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#help-13
cedar kilnBOT
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junior stratus
How do I turn this non straight line into the general equation of a circle?
Coordinates:(-2,3)(-1,-1)(-2,1)
General Equation: ax² + cy² + dx + ey + f = 0
junior stratus
Ahh yes khan academy how refreshing
cedar kilnBOT
@junior stratus Has your question been resolved?
cedar kilnBOT
@junior stratus Has your question been resolved?
junior stratus
https://www.khanacademy.org/math/geometry-home/triangle-properties/perpendicular...
Completely unrelated on the one im talking about
dire geode
Completely unrelated on the one im talking about
Wrong
dire geode
You just plug the three points into general equation of a circle to get three equations and 3 unknowns
cedar kilnBOT
@junior stratus Has your question been resolved?
cedar kilnBOT
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civic coral
even fucntions with positive lead coefficient would alway have a min value
civic coral
vice versa, even function with negetive lead coefficient would, without a exception, have a max value
is that true
sick gazelle
yep exactly
tropic oxide
do you mean "function" or do you mean "polynomial"
long swan
Well consider that the derivative of an even function must be odd (and vice versa)
Odd functions always have a zero
Ergo even functions always have a local extreme
cedar kilnBOT
@civic coral Has your question been resolved?
civic coral
do you mean "function" or do you mean "polynomial"
function
tropic oxide
then what is a "leading coefficient" for a non-polynomial function?
civic coral
didn't every function has a leading coefficient
tropic oxide
no
civic coral
im confused
could you give me a example
of a function without a leading coefficient
tropic oxide
1/cos(x)
civic coral
ohh
tropic oxide
"leading coefficient" is something that only makes sense for polynomials
civic coral
i didn't know that, then i think we are talking about polynomials
cedar kilnBOT
@civic coral Has your question been resolved?
crimson sedge
Super low level but hopeing someone can explain to me where the 25/4 and 35/4 came from? I have a hunch but just want to confirm. I don't get the 25/4 because the fractions multiplied would be 25/16 in my head and the 5*7=35 but why is it over 4?
junior stratus
What do you mean?
elder swan
5*5 = 25
crimson sedge
I mean like, can you break down for me where 25/4 and 35/4 came from?
junior stratus
Oh
crimson sedge
sure but why are they over 4.
junior stratus
25 + 35 = 60
crimson sedge
So 5/4 * 5/4 = 25/4? I thought you had to multiply the denominators too.
junior stratus
5 * 5/4 = 100/16
gritty hearth
but when you're multiplying two fractions you multiply both the numerator and denominator
junior stratus
Yes
elder swan
5 * 5/4 = 100/16
you are trolling right?
junior stratus
No same thing divide it
100/16 = 6.25 and 25/4 = 6.25
Try it.
Thats how I multiply my fractions
crimson sedge
So to simplify my question more, from above just what specifically makes 25/4 and 35/4 like what is actually multiplied in full please?
junior stratus
And you simplify 100/16 by ÷4 you get literally 25/4
7 * 5/4 = too uhhh
7/1 * 5/4
gritty hearth
So to simplify my question more, from above just what specifically makes 25/4 an...
(5) * (5/4) = (5 * 5)/4 = 25/4
junior stratus
Balance the denominators by multiplying both sides of 7/1 by 4
gritty hearth
yuh
crimson sedge
.close
cedar kilnBOT
cedar kilnBOT
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gritty galleon
$$\sum_{i=0}^n 2^n = ? $$
cedar kilnBOT
$$\sum_{i=0}^n 2^n = ? $$
wraith daggerBOT
ItzKraken
gritty galleon
context 👇
tropic oxide
$$\sum_{i=0}^n 2^n = ? $$
did you mean this or did you mean $\sum_{i=0}^n 2^i$
wraith daggerBOT
Ann
tropic oxide
in the latter case it's a geometric progression
gritty galleon
how does $2^k + 2019 \cdot (2^{k-1} + 2^{k-2} + \dots + 1) = 2020 \cdot 2^k - 2019$
wraith daggerBOT
ItzKraken
gritty galleon
in the latter case it's a geometric progression
isnt that formula only applicable when |r| < 1?
tropic oxide
a FINITE geometric progression.
gritty galleon
did you mean this or did you mean $\sum_{i=0}^n 2^i$
well tbh i dont mean either
tropic oxide
$1 + 2 + \dots + 2^{k-2} + 2^{k-1} = 2^k - 1$
wraith daggerBOT
Ann
wraith daggerBOT
ItzKraken
gritty galleon
again this is the sum of a GP
can u send me which formula u using
tropic oxide
so i can use $\frac{a}{1-r}$ where r is not 1 if the GP is finite?
no
$\sum_{i=0}^{n-1} a \cdot r^k = \frac{a(r^n - 1)}{r - 1}$
wraith daggerBOT
Ann
tropic oxide
you just need r to not be equal to 1
gritty galleon
you just need r to not be equal to 1
okayy
tropic oxide
for a finite GP right?
yes
gritty galleon
**ItzKraken**
what about an infinite one? i use this??
