and you have that in terms of x,
replace that u with (x^2+2x+7)
#help-10
high lily
and to make the expression more aesthetically pleasing,
factor the constants out to the front
spiral wraith
high lily
2 can be factored out from (2x+2) as well
dense lodge
dont get part e
obtuse pebbleBOT
dont get part e
haughty coyote
Find the modeled depth at 00:00 according to models D and H
Conclude one of them must be wrong
Conclude Jolene's is wrong
obtuse pebbleBOT
@dense lodge Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
pliant bear
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
strange plover
obtuse pebbleBOT
delicate orbit
how to solve this integral?
obtuse pebbleBOT
how to solve this integral?
delicate orbit
$\int \frac{y d y + x d x}{x^2 - y^2 - 2}$
ivory trout
partial fraq decomposition?
warm shaleBOT
tommy
ivory trout
comp sci student here, my calc ain't that great 😭
delicate orbit
why didn't I separate the sum in the num?
I think I could do this by myself
yeah
got it
brain fart lol
.close
timber spoke
I need to prove that, if n is a multiple of 4 but not 8, then sqrt(1+2+3+...+n) is irrational
obtuse pebbleBOT
I need to prove that, if n is a multiple of 4 but not 8, then sqrt(1+2+3+...+n) ...
timber spoke
first i transformed n in 4(2x+1), but then using n(n+1)/2, it becomes 32x^2+36x+10 and i dont know how to continue
high lily
consider factoring out 2, and parity of the expression in parentheses
obtuse pebbleBOT
@timber spoke Has your question been resolved?
timber spoke
yes, factored its sqrt(2(2x+1)(8x+5)), but how do i prove that by plugging every whole number, it will always be irrational?
high lily
consider the parity of
(2x+1)(8x+5)
timber spoke
so it will always be odd?
high lily
the part i mentioned will be odd, yes
timber spoke
but then it will be even because of the 2
high lily
consider the forms of prime factorisations of perfect squares
timber spoke
im sorry, could you explain?
high lily
e.g. what's would be your thought process for determining whether the following are perfect squares
2^2 * 3^2 * 5
2 * 3 * 5^2
(without using a calculator)
timber spoke
they arent because 5 isnt repeated in 1 and in the second 2 and 3
high lily
and same idea for your question
timber spoke
but, for example 4x(8x+1), can be a perfect square if x=1
timber spoke
and this problem is 2*something odd
high lily
yes
timber spoke
so 2(2x+1)(8x+5) cant be a perfect square because there arent same factors?
high lily
because it only has one factor of 2
timber spoke
and the other 2 are not equal
high lily
what the other two factors are doesn't matter
timber spoke
OH I GET IT
high lily
all that matters is that
(2x+1)(8x+5)
is odd and doesn't have a factor of 2
high lily
it could be a perfect square for some x, but that doesn't mean anything
thorny sky
Hi, can you help me with this problem?
obtuse pebbleBOT
Hi, can you help me with this problem?
median yacht
Do you know the equation of the yz-plane?
obtuse pebbleBOT
@thorny sky Has your question been resolved?
thorny sky
Do you know the equation of the yz-plane?
I can't figure it out. I just know that in yz-plane, x=0.
restive jungle
there are two cases, y = constant, or z = constant
thorny sky
Oh right. The equation of the yz-plane must be x=0.
thorny sky
there are two cases, y = constant, or z = constant
Please help
median yacht
I can't figure it out. I just know that in yz-plane, x=0.
Use the scalar product to find the normal of the plane that you want
restive jungle
Please help
since the plane contains 2, 1, 1, the two possiblites are now narrowed down to y=1 and z=1
errrr just try both
median yacht
Use the scalar product to find the normal of the plane that you want
$\vec{u} \cdot \vec{v} = |u||v|\cos(u,v)$
warm shaleBOT
Rub05
median yacht
cos(u,v) can be found because we know that (u,v) is cos-1(2/3)
thorny sky
I don't follow. Im sorry.
restive jungle
since the plane contains 2, 1, 1, the two possiblites are now narrowed down to y...
