minor silo
Okay so basically. smallest. easiest to go down. would be C and D
formal quarry
but where is F in that?
minor silo
you said in the middle?
formal quarry
Okay so basically. smallest. easiest to go down. would be C and D
yes
minor silo
C, D, F, E, A, B?
formal quarry
C, D, F, E, A, B?
that seems correct to me
minor silo
cd down. F standstill. e slight hill. a, going up. b, struggling to go up
@flint spire we are so back
if i wasnt supposed to @ im sorry i j thought it was funny
and an appropriate time to say something as we transition back to what we were talking about
formal quarry
if i wasnt supposed to @ im sorry i j thought it was funny
i think youre ok
flint spire
CDFEBA
flint spire
slope is decreasing, from a positive value to reach 0 at the top of the hill
minor silo
So we're determing Glenn's maximum velocity during a 10 minute intervavl. We are given Glenn .4 miles from camp at t = 0 and .55 miles from camp t = 5
idk y but its marking them as wron
g
minor silo
but F would still be wrong?
flint spire
well, with the naked eye, it looks like its on the top of the hill, so slope = 0
formal quarry
call me crazy, but i think theres actually none that are zero now that i look at the graph again
flint spire
positive
minor silo
oh right
flint spire
going up, not down
minor silo
a b e f
and
c d
formal quarry
that seems right
minor silo
sorry im back
i got it all
right
sorry its so small
in order to find the rate of change. i need to use the formula at x = 3
find coordinates of [3, 3.01]
this is the last question
uhh i gave up. thank u so much for helping me
.close
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flint spire
but its not BB
flint spire
uhh i gave up. thank u so much for helping me
😮
flint spire
nvm me, nvm me, i misread
i thought B were Graph 2
like ordered..
A, graph1 B, graph2, C graph3.. mb
formal quarry
not gonna lie, i have no recollection of secant lines 
glad it worked out though
minor silo
🤵♂️
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red quartz
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red quartz
im stuck on this last step
do i add the constants
then sqrt it and take it out the integral?
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restive river
hey
restive river
i wanted to ask a question
wicked turtle
!da2a
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wicked turtle
nw, go for it
wicked turtle
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restive river
my professor solved it
wicked turtle
oh i see
i think the final answer is wrong unless i'm unable to do arithmetic in my head (which is possible)
i agree with this though
solid hull
how did you change 8^2 to 8 at the end?
Took out sqrt(1/4) from the square root to make 1/16
versed vault
With pi/6 and pi/4
wicked turtle
Took out sqrt(1/4) from the square root to make 1/16
sqrt(1/4) is 1/2 though
shouldn't it just be 8^2/4 outside the sqrt at the end?
versed vault
Yes the same answer
restive river
can u guys explain it to me please
restive river
uh so guys
wicked turtle
good i'm not crazy haha ```
(1/2)8^2 * sqrt(1/2 + sqrt(3)/4)
ans =
30.9096
8sqrt(2+sqrt(3))
ans =
15.4548
so what happend
wicked turtle
final answer should be 16 times sqrt(stuff), not 8 times sqrt(stuff)
they screwed up the simplification
restive river
is this true?
wicked turtle
well this is not 30.9:
versed vault
Idk where that comes from
wicked turtle
should be 16sqrt(2 + sqrt(3)), which is 30.9
@restive river did you understand the rest of the work?
wicked turtle
which step is the first one you don't get
wicked turtle
they're using this trig identity:
with x = 5pi/12
advantage being that you know cos(2x) in that case
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restive river
no
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bitter marsh
how do we solve this question?
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how do we solve this question?
fair storm
how do we solve this question?
What happens if two vectors are perpendicular?
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bitter marsh
their dot product is zero?
bitter marsh
so (a.b)b is zero, right?
fair storm
decompose the vector a in terms of b and c
fair storm
Also in terms of the direction perpendicular to both b and c (b x c)
bitter marsh
i am not following you there
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i am not following you there
fair storm
Given expression:
[
(a \cdot \mathbf{b})\mathbf{b} + (a \cdot \mathbf{c})\mathbf{c} + \left[\frac{a \cdot (\mathbf{b} \times \mathbf{c})}{|\mathbf{b} \times \mathbf{c}|^2}\right](\mathbf{b} \times \mathbf{c})
]
where ( \mathbf{b} ) and ( \mathbf{c} ) are perpendicular vectors.