junior dome
what about an infinite one? i use this??
yes
gritty galleon
aight
tropic oxide
what about an infinite one? i use this??
kraken are you brainfarting or did you really never learn GPs until now
vagrant elbow
by taking limit
A limit not approximation
gritty galleon
kraken are you brainfarting or did you really never learn GPs until now
i only learnt that one infinite formula and how GPs are defined
gritty galleon
A limit not approximation
limit as n -> infty?
vagrant elbow
yes
junior dome
yes but |r|<1
gritty galleon
kraken are you brainfarting or did you really never learn GPs until now
we arent taught GPs i saw this question on a mock tho (for IOQM)
tysm everyone
.close
cedar kilnBOT
cedar kilnBOT
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mighty shuttle
I was hoping someone could verify if this idea for solving this problem is correct or not
mighty shuttle
My first step was to write it as $(x-1)^4+ (x-2)^4 ....+(x-m)^4)$, after which I took its derivative and equated it to 0(the minima occurs at an inflexion point). After which , I expand the summation of $(x-k)^3$ , (which would be $mx^3-3x^2\sum_{i=1}^m a_i.+ 3x\sum_{i=1}^m a_i^2.- \sum_{i=1}^m a_i^3$, and solve for that
wraith daggerBOT
physicsrocks
mighty shuttle
am I right until here? If this is correct, I think I know how to do the rest
mental trail
What is a_i ?
dim tiger
you should have k instead of a_i and k instead of i
mental trail
you should have k instead of a_i and k instead of i
This doesnt matter, it's a "mute" variable
But a_i should be replaced with i, at least in the first sum
dim tiger
yea ik its a dummy variable but the a_i should be i or k or whatever the index of summation is
mental trail
am I right until here? If this is correct, I think I know how to do the rest
So yeah you know that the a_i are just i
From there, remember the formula for the sum of powers of consecutive integers, $\sum_{k=1}^m k^n$ for $n=1,2$ and $3$
dim tiger
but beaware the f'(x) would be 4(the expansion you got)
wraith daggerBOT
rafilou2003
cedar kilnBOT
@mighty shuttle Has your question been resolved?
mighty shuttle
but beaware the f'(x) would be 4(the expansion you got)
Won't the power be 3?
junior dome
**physicsrocks**
also not relevant but this is a common misconcept, inflection points and extremum points are two different things.
celest ledge
Σ(x-k)^4=((x-1)^4+(4-x)^4)+((x-2)^4+(3-x)^4)>=2((x-1)(4-x))^2+2((x-2)(3-x))^2
cedar kilnBOT
cedar kilnBOT
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scenic delta
cedar kilnBOT
scenic delta
!status
cedar kilnBOT
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
4
wraith daggerBOT
sadkid
celest ledge
It equals (x^4-1)/(x-1) when x doesn’t equal 1
wraith daggerBOT
sadkid
celest ledge
Correct
celest ledge
Np
scenic delta
.close
whole scroll
In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be arranged?
cedar kilnBOT
In how many ways can a pair of parallel diagonals of a regular polygon of 10 sid...
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
2
celest ledge
Diagonals you mean a line segment connecting two vertices?
whole scroll
Yes
ocean mural
and not a side probably lol
celest ledge
And not an edge? I see
Label them with 1 to 10
Then
There are two cases:
Cases like (2,9),(3,8),(4,7), choosing two from three
whole scroll
celest ledge
Or cases like (2,10),(3,9),(4,8),(5,7) choosing two from four
There are only these two cases
whole scroll
Hmm true
celest ledge
Second cases: choosing 2 from 4, also rotation , so multiplied by 5
First cases: choosing 2 from 3, also rotations, so multiplied by let me see
Also by 5
celest ledge
Yes
whole scroll
Got it
celest ledge
Good
whole scroll
Thanks a ton
celest ledge
Np
whole scroll
.close
twin tinsel
cedar kilnBOT
upper ruin
If you don't know substitution, I think it will be much harder (either expanding the 8th power or going with infinitely long integration by parts)
upper ruin
ik substitution, just not well
Well, either you know or you don't
Maybe you have not done too many exercises so far, but that's another thing
If you know how to do it, just take your time and do it step by step
upper ruin
why cant I distribute the x and the ^8?
Can you explain further? Because I don't know if I got what you want to do
twin tinsel
Can you explain further? Because I don't know if I got what you want to do
make it 8x^16+7x^8
upper ruin
make it 8x^16+7x^8
Where does this come from??
twin tinsel
distribution
upper ruin
Nope, this is not distribution, not at all
$$x {\left( 8x + 7 \right)}^8 = {\left[ \sqrt[8]{x} \left( 8x + 7\right) \right]}^8$$
wraith daggerBOT
Alberto Z.
twin tinsel
cool
upper ruin
Of course $${\left( 8x + 7 \right)}^8 \neq {\left(8x\right)}^8 + 7^8$$
wraith daggerBOT
Alberto Z.