@thorny sky try this
obtuse pebbleBOT
@thorny sky Has your question been resolved?
thorny sky
<@&286206848099549185>
ember stratus
obtuse pebbleBOT
@thorny sky Has your question been resolved?
obtuse pebbleBOT
@thorny sky Has your question been resolved?
timid silo
how to do this?:√2 sinα-√6 cosα=2 on the interval 0≤α<2π
obtuse pebbleBOT
how to do this?:√2 sinα-√6 cosα=2 on the interval 0≤α<2π
timid silo
ping me if you reply please
btw i want an answer where you arent squaring both sides
i want help to get an answer i mean
<@&286206848099549185>
carmine coral
how to do this?:√2 sinα-√6 cosα=2 on the interval 0≤α<2π
do you need to find alpha?
timid silo
yes
timid silo
reason i dont want to square is
cuz squaring wont help when it comes to finding maximum and minimum of function
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
I think i may have got a solution
Im almsot done
I have a paragraph solution. I think it is right.
rocky goblet
,rccw
timid silo
i got alpha=7pi/12,13pi/12
warm shaleBOT
timid silo
When i decided theya was 5pi/3 i just changed it to -pi/3 because it was easier
theta*
thats why there is a random line in there that says theta is 5pi/3
opinion on my answer?
.close
wooden spire
how can i find the x-intercepts of this? i made the equation equal to zero and tried to solve for x. i turned 1/√x into x^(-1/2)
obtuse pebbleBOT
how can i find the x-intercepts of this? i made the equation equal to zero and t...
short spruce
you shouldn't be using logs when solving for x
wooden spire
you shouldn't be using logs when solving for x
i changed 1/√x into x^(-1/2) and in order to get x by itself, i wanted to do (-1/2)logx
short spruce
how exactly does that get x by itself
wooden spire
to get rid of the -1/2
short spruce
exponents can be dealt with in ways other than logarithms
taking the log of both sides just puts x inside the logarithm, which makes your problem a lot worse
reminder that $x=\frac{a}{b}\implies \frac{1}{x}=\frac{b}{a}$
warm shaleBOT
a disappointing son
wooden spire
what are the values of a and b in this case ?
short spruce
any real number but zero
obtuse pebbleBOT
@wooden spire Has your question been resolved?
hollow jasper
i dont understand this
obtuse pebbleBOT
i dont understand this
hollow jasper
its saying set courses marks prior to eqao as ur independent variable
idk wht tht means
pallid coral
Oh
so basically, that means that the Course Marks Prior are going to be on the bottom, horizontal line and the result (EQAO Marks) as the vertical line
hollow jasper
hollow jasper
so basically, that means that the Course Marks Prior are going to be on the bott...
thats how im going to label them?
pallid coral
Well x is course marks prior i suppose
pallid coral
where is the data
pallid coral
Well that looks like the good answer
pallid coral
Looks correct to me
ya just need to label th axes and make a title
I mean it is a point graph
hollow jasper
so the x axis is course marks before eqao
pallid coral
yeah
hollow jasper
and the y axis is eqao course marks?
pallid coral
yep
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
onyx lodge
what laws can i use to prove that a certain graph does NOT have a hamilton circuit?
obtuse pebbleBOT
what laws can i use to prove that a certain graph does NOT have a hamilton circu...
onyx lodge
<@&286206848099549185>
obtuse pebbleBOT
@onyx lodge Has your question been resolved?
smoky slate
It's an NP-complete problem so you won't find an answer that works for any graph
astral ivy
what laws can i use to prove that a certain graph does NOT have a hamilton circu...
^
There are some tests that you can try though
There were three points that were made in my textbook to show that a graph does not contain a Hamilton circuit:
A graph with a vertex of degree one cannot have a Hamilton circuit.
Moreover, if a vertex in the graph has degree two, then both edges that are incident with this vertex must be part of any Hamilton circuit.
A Hamilton circuit cannot contain a smaller circuit within it.
obtuse pebbleBOT
@onyx lodge Has your question been resolved?
onyx lodge
> There were three points that were made in my textbook to show that a graph doe...
how do i use #3?
does that just mean i can't join vertices if its gonna create a cycle
astral ivy
See the answer for how to use it
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lusty oar
Help somehow my answer for p and q aren’t correct??? Anyone know what I did wrong and what the correct answer is supposed to be?
obtuse pebbleBOT
Help somehow my answer for p and q aren’t correct??? Anyone know what I did wron...
alpine raven
p is 7(2n+2)(2n+3)
alpine raven
if it wasnt I would have told you
lusty oar
if it wasnt I would have told you
hmmm somehow it still says one of my answers isn’t correct…
It’s the ratio test right
warm shaleBOT
Herels
lusty oar
**Herels**
yea that’s what I have too idk what I did wrong for the webwork not to accept it😭
rocky goblet
7/(2n+3)(2n+2) is a bit ambiguous
is it $\frac{7}{2n+3}(2n+2)$ or $\frac{7}{(2n+3)(2n+2)}$?