Step-by-step simplification:
Since ( \mathbf{b} ) and ( \mathbf{c} ) are perpendicular, we can decompose the vector ( a ) as follows:
[
a = a_b \mathbf{b} + a_c \mathbf{c} + a_{b \times c} (\mathbf{b} \times \mathbf{c})
]
where:
[
a_b = \frac{a \cdot \mathbf{b}}{|\mathbf{b}|^2}, \quad a_c = \frac{a \cdot \mathbf{c}}{|\mathbf{c}|^2}, \quad a_{b \times c} = \frac{a \cdot (\mathbf{b} \times \mathbf{c})}{|\mathbf{b} \times \mathbf{c}|^2}
]
Substitute this into the original expression:
[
(a \cdot \mathbf{b})\mathbf{b} + (a \cdot \mathbf{c})\mathbf{c} + \left[\frac{a \cdot (\mathbf{b} \times \mathbf{c})}{|\mathbf{b} \times \mathbf{c}|^2}\right](\mathbf{b} \times \mathbf{c})
]
Simplifies to:
[
a_b \mathbf{b} + a_c \mathbf{c} + a_{b \times c} (\mathbf{b} \times \mathbf{c})
]
Thus, the entire expression simplifies to:
[
\boxed{a}
]
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Roman_Garland
bitter marsh
that's projection formula right
fair storm
I guess so
bitter marsh
it's not; the formula has mod in the denominator not its square
but i guess i get the idea
i did not know the decomposition thing so didn't know how to go from there
but thank you!
robust berry
u can just use b=i^ and c= j^
bitter marsh
i do not see how that would have helped though
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topaz umbra
Math is not mathing
inland seal
!status
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1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I though I am solving correct and I am pretty sure I did but I reached a question with info I probably should have gotten before but I am searching where and I am not finding
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sacred dock
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wise swallow
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wise swallow
I was sick for two days and missed the one lecture I shouldn't have missed
trim marsh
Just visualize what it approaches
Say the first one
f(f(x))
So the inside approaches 1 as x goes to 0 then the outside approaches 0 because as x goes to 1 f(x) goes to 0
junior chasm
So the inside approaches 1 as x goes to 0 then the outside approaches 0 because ...
why "the outside approaches 0 because as x goes to 1 f(x) goes to 0"
i mean
u got f(x) -> 1 with the limit
now its just f(1)
so thats 0
summer igloo
not even sure if theres a point in asking this here because of how much of a dang mess this is
devout snowBOT
not even sure if theres a point in asking this here because of how much of a dan...
summer igloo
this crap...
not only that but the dang problem is hard for me to create any type of logical example to understand it with
because everything is intertwined within everything else
so its like it forces itself to be complex
so unless i calculated and understood everything simutaneously it wouldnt be easy to solve
junior chasm
where are u stuck
summer igloo
1. I dont understand how you can add one to both sides and keep equality as they want the zeroes so wouldnt this add one to the zeroes?
2. I am still very confused about how the perfect square because they took all 3 X's and found a way to pretty much delete all but X yet the answer still was equivalent to just one of the X being the value making the equation zero.```maybe these questions would be solvable if 900 things werent going on at the same time and i could format them in isolation
damn black box
cant calculate anything as soon as it gets to the perfect square as the complex factoring hides everything in such a way i cant compress it.
may as well try O.O.C. to fix this but dang.
summer igloo
may as well try O.O.C. to fix this but dang.