upper ruin
**Alberto Z.**
This is a common, but very very bad mistake
twin tinsel
is the answer to this intagral somthing stupid massive
upper ruin
is the answer to this intagral somthing stupid massive
No, the answer is the "simple" one that your calculator told you
upper ruin
These two are exactly the same
In the second one, the one at the bottom, the x² has been factored out
twin tinsel
ah
upper ruin
But I hope you are not expected to write those horible numbers
twin tinsel
ok so how do I solve this intigral
upper ruin
With this method, which is the simplest one you can think of for this integral... @twin tinsel
crimson sedge
can anyone awnser this 💀
1, 4, 9 , 16...
find the next four number
obsidian coral
can anyone awnser this 💀
1, 4, 9 , 16...
find the next four number
Do you see something in common with those numbers?
crimson sedge
starts with 3, 3+2, 5+2
obsidian coral
Nope
crimson sedge
breh
crimson sedge
idk i suck at math 😭
crimson sedge
next is 25?
crystal raptor
Note that your "add two more each time" pattern also worked fine
whole scroll
Note that your "add two more each time" pattern also worked fine
how
lunar lynx
<:hmmCat:831508801646755850> how
Because squares can be written in form of sum of odd numbers.
1
1+3
1+3+5
and so on
whole scroll
"Add two more each time"
I thought he meant adding +2
lunar lynx
No. He meant that increasing term was increasing two at a time.
crystal raptor
Yeah the wording left something to be desired but i would've just said add two each time for what you thought
"Increase the amount you increase by, by 2 each time" is just a bit of a mouthful
lunar lynx
Well, it works. Also, i don't think that it's at all convoluted to understand.
cedar kilnBOT
@crimson sedge Has your question been resolved?
haughty wadi
i need somebody to check my work and any tips if possible would be great
cedar kilnBOT
i need somebody to check my work and any tips if possible would be great
@haughty wadi Has your question been resolved?
haughty wadi
please i reallt need help bro
cedar kilnBOT
@haughty wadi Has your question been resolved?
haughty wadi
NO
cedar kilnBOT
@haughty wadi Has your question been resolved?
static fern
@haughty wadi check your value of y
brave pike
Hi, I was just wondering why the +c would not be added to both sides in this equation:
crystal raptor
you certainly could do that, you could have ln|y| + d = kt + c, but then you could just move the d over to get ln|y| = kt + c - d, now c-d is still just some arbitrary constant so might aswell relabel it to C (capital)
so we generally just skip all that and just put a constant on one side
brave pike
Ah so thearedically there is still a +c on the left side, but because the constant would just subtract the other constant on the other side we only write it once
any rule of thumb on which side to write it on?
crystal raptor
generally the side that doesn't have the function you're solving for (in this case y) since you're going to be rearranging for y anyway
brave pike
Ok that makes sense, thank you so much
crystal raptor
if you did leave it on the left, at some point you would move it over anyway 🙂
brave pike
Yeah I understand now, since we are solving for y it will end up on the other side reguardless
Thank you so much lol im jsut starting diff eq and my teacher doesnt do lectures so these basic things are starting to build up
.close
cedar kilnBOT
brave pike
.reopen
cedar kilnBOT
✅
brave pike
Wait @crystal raptor if you are still here
I know we can do this but thearedically its not exactly whats going on:
Im talking about crossing off the dt
any reason why we can end up doing that?
crystal raptor
short answer: this type of notation for derivatives and differentials is really good because it lets you treat the dy and dt as fractions in this particular way. its why it was so sucessful after leibniz introduced it because it let him do things like this with no trouble. in reality its a neat trick of the notation that is hiding more rigourous things
brave pike
ok, so if I were to write it like this would that be wrong for higher level math
or did i represent it in the proper way
brave pike
because from what I remember you are just basicly redefining dy, so its not exactly crossing it out and dont want to get bad habbits
alr perfect thank you so much again lol
.close
crystal raptor
cedar kilnBOT
cedar kilnBOT
✅
brave pike
can I just move the dt to the right
and represent it like that
if we are treating it as a variable
@crystal raptor
crystal raptor
no they are both locked inside the integral
brave pike
Because if its the same thing as deviding by 1/dt cant I multiply the other side by the dt and intigrate like that
like in this step
crystal raptor
oh you mean from the start
crystal raptor
you can do that, but again its a notational trick, because then you're really not doing the same thing to both sides when you come to integrate
but its perfectly fine and what most people do
brave pike
hmm ok
im just wondering what the limits of this would be lol
but thats so much cleaner
crystal raptor
I know we can do this but thearedically its not exactly whats going on:
its a shortcut for this
and we love shortcuts
crystal raptor
yep! its good
raven lake
how do u kbow all that
crystal raptor
v is not x/t, its the derivative of x with respect to time
average speed is distance travelled over time taken
but this is instantaneous speed at a single moment
yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
opal crystal
How's this wrong? I don't believe it can be simplified anymore than that
dire geode
How's this wrong? I don't believe it can be simplified anymore than that
Your answer is just wrong
opal crystal
What did I do wrong
dire geode
show your work
opal crystal
dire geode
It's 3(x+2)^2 not (3(x+2))^2
opal crystal
I thought you're able to distribute the 3 before you expand it out into two different sets of parenthesis?
obsidian coral
No
dire geode
I thought you're able to distribute the 3 before you expand it out into two diff...