warm shaleBOT
bee
rocky goblet
if the second one is correct, which it looks like it is, then it might have interpreted what you wrote as the first one, and then said that's not correct
or
wait hang on
they explicitly ask you to write the answer as $\frac{p}{q}$
warm shaleBOT
bee
rocky goblet
they probably want p = 7, q = (2n+3)(2n+2)
lusty oar
they probably want p = 7, q = (2n+3)(2n+2)
RIGHT tysm it worked finally
obtuse pebbleBOT
@lusty oar Has your question been resolved?
quick totem
trail cloak
thick chasm
thick chasm
<@&286206848099549185>
pallid ingot
Hey
Ok so the way to look at this is
Cos(0) = 1
So you get 1 -root1 - 3root 1 etc…
Now no matter what root u are doing … root 1 will always be 1
obtuse pebbleBOT
@thick chasm Has your question been resolved?
tardy epoch
Did you try using Taylor expansion and binomial theorem on each root term
(cos(2x))^(1/2) ~ (1- (1/2)(2x)^2)^(1/2) ~ 1-(1/2)(1/2)(2x)^2 = 1-(1/4)4x^2=1-x^2
thick chasm
Did you try using Taylor expansion and binomial theorem on each root term
Every term?
tardy epoch
(cos(2x))^(1/2) ~ (1- (1/2)(2x)^2)^(1/2) ~ 1-(1/2)(1/2)(2x)^2 = 1-(1/4)4x^2=1-x^...
There should be a very similar pattern to this expansion
tardy epoch
Just do the calculation one cos term at a time
tardy epoch
(cos(2x))^(1/2) ~ (1- (1/2)(2x)^2)^(1/2) ~ 1-(1/2)(1/2)(2x)^2 = 1-(1/4)4x^2=1-x^...
Like this for the first term. Then multiply all of them
timid silo
obtuse pebbleBOT
timid silo
For part 2, the answer should be B, can someone explain why
wooden cipher
Yes
timid silo
oh
wooden cipher
Are you allowed a calculator?
timid silo
should it be 83/234 = x/2000
timid silo
Are you allowed a calculator?
yes
wooden cipher
Yeah, that proportion works
wooden cipher
,w 2000*83/284
warm shaleBOT
timid silo
nevermind
wooden cipher
Can you show how you got 709?
wooden cipher
Oh lol
wooden cipher
Youre welcome, have a good one 
woven badge
obtuse pebbleBOT
restive jungle
Where are you stuck on
fathom flicker
what makes you think it should be E to begin with?
fathom flicker
the limit as x->0 for f(x) definitely does exist
the function graphed is f(x)
but it wants to know for f(1-x^2) instead of for f(x)
so what might you do?
woven badge
well
so we want as x->0 of 1-x^2
so we find x=1
lim x->1 of f(x)
thats not right tho
@fathom flicker
restive jungle
Jesus christ wait x^2 is always positive
restive jungle
That is the trickiest thing i have ever seen
woven badge
COLLEGE BOARD IS WILD
restive jungle
Based
woven badge
also
this isnt related to that question
but say i d
do
$\frac{d}{dx}\int_{0}^{x^2} x ,dx$
restive jungle
Wtf damn
woven badge
bruh
restive jungle
💀
warm shaleBOT
Bubbles
woven badge
finally
restive jungle
That looks really bad
woven badge
ok so when i do this
restive jungle
Mhm
wild swallow
please, don't ever write something like $\ds \int_0^{x^2} x \dd x$
warm shaleBOT
woven badge
wait why 😭
restive jungle
please, don't ever write something like $\ds \int_0^{x^2} x \dd x$
whynot
wild swallow
the notation is nonsensical
woven badge
how else do i write it
rocky goblet
you're using the same letter for two distinct variables, which is very confusing
just use two different letters
wild swallow
[ \int_0^{x^2} y \dd y ]
woven badge
ohhhhh
warm shaleBOT
woven badge
i didnt even realise tha
that
is it ok if i just finish the practice test here and yall tell me if im doing it right
restive jungle
sure
fathom flicker
If the questions are going to take you awhile to complete, I suggest opening a new help channel when you need confirmation for your answer. If not, then continue as you are
woven badge
integral of v(t) from 0 to 2
fathom flicker
I assume you are studying for the AP test, so I might also point out that you would be best suited to really try your best to solve these on your own without any assistance, before asking for any help here. Would probably prepare you better, but do as you wish
woven badge
yeah ur right
im just gonna go though and find the ones i cant do
idk how to do this
dp/dt=kt???