junior chasm
```lua
1. I dont understand how you can add one to both sides and keep equality ...
- lets say x = 4, if u add +1 to both sides it'd be x+1=4+1 -> x+1=5
x+1=5 -> x=4
x is still 4
adding 1 to both sides didnt change anything
summer igloo
oh
yes
thank you you managed to do what i was trying to do but couldnt because i was getting overwhelmed and im new to that type of reasoning
summer igloo
1. lets say x = 4, if u add +1 to both sides it'd be x+1=4+1 -> x+1=5
i love this
summer igloo
o
restive river
hey u
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trim marsh
now its just f(1)
it would still be a limit you cant assume that lim f(x) = f(lim x)
trim marsh
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trim marsh
it would still be a limit you cant assume that lim f(x) = f(lim x)
mb for the chat but since f isnt continuous and there could be a question involving some of those discontinuities
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junior chasm
it would still be a limit you cant assume that lim f(x) = f(lim x)
but its lim f(1) (after inner f(x) approaches 1)
devout snowBOT
but its lim f(1) (after inner f(x) approaches 1)
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zenith mantle
Continuity and Discontinuity
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Continuity and Discontinuity
warm fulcrum
zenith mantle
Question number 7
I'm just not sure how to tell if it's continuous or not continuous
Now logic says that since both sides are infinity then it'd be continous
But we are looking at x=0 and x= 2
@warm fulcrum
But also for this
For x/x^2-x
This is the graph
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limber kernel
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limber kernel
I need help graphing this
i know amplitude is -2
period would be 2pi
i just dont think i understand the horizontal shifiting part
dense jay
do you know how shifts work generally?
limber kernel
i know how they work, but in trig functions not so much
in regular functions i have no problem
i know that shifts to the right
dense jay
its exactly the same process
limber kernel
also is my amplitude wrong?
dense jay
we wouldnt say an amplitude is negative, the amplitude is 2
you just also have a reflection
limber kernel
its exactly the same process
but how would it shift pi/6 to the right
dense jay
do you mean how would you graph it?
limber kernel
yea
dense jay
wherever sin is normally 0, push it pi/6 to the right, same with the stationary points
once youve done a cycle you should be fine
or half of one even
limber kernel
i think i have a problem with pi notation
i might not understand it very well
i know where pi is, and i know the graph comes from the unit circle
dense jay
pi radians is equivalent to 180 degrees
pi/6 radians is thus equivalent to 30 degrees
if that helps
dense jay
make sure you work on your radians though, at a point degrees wont be very useful anymore
dense jay
yeah
dense jay
nw
limber kernel
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sage pawn
Need some help sketching the solution given the slope field
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Need some help sketching the solution given the slope field
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tender cobalt
Need some help sketching the solution given the slope field
all you do is draw a curve that follows the hairs on the picture
for example you can begin drawing the curve like this:
sage pawn
all you do is draw a curve that follows the hairs on the picture
How do you know that is the right curve, seems to me there could be multiple
This what I mean
cyan laurel
How do you know that is the right curve, seems to me there could be multiple
You'll be given a initial condition
Like the curve passes through the point (1,2) or something
sage pawn
Doesn't say anything like that
tender cobalt
How do you know that is the right curve, seems to me there could be multiple
wdym "right curve" theyre all right
also the slope field isnt saying to draw a straight line for a curve
near y=0 and y=1 the slopes are almost horizontal
at y=0 and y=1, the slopes are completely horizontal
this is your cue to start and end the curve at horizontal asymptotes
sage pawn
I remember seeing this shape during a lecture but it’s confusing with these slope things
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tired igloo
Sup, can someone check my solution please
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Sup, can someone check my solution please
pure flower
!original
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
pure flower
I have no idea what you're tryingg to do
tired igloo
Sry, I’m trying to find domain of this function
faint gorge
Sry, I’m trying to find domain of this function
there are many functions
cursive thicket
I don't understand spanish
tired igloo
Sry, I’m trying to find domain of this function
We’re looking for domain of function g
tired igloo
also *is* that spanish
It’s Portuguese tho
pure flower
Sry, I’m trying to find domain of this function
mm
faint gorge
We’re looking for domain of function g
what do you know about logarithms domain?
tired igloo
what do you know about logarithms domain?
They’re should be more then zero
cursive thicket
yeah
tired igloo
But isn’t it include in my answer, I mean it’s already more then that
Like from 1 to infinity
Where does this guy go ?
faint gorge
Like from 1 to infinity
that's only part of the answer
tired igloo
U mean answer should be (-3;-2) U (1; inf)
tired igloo
But is it necessary, cause it can’t be negative anyways
faint gorge
If you consider (x-3)/(x²+x-2) > 0 then you have these two cases (x-3) > 0 and (x²+x-2) > 0 or (x-3) < 0 and (x²+x-2) < 0
tired igloo
So I need to define it for all cases in answer?
faint gorge
the problem here with the table is you cant tell what's happening within those integer values
tired igloo
Forget to put SS in -3 table, I meant that it not defined
Cause it will be equal to zero
A little bit gross
tired igloo
A little bit gross
faint gorge
(x-3)/(x²+x-2) = (x-3)/[(x-1)(x+2)]
You know from the right it goes to up infinity as x -> 1
then since (x-1)^1 has an odd power, the function approaches -infinity from the left as x -> 1.