No
What you did was introduce a new factor of 3
opal crystal
Ahh okay, i see what I did wrong
So it should be 3x^2+12x+14
Thank you!!
.close
wary forge
How would I go about showing that these two things are equal?
wary forge
,rotate
wraith daggerBOT
wary forge
How would I go about showing that these two things are equal?
buoyant latch
Looking like IBP to me
wary forge
Tried and and it works when you set a to a constant but if you want a general form there’s no obvious stopping point
<@&286206848099549185>
cedar kilnBOT
@wary forge Has your question been resolved?
cedar kilnBOT
@wary forge Has your question been resolved?
wary forge
Ok so I did a u substitution for u = ln(x) and it made IBP through the tabular method much easier
But I’m still feeling like what I’m getting is a bit arbitrary
I need to finish writing something and then I’m going to ask how justified this method is
,rotate
wraith daggerBOT
harsh vault
if i can just get a hint
slate lintel
should you have an x somewhere in there?
cedar kilnBOT
harsh vault
how can i check continuity of this function?
cedar kilnBOT
Available help channel!
vagrant walrus
what does it mean when the normal distribution is shorter than the relative frequency histogram, but the cumulative probabilities at multiple points is almost the same between both graphs.
vagrant walrus
and is it correct to say that the combined area under the histogram should be equal to 5 instead of one? Since the x-axis is in intervals of 5?
Its almost as if the relative frequncy histogram is just scaled? idrk what im talking about tho
cedar kilnBOT
@vagrant walrus Has your question been resolved?
vagrant walrus
<@&286206848099549185>
cedar kilnBOT
@vagrant walrus Has your question been resolved?
cedar kilnBOT
@vagrant walrus Has your question been resolved?
cedar kilnBOT
@vagrant walrus Has your question been resolved?
crimson sedge
cedar kilnBOT
crimson sedge
Idk how to get the angle other than to take the arctangent of 1/4
Since -1 gives syntax error
And it’s asking for radians and decimal form too
i tried arc cos that gives me .24 also
hmm
arc sin is giving me .25
i could try that but it's my last try
how do i know which trig function to use
💀💀💀💀💀
Pls someone explain how they got that
They didn’t even round it too
slate lintel
Idk how to get the angle other than to take the arctangent of 1/4
would be arctan of -1/4
slate lintel
yeah then they want an answer in [0, 2pi)
so you'll have to find the equivalent angle
instead of going negative (clockwise) around the circle go positive (widdershins) around it to get to the same angle
crimson sedge
barren canopy
<:ST_ducksweat:928327764392685659>
its shoud be something like 2pi - 0.2449 ?
barren canopy
to get a anticlockwise angle
barren badge
how do I label line
cedar kilnBOT
how do I label line
barren badge
goemorty
cedar kilnBOT
@barren badge Has your question been resolved?
left warren
just one quick one i dont get how gcd(a,b) = gcd(b,r)
cedar kilnBOT
just one quick one i dont get how gcd(a,b) = gcd(b,r)
patent hearth
great!
patent hearth
yes perfect!
cedar kilnBOT
dull oxide
Depends on the function
wraith daggerBOT
Şêro
dull oxide
You must show that for every real number y, there is some real number x such that y=ln(2x-1)
wraith daggerBOT
dull oxide
You must show that for every real number _y_, there is some real number _x_ such...
you can do that is by solving for x, given y
it does
static hemlock
Is this correct? Feels like im doing sumthing wrong / illegal here
Task is:
Use the formal definition of limit value (“-δ definition”) to show that:
static hemlock
Dont worry about the writing mistakes like delta = |x-1|
And on the second last line there should be a break between 2epsilon and two delta
cedar kilnBOT
@static hemlock Has your question been resolved?
static hemlock
.reopen
cedar kilnBOT
@static hemlock Has your question been resolved?
cedar kilnBOT
@static hemlock Has your question been resolved?
cedar kilnBOT
@static hemlock Has your question been resolved?
short magnet
@static hemlock You want to have $\left|\frac{2(x-1)}{x-2}\right|<\epsilon$
wraith daggerBOT
SkyTwX
short magnet
Since $|x-1|<\delta$ then we want $\left|\frac{2(x-1)}{x-2}\right|<\left|\frac{2\delta}{x-2}\right|<\epsilon$
wraith daggerBOT
SkyTwX
short magnet
Hence we need to choose $\delta<\frac{1}{2}|x-2|\epsilon$
wraith daggerBOT
SkyTwX
short magnet
Choosing $\delta<1$ then $|x-1|<\delta<1\implies |x-2|<2$
wraith daggerBOT
SkyTwX
short magnet
All in all, we deduce that we can choose $\delta<\min{\epsilon,1}$
wraith daggerBOT
SkyTwX
static hemlock
bruh my x-2 dissapeared in my calculations
should have got some sleep instead of doing math
thx bro
short magnet
Np @static hemlock , don't forget to close if you're satisfied 🙂
static hemlock
.close
cedar kilnBOT
royal loom
cedar kilnBOT
royal loom
Hi, I was hoping someone could check my work here.