oh seperable differential equation
rocky goblet
(i don't think you actually have to solve the equation if that's what you're saying)
fathom flicker
it's not asking you to solve any of those btw
rocky goblet
we're given some information about the state at noon: how many students have heard the rumor, and how fast P is increasing
these equations relate P to the derivative of P, and exactly one of them is compatible with this information
(i'm not a guy)
woven badge
these equations relate P to the derivative of P, and exactly one of them is comp...
do they expect me to know how to find the differential equaition or to just plug in numbers
fathom flicker
<@&268886789983436800> trolls
woven badge
rocky goblet
...pinging moderators is literally the opposite of backseat modding
woven badge
wait
fathom flicker
Bubbles is studying for an important test, and you are interrupting to troll, it's just immature and annoying. no one thinks it's funny besides you
rocky goblet
(don't just give answers)
woven badge
do yk how to find the logistic differential equation
im so confused bc why did they get the answer right but their trolls
ok
rocky goblet
well you could pretty easily just plug it in to each one, but also if you know that it's going to be $\dv{P}{t} = kP(500-P)$ for a constant $k$ then you can solve what $k$ is from the given information without needing anything else about the answers
woven badge
nvm
warm shaleBOT
bee
woven badge
yo mamma 💀
woven badge
**bee**
alr thx
when i do integral test is the value i get bigger or smaller than the real sum?
nvm i got it
thx for the help everyone
appreciate it
.close
finite token
obtuse pebbleBOT
finite token
having trouble finding the eigenvector for matrix T for the eigenvalue sqrt 5
jolly ginkgo
Why?
jolly ginkgo
It’s supposed to be more simple i think
That's just what you hope for
daring salmon
i dont know how to start
obtuse pebbleBOT
i dont know how to start
jolly ginkgo
Differentiate
daring salmon
4y - 2
worn yoke
you need to do implicit differentiation here
carmine coral
i dont know how to start
3/2 ~ 1.5?
daring salmon
?
carmine coral
am i supposed to tell the answer?
daring salmon
i dont even know the steps or answer
warm shaleBOT
S4MMY
daring salmon
oh wow
carmine coral
4 being constant, you can separate it out and differentiate 'xy'
daring salmon
wdym separate it
carmine coral
not taking it with xy term
daring salmon
i dont understand
daring salmon
you got the derivative of 4xy = 2x - 6
daring salmon
why did you have to make 4xy equal to 2x-6
carmine coral
simply
like
you can do without doing 4xy equal to 2x-6 also
i just wanted the 2x term to be positive
carmine coral
4(-1 + (1)(-1)) = 2
noo
you cant substitute y'
only x and y
y'--> dy/dx
the questions says to find the value of y'
daring salmon
so just plug in for x only?
obtuse pebbleBOT
@daring salmon Has your question been resolved?
blazing tusk
Wait I can do this
blazing tusk
I can write to you
daring salmon
4(-1 + (1)(y')) = 2
carmine coral
4(-1 + (1)(y')) = 2
yep
solve for y'
find its value
thats your answer
and thats what they asked
daring salmon
solve for y'
do i move everything to the right side of y' and then get the derivative of it?
i cant get the answer
obtuse pebbleBOT
@daring salmon Has your question been resolved?
daring salmon
<@&286206848099549185> s
obtuse pebbleBOT
@daring salmon Has your question been resolved?
ornate sky
<@&286206848099549185>
obtuse pebbleBOT
<@&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.
ornate sky
Events A and B are such that P(A)=0.4, P(A|B)=0.25, and P(AUB)= 0.55. Find P(B)
i know very little about probability so id appreciate it if we went step by step
mighty geyser
Since we have the events A, B, we can combine them in various ways
P(A and B)
P(not A and B)
P(A and not B)
P(not A and not B)
so you can try expressing the above information in terms of these four
ornate sky
so U means "and"
ornate sky
i dont get it
mighty geyser
the idea is that A is a set of possibilities, and so is B
so when you union the two sets, you get all the possibilities of A and the possibilities of B, so the event is when A happens or when B happens
ornate sky
ok i got that
what about P(A | B)
or could i disregard that and subtract P(AUB)-P(A)
runic stream
if 2^x=y then 2^x+2=?
obtuse pebbleBOT
if 2^x=y then 2^x+2=?