Now fron the left as x -> -2 it goes to up infinity (try some values) and then the same (x+2)^1 has an odd power so from the right as x -> -2 it goes to -infinity.
Also at x = -3 there is a root.
So by that you might draw a sketch of how your function looks like and deduce the intervals where it's positive
tired igloo
K but still doesn’t it will start from 1 and approach to infinity
faint gorge
(1,inf) is a correct solution
but it's not the total solution
because as explained
at x = -3 you have a root there
and from there as you approach -2 from the left
it becomes positive
So there is this additional interval (-3,-2) that you need to include
faint gorge
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gray badger
This is probably incorrect what is the right way? The answer should include f and f prime
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inner ibex
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inner ibex
guys plz help
soft umbra
Wat have u tried
inner ibex
idk where to satretr
soft umbra
Do u know c
opal cloak
start by subbing in known points
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lunar kiln
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lunar kiln
here are teh solutiosn
for projectile motion quetsions can someone help me understand the physical intiutio nof these equations
like for part ii
the original equation was in terms of y and x
when we sub in a and b
why does it all of a sudden become in terms of tan theta
and what does tan theta have to do with this
and for part iii i dont understand the physical understanding of the solution
hollow ice
Do you understand that there would be multiple trajectories that pass thru the same point (a,b)?
lunar kiln
uh yeah depending on theta and v i guess
lunar kiln
right
hollow ice
So, when you substitute the values a,b in original equation, we can expect multiple values of theta to satisfy the equation
lunar kiln
right
so what does that have to do with the number of solutions
and using dicriminant
hollow ice
you got a quadratic in tan theta
so, if a,b is supposed to be on the trajectoriees, the equation would have a real solution
hollow ice
discriminant > 0 is checking if two trajectories are not the same
lunar kiln
discriminant > 0 is checking if two trajectories are not the same
wdym
so if we get two sols
then one if for theta 1 and other for theta 2
hollow ice
discriminant < 0 means imaginary, =0 means identical trajectories, >0 means different solutions for tan theta
lunar kiln
uh huh
i see
so basically for the projectile to pass thorugh a and b tan theta must have a real distinct solution
we need to product two solutions
hollow ice
yes
lunar kiln
cause ther are two trajectories
hollow ice
we need to product two solutions
produce two distinct solutions for two different trajectories
lunar kiln
produce two *distinct* solutions for two different trajectories
right
so we let discrimant be > 0 and not = 0
ok ok
hollow ice
yea
hollow ice
Its just an intuitive observation
lunar kiln
Its just an intuitive observation
whats the logic behind it
hollow ice
we know that the tan theta for an angle smaller than 45 deg is less than 1
lunar kiln
or is it prely mathematical intuition
hollow ice
or is it prely mathematical intuition
yea, somewhat that. We can see that the product of solutions is larger than 1, and we know individually they are both smaller than 1 according to the assumption
lunar kiln
yea, somewhat that. We can see that the product of solutions is larger than 1, a...
huh i guess i just have to practice more to see this instantly in an exam
ok so when we multiple bounds, how do we do it proprely, do we just multiply it
hollow ice
ok so when we multiple bounds, how do we do it proprely, do we just multiply it
Im sorry I do not understand what you are trying to say
lunar kiln
Im sorry I do not understand what you are trying to say
uhh
in lines 7 8 9
they first write out the bounsd individually
then multiply them
hollow ice
what do you mean by multiply bounds
hollow ice
like 0 < x,y < 1 so xy < 1 ?
lunar kiln
like 0 < tan theta 1 < 1 and 0 < tan theta 2 < 3 for example, so 0 < tan theta 1 * tan theta 2 < 3 ?