So since Holder continuity gives me that $|f(x)-f(y)|\leq C|x-y|^{\lambda}$
wraith daggerBOT
Austin
solid juniper
@royal loom
royal loom
then this delta only depends on epsilon so it works for uniform continuity
wraith daggerBOT
Austin
royal loom
<@779131727338930196>
@solid juniper
royal loom
I know this time I tagged you back to see if you actually can do math or not
solid juniper
i cannot
solid juniper
that looks about right on first read through
lemme read it closer
yea that's good 
lost swift
cedar kilnBOT
lost swift
Hi so I used permutations and did 7p4 since 7 digits in total and i can select 4 specific ones
zealous compass
yeah
lost swift
Alright thanks I ended up getting 840 as my answer just wanted to make sure
patent ivy
that looks right
lost swift
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
mossy garnet
Hi, I need help with how reciprocals work in this limit of trigonometric functions. So I did change tan(theta) to sinθ/cosθ, but what comes next after that? I know it uses reciprocals, but I don't genuinely know where I should do it. The limit that was given is 3
flint plinth
Hi, I need help with how reciprocals work in this limit of trigonometric functio...
maybe try using a trig identity for sin(2theta)
do you really need to simplify it at all in order to compute the limit though?
pi/6 doesn't cause any trouble
mossy garnet
Apparently so, my professor highly suggested us to use reciprocals since we are just getting started. I'd want to use derivatives and other methods, but yeah, I need to simplify all of it
flint plinth
ok, using an identity for sin(2theta) should be a good next step
that will give you more stuff that cancels
cedar kilnBOT
@mossy garnet Has your question been resolved?
mossy garnet
Are there any further steps?
livid hound
expressing tan(t) as sin(t)/cos(t)
wasnt needed
you can pretty much just plug in the specified value
mossy garnet
Yeah, but in this case, it is necessary for us to change it with trig identities as well as understanding it since the teacher expects us to use reciprocal function in this equation.
cedar kilnBOT
cedar kilnBOT
Available help channel!
ebon drift
hi this is a weird question
cedar kilnBOT
hi this is a weird question
ebon drift
but i missed a question in a math test where one angle of a quadrilateral and 4 sides were given
and we were meant to find the rest of the angles
I could've used the sine law
but I can't find any question like that online
ebon drift
and we were meant to find the rest of the angles
so could someone help me find or give me a question like that? thank you
ebon drift
sounds to me like it might not be enough
it would be, no?
you could split up the quadrilateral and use the sine law
tropic oxide
well let's see
let's say your quad is called ABCD and you're given all sidelengths and angle A
BD can be found via law of cosines sure, but then you have two different positions for vertex C based on triangle BCD
which you could imagine as being 'glued' to triangle ABD in one of two possible ways
unless BC=CD or something
ebon drift
unless BC=CD or something
i think the question stated something like that
tropic oxide
well we're going in blind
ebon drift
so it wouldn't be possible?
ebon drift
then 2 angles and 4 sides should be doable right
tropic oxide
that might actually be overdetermined unless you're just lucky
ebon drift
oh ok
cedar kilnBOT
@ebon drift Has your question been resolved?
cedar kilnBOT
@ebon drift Has your question been resolved?
wraith daggerBOT
BrotmitHonig
cedar kilnBOT
@karmic jungle Has your question been resolved?
high coyote
Let A, B, C be the events of A working well, B working well, C working well.
Then P(A)=0,6, P(B)=0,9 and P(C)=0,7.
So what is P(A and B and C)? You can assume that A, B and C are independent
deft gale
^ this is the correct approach
cedar kilnBOT
@karmic jungle Has your question been resolved?
cedar kilnBOT
@karmic jungle Has your question been resolved?
celest sentinel
It might help to consider another pair of independent events and seeing how that works:
Let $X$ be the probability of getting at least 5 on a fair 6-sided dice. ($P(X) = \frac{1}{3}$)
Let $Y$ be the probability of getting a heads on a fair coin ($P(Y) = 0.5$)
How would you calculate $P(X \text{ and } Y)$, the probability of getting at least a 5 on a fair 6-sided dice and a heads on a fair coin?
wraith daggerBOT
@celest sentinel
cedar kilnBOT
@karmic jungle Has your question been resolved?
wraith daggerBOT
BrotmitHonig
celest sentinel
Yep, exactly @karmic jungle
crimson blade
I do not understand
cedar kilnBOT
I do not understand
simple bane
I do not understand
does that "m" infront of the "p" mean anything?
earnest robin
you know $\measuredangle P + \measuredangle Q = 180°$ and $\measuredangle P = 2\cdot \measuredangle Q -3$
wraith daggerBOT
Homelama
crimson blade
Ok
blazing dune
@crimson blade
You should be able to solve it just by substituting P with the right equation
crimson blade
2q-3?
earnest robin
yes
forest glade
N = 11 has only one distinct digit, while N^3 = 1331 has two distinct digits
different. Therefore 11 is not a deficient number.