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
no
mighty geyser
is there missing information?
runic stream
no theres just
mighty geyser
can I check that the question looks like this:
if $2^x=y$ then $2^x+2=?$
warm shaleBOT
Element118
oak bear
it would just become y + 2 then
right?
Is this like a mathematic notation lesson?
Cause that is only an exponential function just moved up by 2
runic stream
should i send the problem?
runic stream
warm shaleBOT
obtuse pebbleBOT
@runic stream Has your question been resolved?
sudden pelican
try write 64 as 2 to the power of smt
runic stream
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
solid flare
was getting help on this earlier, I have the answer key and my answer is also quite near but never the same as on the key. I know I need to look at it as if its asking me at least 3 kings instead of at most three kings
obtuse pebbleBOT
was getting help on this earlier, I have the answer key and my answer is also qu...
@solid flare Has your question been resolved?
solid flare
<@&286206848099549185>
pallid ingot
You need to draw a probability tree are you familiar with those ?
pallid ingot
Ok well
The most important thing to remember in a question like this is that we are using the same deck for all 5 cards delt
And not replacing the cards
solid flare
yep
pallid ingot
So let’s start with first card
We have a 4/52 chance to get a king
And a 48/52 chance to not get a king
solid flare
yes
pallid ingot
Ok let me get on my pc so I can draw something for u
solid flare
thank you
pallid ingot
So this represents the first card beeing pulled
Now scince we are using the same deck and not replacing it , card two will depend on what we get for card 1
pallid ingot
Yes!
The tree would look like this where the green lines represent pulling a king
solid flare
yeah
pallid ingot
So now we do a similar thing for the third pull fourth pull and fifth pull
solid flare
there will be so many options
pallid ingot
Yes but note we really only have to work out the paths which have three geeen lines
Actually sorry take that back
We only need to work out the probability that we pull 4 kings
And minus it from the total probability
Then we will know the probability of having at most 3 kings
solid flare
thats right
pallid ingot
Slightly confusing wording in the question there
solid flare
i didnt think of that
solid flare
Slightly confusing wording in the question there
teacher just trying to make it more difficult
pallid ingot
Note that we have 5 cards to pull and only 4 kings
solid flare
yep
pallid ingot
So the probability tree will still need to be drawn , and all the probability’s of pulling 4 kings need to be added up
pallid ingot
No worries I’ll mark this at solved ?
solid flare
sure
pallid ingot
.solved
rancid cliff
$(\cos(x) - 1)(\cos(x) + 1)$
obtuse pebbleBOT
$(\cos(x) - 1)(\cos(x) + 1)$
warm shaleBOT
Chuti | Spanish
warm shaleBOT
Chuti | Spanish
mellow beacon
yes
wdym by "equal"
there is no equal in the images you posted
do you mean how are the 2 cosines equal?
mellow beacon
ohhh
rancid cliff
(if it is 😄 )
I've written that down in my notes and I dont remember why
I dont understand it
rancid cliff
like what was the process to get to this
mellow beacon
I think you might have the second photo wrong
rancid cliff
also, shouldnt it be
$(cos(x-1))^2$ in either case?
warm shaleBOT
Chuti | Spanish
rancid cliff
why $cos^2(something)$
warm shaleBOT
Chuti | Spanish
rancid cliff
I think you might have the second photo wrong
probably
rancid cliff
mellow beacon
its just distributing
rancid cliff
my professor wrote $cos^2(something) instead of cos(something)^2$
warm shaleBOT
Chuti | Spanish
rancid cliff
whats the difference?
quasi horizon
- For a particle moving in a straight line, its displacement s m from a point O on the line is given by s=t^2-5t+6, where is the time in seconds from the start. Find (a) the initial distance of the particle from O. its initial velocity, (b) (c) when it is at instantaneous rest, (d) at what time(s) after the start it passes through O, (e) the distance travelled in the first 3 seconds.