hollow ice
since its multiplication, you can just observe and see, since its all positive, its gonna multiply and give positive answer and since max value is 1, you know its product is capped at 1
I mean theres concrete way to say that but, its case by case you know. I cant just put it here like that in 2 min
lunar kiln
sure ok
uhh i guess i understand the solution
so theres no really any physical logic behind part 3 is there
just purely mathematical bounds and stuff
hollow ice
just maths and intuition id say
lunar kiln
o so just more practice an dkind of rote learning i guess
hollow ice
I mean there is physics reason too
the max trajectory is at 45 deg launch angle
and min at 0 degree
so the path monotonically grows from 0 range to max range
and since all those paths are parabolic, you cant have intersections for two launch angles smaller than 45 deg
hollow ice
You can see how the higher you throw the farther it falls right?
lunar kiln
yeahg
hollow ice
so say yellow is 45 deg throw, it falls the farthest
hollow ice
and red being smaller angle it falls closer
lunar kiln
will not intersect
hollow ice
yea
lunar kiln
we found the thetas that intersect in problem 2
no we found the conditions for theta to intersect
so the conditions for them to interserct
are the oens we found on ii and that at least one fo the launch angles have to be above 45
so there are two conditions for them to intersect?
hollow ice
no we found the conditions for theta to intersect
the solution you get from solving that determinant is the thetas that intersect
hollow ice
are the oens we found on ii and that at least one fo the launch angles have to b...
the condition gets satisfied only if one angle is more than 45 and other is smaller than 45. That means, the thetas are gonna be like that as long as the determinant exists and is greater than 0
that means the condition in problem 3 is not a new condition, but a more clear explanation of the condition in (ii) since you did only algebraic manipulations on (ii) and used nothing else
lunar kiln
so condition in ii is under the presumption that both angles are not less than 45
hollow ice
there is no presumption
hollow ice
determinant gives you a positive and a negative sqrt. That ensures the angles would be such that one of them is smaller than 45 and the other would be larger
You can think of problem 3 as the text that describes the condition 2
lunar kiln
doens the determinant just check whether or not the quadracti has 2 solutions
we havent actually found the oslutions
hollow ice
you know the quadratic formula right? (-b + det)/2a is one solution and (-b - det)/2a is the other
you dont need to do anything else
lunar kiln
oh ok
hollow ice
you have found the solutions
lunar kiln
oh yeah
so what question 3 is basically asking us to find tthese solutions? and show that they both cannot be less than 45
how would u have approached question 3 without the solutions?
hollow ice
This way is pretty good
from the a^2 term in leading coefficient and in constants, you can see that product of solutions has to be more than 1
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runic thicket
the equal sides of an isosceles triangle are 3cm less than the base and the scope is 18cm find the area of the triangle
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the equal sides of an isosceles triangle are 3cm less than the base and the scop...
runic thicket
can someone please help me
winter patrol
scope?
twilit comet
you mean perimeter?
mortal steppe
draw it
runic thicket
whats that "S" in the formula
mortal steppe
i think you'd probably have to use heron's formula
what?
for an isosceles triangle?
ripe hollow
whats that "S" in the formula
semi-perimeter which is perimeter/2
runic thicket
semi-perimeter which is perimeter/2
thanks
what do i do if the triangle is an isosceles triangle
the s-a s-b s-c formula doesnt apply
mortal steppe
it does
runic thicket
theres only a and b no c
mortal steppe
c is the base of the triangle
runic thicket
but what are a and b then
mortal steppe
the other two sides of the triangle
runic thicket
then how do i do the formula
ripe hollow
Isosceles triangle have 2 sides equal and different other side
mortal steppe
by putting the lengths of the sides into the formula
ripe hollow
the equal sides of an isosceles triangle are 3cm less than the base and the scop...