Now, notice that N = 173 has three distinct digits, while N^3 = 5177717
It has three different numbers. Therefore, 173 is not a deficient number.
(a) Determine whether N = 192 is deficient or not.
(b) Find a deficient number.
(c) State and explain an algorithm or procedure to generate the number of
deficient numbers as desired.
forest glade
I know for a fact that 192 is not a deficient number
I need help finding a deficient number and with the algorithm
crimson delta
you havent given the def of what a deficient number actually is
only two examples which arent deficient
mental trail
It is :
"A number is deficient if it has more distinct digits than its cube"
forest glade
Oh sorry
mental trail
I'm sure there is a 4 digit answer but I'm really not ready to explain how or why or if this is true
I just started with 102 and kept adding digits
You're allowed to use a calculator right ?
forest glade
Nope
I did by hand
The first one lol
Lol 1920
Its deficient
I need tha algorithm
the*
mental trail
Oh wait yes
Mb
Since you found that 192 and 192^3 have the same amount of distinct digits, AND one of the digits of 192^3 is 0
Since 1920^3 will only add zeroes, you get 1 more digit for the base number and 0 more for the cubed number
After you do this, multiplying the base number by 10 will just multiply the other by 1000, so no distinct digits added
And the deficient property is preserved
earnest robin
i don't get (c) do you just have to get infinitly many or what is it asking?
mental trail
i don't get (c) do you just have to get infinitly many or what is it asking?
Yeah, find an algorithm to generate more deficient numbers
And we got it
forest glade
So
Add zeros to 1920
Hehehehe
Thats my algorithm
I mean it works
In a triangle ABC, consider the midpoint M of the side BC and its
gravity center G on AM. Consider also a line k through G, which intersects
to the sides AB and AC. Finally, let X, Y and Z be points on k such that AX, BY and CZ
are all perpendicular to k. Prove that AX=BY+CZ.
<@&286206848099549185>
cedar kilnBOT
@forest glade Has your question been resolved?
silent finch
In a triangle ABC, consider the midpoint M of the side BC and its
gravity center...
drop the perp from M to k and the result becomes clear
silent finch
let the perp from M to k hit k at W, then MW=(BY+CZ)/2 and 2MW=AX because AXG is similar to MWG with a 2:1 ratio
silent finch
??? thats the solution
silent finch
yes
forest glade
Lol
Thanks
Im going to do like shit tomorrow then
hehehe
What about it?
Im literally studying, so if thats the problem
silent finch
nvm then
silent finch
eyah thats why i posted it
forest glade
You use AOPS?
silent finch
yes
forest glade
There are one thousand balls numbered 000,001,002,...,998,999 and one hundred boxes numbered 00,01,02,...,98,99. It is allowed to place a ball inside a box. if the number of the box can be obtained by deleting one of the digits to the number of the Basque ball. For example, the ball with the number 367 can be placed only in one of the boxes with the number 36, 37 or 67. Show that the thousand balls can be placed within 50 boxes.
Lol
<@&286206848099549185>
<@&286206848099549185>
.close
elder elm
This statement can be proven true using the intermediate value theorem?
quartz frost
yes
look at the 2 limits
as x->oo and x->-oo
there are exceptions tho
think about a=0, b=0, c=0, d=1
then p(x)=1 is never 0
but the coefficients are real numbers
they probably forgot the "non negative"
elder elm
yes
So can I phrase it like this: The statement is true. A cubic polynomial p(x)=ax3+bx2+cx+dp(x)=ax3+bx2+cx+d with real coefficients has opposite end behaviors, meaning it goes from negative to positive or vice versa as xx moves from −∞−∞ to ∞∞. By the Intermediate Value Theorem, it must cross the x-axis at least once, confirming at least one real root.
Or should I elucidate more on the proof
like, go step by step.
limber thistle
hi
elder elm
but only if a is non zero
oh
quartz frost
I would probably write something like this:
since lim[x->-oo]f(x)=-oo, lim[x->oo]f(x)=oo or lim[x->-oo]f(x)=oo, lim[x->oo]f(x)=-oo and that f is continuous on all of R, it follows with the intermediate value theorem that there exists an x0 such that f(x0)=0. Therefore this x0 is a root of f.
although actually, my homework stuff usually uses as little words as possible so i would probably shorten it even further, but i guess that is just personal taste
limber thistle
martin, i need help
quartz frost
limber thistle
not working
stiff totem
just send your question into any of the channels in this section
robust wind
I need help with a volume problem
cedar kilnBOT
I need help with a volume problem
robust wind
I just cat figure out how to intergrate the last part to find my answer
<@&286206848099549185>
i dont belive so
the answer will most likely be in the form of (X)pi^2 - (X)pi
<@&286206848099549185>
Can I get any help at all?
short magnet
I just cat figure out how to intergrate the last part to find my answer
Can you show your work? last part is pretty vague
rustic coyote
banned
robust wind
thats the thing the last part is what im struggling with, I dont know how to properly evaluate the expression]
also ty
short magnet
thats the thing the last part is what im struggling with, I dont know how to pro...