I have worked the answer from a-d
Answers are
(a) s=6
(b) v=-5
(c) t=2.5 s
(d) t = 2 or t = 3
How to do for (e) please?
obtuse pebbleBOT
3. For a particle moving in a straight line, its displacement s m from a point O...
mellow beacon
3. For a particle moving in a straight line, its displacement s m from a point O...
"(e) To find the distance travelled in the first 3 seconds, we need to find s when t=3 and subtract s when t=0:
s(3) = (3)^2 - 5(3) + 6
s(3) = 0
So, the particle is back at O when t=3 seconds.
Distance travelled in the first 3 seconds is:
distance = s(3) - s(0) = 0 - 6 = -6 meters
Since distance cannot be negative, we take the absolute value and get the particle travelled 6 meters in the first 3 seconds."
honestly, I didnt do any of this
try using chat gpt
quasi horizon
"(e) To find the distance travelled in the first 3 seconds, we need to find s wh...
the answer is 6.5, i tried chat gpt too 😭
mellow beacon
oof then idk
obtuse pebbleBOT
@quasi horizon Has your question been resolved?
toxic hollow
Integrate over the displacement
obtuse pebbleBOT
@quasi horizon Has your question been resolved?
novel geyser
obtuse pebbleBOT
obtuse pebbleBOT
@novel geyser Has your question been resolved?
novel geyser
.close
dense lodge
,rotate
warm shaleBOT
dense lodge
This is uniform rod with weight 20N
When u take moments about C do u just always assume that weight acts in opposite direction to the other forces
sudden garnet
Gravity be like: why am I here, just to suffer?
ruby path
When u take moments about C do u just always assume that weight acts in opposite...
What you should do is imagine pivoting the system about the point that you're calculating the moment about, and rotate it in the direction of the force.
Clockwise rotations are conventionally negative, and counterclockwise rotations are positive
ruby path
In this case, if you pivot the system about C, R_0 is giving counterclockwise torque, while the weight it giving clockwise torque
So their signs would be different
ruby path
The square root gives you the number that multiplying itself with gives you the number under the root
$2^2 = 4 \implies 2 = \sqrt 4$
warm shaleBOT
NEONPerseus
high lily
recognising that 81 = 9 * 9 is sufficient
which is probably how you were able to conclude that the square root of 81 is 9
warm shaleBOT
NEONPerseus
ruby path
Since you know $(-x)^2 = x^2$
warm shaleBOT
NEONPerseus
high lily
for bigger numbers, factorise as a product of smaller numbers if needed
go for the primes if you feel the need
but its more efficient if you can immediately identify perfect square factors
.e.g
$$\sqrt{1600} = \sqrt{16}\cdot\sqrt{100}$$
warm shaleBOT
ℝamonov
ruby path
Well think about it
raven hazel
obtuse pebbleBOT
fervent nexus
Are you aware of law of exponents
raven hazel
Are you aware of law of exponents
No
fervent nexus
like (a^x)^y =a^(xy), where ^ is the raised to sign
raven hazel
like (a^x)^y =a^(xy), where ^ is the raised to sign
Yeah i understand that
fervent nexus
you can use that first in the second question
raven hazel
you can use that first in the second question
so would it be G or F?
fervent nexus
oh, I should have clarified I was talking about the positive exponent question
raven hazel
oh, I should have clarified I was talking about the positive exponent question
did i do it correct so far?
i got c5c4/c3 but with the -2 on the outside dont I flip the whole expression?
and change it to a positive 2?
fervent nexus
now, the negative exponent indicates a reciprocal i.e. you would have to flip the fraction inside to make the -2 into a +2
raven hazel
now, the negative exponent indicates a reciprocal i.e. you would have to flip th...
so it would be (c3/c5c4)^2 as the answer?
fervent nexus
which you did, now you just have to multiply the exponent by 2
fervent nexus
so it would be (c3/c5c4)^2 as the answer?
yes
but, it would not be the complete answer
raven hazel
but, it would not be the complete answer
would I mutiply every exponet by 2?
fervent nexus
yes, before simplify the c^5.c^4 = c^9
raven hazel
yes, before simplify the c^5.c^4 = c^9
so would the final fully simpliefed answer be c6/c18?
cuz i mutiplied by 2
fervent nexus
yes, but can you think of further simplification which leads to a positive exponent
raven hazel
yes, but can you think of further simplification which leads to a positive expon...