According to the question the two sides are smaller by 3cm than the base
Now try to make sense of it
runic thicket
idk im dumb
ripe hollow
idk im dumb
Okay let's assume the length of two sides to be x
then what will be the length of the third side?
ripe hollow
The question said the other two sides' length is 3 cm less than the base
So if the other two sides are x
Then the base shall be
runic thicket
x+3
ripe hollow
Absolutely
runic thicket
so then waht
ripe hollow
Now you can put it into the formula
Let a and b the equal sides
And c be base
put the values
runic thicket
if the o=18 then s= 9
ripe hollow
Correct
ripe hollow
All you need to use heron's formula is
runic thicket
i got 9x(9x)(9x)(9x+3)
runic thicket
idk man im not smart
ripe hollow
i got 9x(9x)(9x)(9x+3)
That doesn't look like heron's formula
runic thicket
then what i s the herons formula
ripe hollow
idk man im not smart
C'mon don't be like that
ripe hollow
then what i s the herons formula
Lemme share
runic thicket
ok
ripe hollow
put the values and tell me what should it be
Don't calculate
Just put the values and tell me
runic thicket
i dont have any of the sides
ripe hollow
Okay let's assume the length of two sides to be x
.
runic thicket
81-9x(9-x)(9-x+3)
runic thicket
729-81x-81x+9xsquared x (9-x+3)
idk how to
this is supposed to be one of the easier querstions too
im fucked
can i do it thourgh the perimeter
ripe hollow
can i do it thourgh the perimeter
Is the scope perimeter for sure?
runic thicket
i did it and got b=7 and a=4 and the results got messed up
runic thicket
Is the scope perimeter for sure?
yeah
can someone good quickly solve it pls
idk
i cant
i spent like half and hour on this problem
where do i find someone tha can
i dont have that much money to spend on private classes
and the book doesnt tell me anything about those kinds of questions
theres nothing on youtube or google
IM NOT THAT SMAR T HRO
im just a kid
i barelky manage to get a passing grade in math
there are two sides and one is x-3
so both of themn are x-6
and through that i got that a is 10cm
so i get the height through the hypotenuse
ripe hollow
so i get the height through the hypotenuse
Just don't
ripe hollow
That's way too complex
I have the method
All you do is have to understand
We have perimeter that is 18
We know perimeter = sum of sides
runic thicket
and then i get base x height
ripe hollow
so a + b + c = 18
runic thicket
4x3 = 12 which is the solution i nthe text book
thanks for the help i figured it pout somehow
ripe hollow
Oh good job then
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livid palm
can anyone help me with this?
devout snowBOT
can anyone help me with this?
boreal helm
Do u know the property
livid palm
Do u know the property
which one?
boreal helm
f(x) integration from a to b= f(a+b-x) from a to b
livid palm
yeah ik
boreal helm
Kings'
livid palm
what?
boreal helm
This one do u know?
That integration of f(x) from a to b= integration of f(a+b-x) from a to b known as king's rule
livid palm
yeah i know this one
boreal helm
Now try to apply it
livid palm
but why to use that property here?
supple knot
can anyone help me with this?
Should get your original integral
Or maybe add it to your original integral and combine the integrand
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mental shell
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dense lynx
what is ur q
mental shell
how would you go over the limit of this function when x approaches 0 from the right
but the catch is you are only allowed to use factorization and
what's it called in eng? conjugate expressioons?
dense lynx
conjugate yes
dense lynx
yeah and I'm kinda struggling can you help ?
can you identify a conjugate to multiply by
ancient sluice
mental shell
what i tried is sqrt(x+1) + sqrt(1-x) + sqrt(x+4)
but got stuck afterwards
I couldn't find anything to cancel out
I was trying to cancel the sqrt(x) in the denominator but found nothing
dense lynx
what i tried is sqrt(x+1) + sqrt(1-x) + sqrt(x+4)
ok this is good
multiply numerator and denominator with that, and proceed
if you get stuck, you can show work here and ask for more assistance
mental shell
if you get stuck, you can show work here and ask for more assistance
okay thank you ima write my progress down cleanly and provide it
mental shell
if you get stuck, you can show work here and ask for more assistance
this is as far as I've come
dense lynx
this is as far as I've come
looks fine, but it seems your denominator has a minus where it should have a plus
to continue, identify another conjugate you can multiply by
mental shell
looks fine, but it seems your denominator has a minus where it should have a plu...
well that should be -x - 2 - 2sqrt(1-x^2)
dense lynx
yes v good
mental shell
mental shell
yes v good
now I factorize sqrt(x) and cancel?
dense lynx
now I factorize sqrt(x) and cancel?
you can just cancel it out yes
mental shell
you can just cancel it out yes
tbh I did all of this but when I reached this step I was like this a damn long denominator I must have made a mistake and just abandonned the method
dense lynx
tbh I did all of this but when I reached this step I was like this a damn long d...
ye that is fair
from how u handled this problem it seems u have good understanding of how this process works
this problem is just a bit long is all
mental shell
from how u handled this problem it seems u have good understanding of how this p...