Oh yeah I see, just replace y by the upper bound in the expression and then by the lower bound and take the difference
wraith daggerBOT
SkyTwX
short magnet
so first you replace y by pi/3 you get 324pi/3-81tan(pi/3)=108pi-81sqrt(3)
then you replace y by 0 you get 324*0-81tan(0)=0
Then you take the difference and you obtain 108pi-81sqrt(3)
Final answer is 108pi^2-81sqrt(3)pi
I used than tan(pi/3)=sqrt(3)
cedar kilnBOT
@robust wind Has your question been resolved?
short locust
cedar kilnBOT
upper ruin
Yes, that's correct
If you've done it, it would be faster to use the remainder theorem
short magnet
f(4)=9 is way faster indeed
short locust
If you've done it, it would be faster to use the remainder theorem
can u show me how that works?
with this function
short locust
short locust
Just evaluate f(4)
i drew it and got this
upper ruin
5·4² = 5·16 = 80, not 400
short locust
5·4² = 5·16 = 80, not 400
okay yeah i got it
cedar kilnBOT
@short locust Has your question been resolved?
latent pilot
Let $p$ and $q$ be non-negative integers. If $p+q$ is even, prove that the integer $2^p+2^q$ can be written as their sum of two square numbers, not necessarily different.
wraith daggerBOT
Emo-Kid
latent pilot
Without loss of generality, suppose $p\geq q$. $2^p+2^q=2^q\left(2^{p-q}+1\right)$ and since $p-q$ is even, $\frac{p-q}{2}$ is an integer so $$2^p+2^q=2^q\left[\left(2^{\frac{p-q}{2}}\right)^2+1^2 \right]$$
\medskip
If $q$ is even then $2^q=\left(2^{\frac{q}{2}}\right)^2$ so $2^p+2^q=\left[\left(2^{\frac{q}{2}}\times2^{\frac{p-q}{2}}\right)^2+ \left(2^{\frac{q}{2}}\right)^2\right]$
\medskip
Now, considering that $$\left[\left(a+b\right)^2+\left(a-b\right)^2\right]=2\left(a^2+b^2\right)$$ if $q$ is odd then $2^q$ is twice some square number and we can use this to express $2^p+2^q$ in terms of squares.
wraith daggerBOT
Emo-Kid
latent pilot
Is this correct
celest ledge
Is this correct
Yes
celest ledge
Np
hollow ember
hi, could someone check my answer for this exact differential equation with an integrating factor question ?
hollow ember
this is the question
and my answer is (x^3)y-x^2(y^-1)=C
I made it exact with the integrating factor x
celest ledge
Correct
cedar kilnBOT
cedar kilnBOT
Available help channel!
mortal sable
I need to find the area of this triangle, but i don't know where to begin
bitter kayak
Have you learnt the sine law?
All angles of the triangle add to 180 degrees. Can you find A?
mortal sable
Have you learnt the sine law?
i don't really know
solemn quail
Have you learnt the sine law?
No need for sine law in a right triangle
bitter kayak
No need for sine law in a right triangle
Well, you at least need 30/60/90 triangle ratios here.
bitter kayak
i dont even know where to begin
Can you find A?
mortal sable
probably i just dont know how
solemn quail
OP might not even know any trigonometry at all. I teach this to grade 9 students without any trig.
mortal sable
im in the 9th grade rn
mortal sable
Can you find A?
how do i find A
bitter kayak
You have angles 60 and 90 degrees, what is the last one?
All angles in a triangle add to 180, right?
mortal sable
yea
but thats not what i need to in this task
in this task its pythagoras
so i dont need the degrees
bitter kayak
c = 14 from triangle ratios, right?
willow bridge
arent you guys just complicating it?
bitter kayak
Then you can find b from pythagora's.
willow bridge
if he knows sin60 then he can solve it easily
mortal sable
how
bitter kayak
I know, but he doesn't know trigonometry.
willow bridge
you dont appolo?
bitter kayak
An equilateral triangle has 60 degrees for each angle, right?
willow bridge
what does this have to do with this problem
mortal sable
you dont appolo?
but i need to find what A and C is and then i can add them all together to get the answer
bitter kayak
Cut the equilateral triangle in half, like this. You see that c = 14 since it is the double of b.
willow bridge
do you know what the innkeeper tries to do?
mortal sable
no
bitter kayak
Are you able to follow?
mortal sable
no singular clue
bitter kayak
I am trying to prove that c = 14.
mortal sable
well in the top of my task it says trigonometry
willow bridge
alright if it's trigonometry then it's easy
willow bridge
so if you study trigonometry you have to use sine and cosine
willow bridge
you know the trigonometric numbers for 60 degrees?
mortal sable
huh
bitter kayak
sin(60 degrees) = sqrt(3)/2, right?