<3
.close
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dense lynx
yw 
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celest rain
given a set of coords, how do you determine if a point is on a unit circle?
winter patrol
see if the point(s) satisfy the unit circle equation
acoustic leaf
the unit circle is the set of all points satisfying x^2 + y^2 = 1
celest rain
i got the coords (sqrt10/5, sqrt15/5) and when i plugged that into the unit circle equation i got 2 + 3 = 1
oh just realized im doing my arithmetic wrong
supposed to square the numerator and the demoninator oops
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frosty dirge
A coin was flipped 6 times. 4 heads and 2 tails was the result. Was the coin toss fair?
- It was fair because it resulted in both heads and tails
- It wasn't fair because the results are not enough
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A coin was flipped 6 times. 4 heads and 2 tails was the result. Was the coin tos...
upper schooner
6 coin tosses isn’t an awful lot
(On which note, what’s that phrasing of “the results are not enough”, as in not enough tosses were made, or that of the ones you did, they weren’t e.g. evenly distributed as 3 heads 3 tails?)
dense scroll
there needs to be some threshold of unlikely-ness for something to be considered "unfair"
if the threshold is really low that means that any even number of coin tosses without an equal number of heads and tails would be unfair, which is unrealistic, and a really high threshold would leave any distribution being fair
frosty dirge
what are your standards of "not fair"
That's what the question asks
It doesn't say
The question is a bit simplified but that's about it
dense scroll
if you aren't going that deep then you can just say that there's not enough tosses to be sure
because 6 tosses is practically nothing statistically
frosty dirge
if you aren't going that deep then you can just say that there's not enough toss...
I see
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whole iron
What do you do to solve for A in this situation?
devout snowBOT
What do you do to solve for A in this situation?
faint gorge
did partial fraction decomposition go wrong?
faint gorge
(X-3)
faint gorge
[ 33x+6 = Ax(x-1)(x-3) + B(x-1)(x-3) + Cx^2(x-3) + Dx^2(x-1) ]
woven radishBOT
bacc
faint gorge
Like 2?
no looks like something went wrong
Here you can make equations by comparing the coefficients
whole iron
Yea ik
whole iron
But you can set x = 1 to solve for C
You can set x = 3 to solve for D
Set x = 0 to solve for B
But what about A?
whole iron
Your just canceling out other facors to make it simpler
If you plug-in 0
Ax(x-1) = 0
faint gorge
I see
faint gorge
So 6 = 3B
whole iron
I got C to equal 39/-2
faint gorge
yes
whole iron
Set x = 3
Your solving D
Which I got to be 105/18
But for A, idk what to plug-in for x
faint gorge
x = 3 then
105 = 18D
whole iron
Yea
faint gorge
Ok I see what you mean
whole iron
Yea
faint gorge
I mean what I would do is now
0 = Ax³ + Cx³ + Dx³
0 = A + C + D
A = -(C + D)
you know C and D
,w -( -39/2 + 105/18)
whole iron
Where did those cubes come from
woven radishBOT
faint gorge
Where did those cubes come from
This is my method
called coefficient comparison
I can say 33x+9 = 0x³+33x+9
faint gorge
**bacc**
Here I look in my head for all coefficients that involve x³ and then do
0x³ = Ax³ + Cx³ + Dx³
whole iron
Why cubed? Why not squared?
faint gorge
We can also take square
Just makes it a bit more complicated to evaluate the square term for A
0x² = -4Ax² + Bx² -3Cx²-Dx²
0 = -4A + B - 3C - D
whole iron
I think I will need to look at this method more in depth
faint gorge
,w 0 = -4A + 2 - 3(-39/2) - 105/18
woven radishBOT
faint gorge
See
but the square terms were a bit more tedious than the x^3 terms
and so if you do this for
x^0 = 1
x^1
x^2
x^3
whole iron
I’m probably gonna look at a video on this method
faint gorge
,w partial fraction decomposition (33x+6)/(x^2(x-1)(x-3))
woven radishBOT
faint gorge
our factors match
A, B, C and D
the rest is easy now to integrate
3 logs and and one -2/x
faint gorge
Also don't forget the absolute value in the log
whole iron
Alrigjt thanks, I will look into this method a bit more
Because it seems to work for this integral
devout snowBOT
@whole iron Has your question been resolved?
faint gorge
<@540300959302287372> Has your question been resolved?
react to this first
otherwise it closes
whole iron
because I thought I got A wrong
it was like 82/6
but i realized that what you put was just simplified
nvm
i typed it in wrong
faint gorge
i dont see a mistake
whole iron
i put 19
faint gorge
also 105/18 can be reduced
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steady forge
notation question; if I had dy/dx and I wanted to plug in the point (x1, y2), would I write dy/dx, a line to show im plugging in, then (x1,y2)? or would I write dy/dx, the line, and then x = x1, y=y1
devout snowBOT
notation question; if I had dy/dx and I wanted to plug in the point (x1, y2), wo...
lunar harbor
notation question; if I had dy/dx and I wanted to plug in the point (x1, y2), wo...
y2 and not y1, but either is fine
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pliant briar
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junior chasm
How do I even solve this
for the turning point
set the derivative of g(x) = 0
so $2ax \pm 2\sqrt{ac} = 0$
woven radishBOT
Astar777
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limpid osprey
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limpid osprey
is it right
because as the limit is coming from the negative side
it cant be negative because of the absolute value
therefore making it
not existant
rich lintel
i would think of it as splitting it into two limits
one is negative infinity, one is positive infinity
it becomes indeterminate form
your answer is right but if im understanding your reasoning, i dont think your reasoning is right
but im also unsure of indeterminate form of -infinity-infinity which might be -infinity still
sacred hound
I think DNE is wrong, like if you plot it, it should be clear that it can't be DNE
This function (on $\mathbb{R}\setminus{0}$) is essentially:
$$f(x) = \begin{cases}
\frac{4}{x} & x < 0 \
0 & x > 0 \
\end{cases}$$
woven radishBOT
everyone
sacred hound
so the limit does not exist, but one-sided limit exist for both
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restive river
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restive river
I've checked my answers multiple times and can't find anything wrong. It's saying that I got 96% correct, which would mean one is wrong
Am I not seeing something?
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@restive river Has your question been resolved?
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restive river
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alpine moat
Hello could someone suggest how to do this question
devout snowBOT
Hello could someone suggest how to do this question
@alpine moat Has your question been resolved?
ancient wolf
prove this x3+y3+z3=k
devout snowBOT
@alpine moat Has your question been resolved?
ancient wolf
@devout snow solve this x3+y3+z3=k
dense lynx
you can treat it like |x| * x^2
cyan laurel
Probably because as x approaches 0 sinx behaves like x
void knot
can we just assume x approached 0? I'm not very sure
upper schooner
Well, you want the nth derivative at zero…
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void knot
So Is the answer 4?
upper schooner
I’m a bit fried atm 
literally about to fall asleep 
void knot
Ooh ok gnite!
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gilded gorge
can someone help me with this please? I'm trying to figure out how to factorise this
devout snowBOT
can someone help me with this please? I'm trying to figure out how to factorise ...
restive river
can you stop spamming it
gilded gorge
wait shit
restive river
can you stop spamming it
gilded gorge
lim x-> -2 (x^3-x^2-x+10/x^2+3x+2 = ?)
gilded gorge
or \lim _{x\to :-2}\left(\frac{x^3-x^2-x+10}{x^2+3x+2}\right)
junior chasm
$\lim_{x \to -2} \frac{x^3-x^2-x+10}{x^2+3x+2}$
woven radishBOT
Astar777
devout snowBOT
@gilded gorge Has your question been resolved?
gilded gorge
no
devout snowBOT
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steep cipher
(1/-3)^4=1/81?
devout snowBOT
(1/-3)^4=1/81?
steep cipher
Am I right?
dense jay
sure
steep cipher
Calculator says its 1/-81
dense jay
an even exponent of a real number isnt going to give a negative number
steep cipher
an even exponent of a real number isnt going to give a negative number
I forgot the negative on 3
dense jay
still 1/81