willow bridge
ok so &&sin:=:\frac{opposite}{hypotenuse}$$
wait
$$ sin:=:\frac{opposite}{hypotenuse} $$
wraith daggerBOT
TubyconB
wraith daggerBOT
TubyconB
willow bridge
cos I mean
so if you know the trigonometric numbers for 60 degrees
you can use the identities to find out what the hypotenuse (c) is
I know you are lost so ask me
mortal sable
would this be correct then
mortal sable
now i have named them but how do i calculate it to be correct
a = 7 and the angle is 60
but i need to find H and O and then add them to find the answer
so 7 + H + O
willow bridge
$$ cos60:=:\frac{1}{2} $$
wraith daggerBOT
TubyconB
$$ cos60\:=\:\frac{1}{2} $$
mortal sable
huh
bitter kayak
but i need to find H and O and then add them to find the answer
I thought you were calculating the area?
mortal sable
i am
willow bridge
the trigonometric numbers are the same for each angle
have you learned the trigonometry table?
mortal sable
idk maybe
mortal sable
no
willow bridge
then you aren't doing trigonometry
the only other way to solve this is using innkeeper's method
mortal sable
i am doing trigonometry i just havent learned that
mortal sable
i have
im just not that good at it
i just looked through some of my notes and i think i have the sides.
B = 60degrees
C = 14
A = 7
according to my calculations
mortal sable
i did 7/cos(60)
willow bridge
yeah but you must know that cos(60) is 1/2
mortal sable
huh
willow bridge
you said you did 7/cos(60) and got 14
mortal sable
yes
willow bridge
you are allowed to use it or you used it on your own
mortal sable
wdym
willow bridge
are you excepted to use a calculator or are you supposed to do it on your own
mortal sable
im just suppost to do the task
i can use a calculator if i wanna
its homework i just don't know how to do this task
willow bridge
yeah but if it's homework you are supposed to know all the information
if you are supposed to use trigonometry and you have to use a calculator to find sin(60) then you haven't learned trigonometry
I am not trying to be mean or anything, sorry if it sounds that
way
mortal sable
bro i just need to find the numbers
willow bridge
welp since you found that c = 14 you can now just use pythagorean theorem
mortal sable
rn i have the angle(60) and the adjecent(7) and the hypoteneuse(14) and now i need the Opposite
mortal sable
so is it 15,65
wraith daggerBOT
TubyconB
willow bridge
so if that's around 15.65 then it's correct
but that can't be correct because c = 14
and b has to be less than that
mortal sable
i did
1414 = 196
77 = 49
196 + 49 = 245
sqrt 245 = 15,65
now i have the numbers but how do i find the area of it
mortal sable
c^2 - a^2 = b^2
willow bridge
yeah
willow bridge
ok so do you know the formula for the area of a triangle
crimson sedge
In computer science, why do linear congruential generators derive new seed from older seed?
cedar kilnBOT
In computer science, why do linear congruential generators derive new seed from ...
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
crimson sedge
<@&286206848099549185>
cedar kilnBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
celest ledge
Notice that two functions of x, they both increase
crimson sedge
Please only use the <@&286206848099549185> ping **once** if your question has no...
dang
crimson sedge
Notice that two functions of x, they both increase
yes
celest ledge
So…?
It’s obvious then…
I am sorry first one decrease the second one increase
But still
Then the answer is obvious…
One strictly decreases, the other one strictly increases… m=n=1 immediately…
crimson sedge
One strictly decreases, the other one strictly increases… m=n=1 immediately…
so its a
crimson sedge
If we are forced to select one, sure a
ok
thx bro
i thought this will take along time to do
celest ledge
Np
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@456226577798135808> Has your question been resolved?
heck yah
ashen shard
u have to say .close
rain jasper
so im kinda confused where to start on this. For part (a.) I know the answer is 1/2 because I plugged it into mathway but I would like to know why.
rain jasper
one second trying to send some work
but my ipads discord no load
I know that lim x->0 (1-cos(x))/x = 0
thorn lotus
use 1 - cos x = 2 sin^2 (x/2)
foggy merlin
-1 <= cos(x) <= 1
-1 <= -cos(x) <= 1
0 <= 1 - cos(x) <= 2
0 <= (1-cos(x))/x^2 <= 2/x^2
squeeze theorem or anything and done
thorn lotus
then you want to get to a point where you can use lim sin x/x = 1
rain jasper
use 1 - cos x = 2 sin^2 (x/2)
is the substitution of 2sin^2(x/2) just apart of trig?
thorn lotus
yeah. i used the half-angle formula for cos
thorn lotus
I'm guessing you guys already did squeeze thm
thorn lotus
Then just get the limit expression to this and manipulate the location of the limit $2\frac{\sin^2(x/2)}{x^2} \frac{4}{4}$
wraith daggerBOT
TooManyCooks
thorn lotus
1/2 pops right out
river pewter
not urgent. this graph wants me to find points A and B (x,y) using the distance formula where distance is already given. i saw that if i just plug in random values into x1-x2 y1-y2-y1 and see what gives me the equivalent value of the given distance squared then i usually get it right. but its a guessing game and takes too much time. any way to speed things up?
crimson sedge
here is the graph
heard about vectors
and the absolute value of vectors and etc?
of course in 2d lol
cedar kilnBOT
@river pewter Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
spare palm
cedar kilnBOT