1/c12?
fervent nexus
yes correct
raven hazel
as you can further expand G
Thank you bro this is a graded assignment for the alebrga keystone im taking soon so thanks for the help
fervent nexus
no problem, best of luck
obtuse pebbleBOT
@raven hazel Has your question been resolved?
digital geode
How would I solve these with L'Hopital's or is it even possible to? Not sure what the question means by that.
obtuse pebbleBOT
How would I solve these with L'Hopital's or is it even possible to? Not sure wha...
digital geode
Like if it were to be placed in a calculator you would get an answer but how would you solve this by hand and without the knowledge of knowing what the function looks like?
<@&286206848099549185>
fervent nexus
If, the limit is of the form 0/0 or infinity/infinity then L Hospital is applicable
digital geode
would it count if it is 1/0? so for a, no matter how you derive it there will always be the x in the denominator?
and for the b it wouldnt count as l'hopitals?
fervent nexus
nope, has to be 0/0 or infinity/infinity form
jaunty stone
obtuse pebbleBOT
jaunty stone
How does the mark scheme get from equation 1 to equation 2
Cant figure it out
<@&286206848099549185>
jaunty stone
Hello
jaunty stone
explain your query
_no trying to be an ai_
My query is
How does the mark scheme
Go from the first equation to the second
It just skips the steps so i cant figure it out
steel socket
Go from the first equation to the second
try simplifying the first equation
jaunty stone
try simplifying the first equation
I have and cant get it right
rancid sundial
so (a^b)^c = a^(bc)
and then (ab)^c = a^c * b^c
use these two and problem solved
steel socket
I have and cant get it right
Do you know how to use exponent rules?
You have to use exponent rules to simplify it
$(a^b)^c = a^{bc}$
warm shaleBOT
Ars Gratiae
steel socket
Yhyh ik that 1
well, your first step should be to multiply the fractions in the first equation
which will give you $\frac{9x^6y^3}{x^4y^4}$
warm shaleBOT
Ars Gratiae
steel socket
But cant get to the answer
Now, cancel out the common factors
jaunty stone
Now, cancel out the common factors
Whats y^3/y^4
warm shaleBOT
Ars Gratiae
jaunty stone
use exponent rules to figure that out
Yhh but wont it be y^-1
jaunty stone
So im at
jaunty stone
y^-1 is just 1/y
x^2 x 1/y = 4
steel socket
x^2 x 1/y = 4
$\frac{x^2}{y}=4$
warm shaleBOT
Ars Gratiae
steel socket
x^2 x 1/y = 4
do you think you can turn this into $x^2=4y$?
warm shaleBOT
Ars Gratiae
sonic charm
Doing a piece where i am proving that pi is irrational. I need to write the formulas for f^n(0), f^{n+1}(0), f^{n+2}(0), f^{2n}(0) where n is the n'th derivative and apparently the second image has the wrong equations. Anyone that can check it out and see why its wrong?
obtuse pebbleBOT
Doing a piece where i am proving that pi is irrational. I need to write the form...
@sonic charm Has your question been resolved?
obtuse pebbleBOT
@sonic charm Has your question been resolved?
obtuse pebbleBOT
@sonic charm Has your question been resolved?
obtuse pebbleBOT
@sonic charm Has your question been resolved?
sonic charm
.close
last basin
Can someone explain this to me?
obtuse pebbleBOT
Can someone explain this to me?
woven badge
Can someone explain this to me?
say i have a 2 cubes 1 with side length x one iwth side length y
the ratio of sides is x:y
ratio of surface area or bases is x^2:y^2
ratio of volume is x^3:y^3
does that help
acoustic parrot
obtuse pebbleBOT
acoustic parrot
Is this no?
i found some formula where its like
n(n-1)/2
so 10(10-1)/2 which is 45
so minimum amount of edges for 10 vertices is 45?
warm canopy
well the minimum amount of edges is 0
acoustic parrot
isnt it 45
odl
idk
this is for a connected multigraph or whatever its called
warm canopy
the minimum amount of edges, is just no edges
warm canopy
graphs dont need any edges
acoustic parrot
ok
assume this graph
that i need to form
needs edges
and it needs 10 vertices
and it needs to be a connected multigraph
warm canopy
okay even if you assume it has to be connected, the minimum still isn't 45
acoustic parrot
ok maybe im thinking about it wrong
instead of minimum
is 42 edges too much
for 10 vertices
warm canopy
also if you're assuming its a multigraph, then it can have pretty much any amount of edges
then you should be thinking about what the maximum number of edges is
which is what your formula tells you
warm canopy
indeed
acoustic parrot
ok i kinda get it
also
im kinda interested
how would you go to start this problem
cause i was told earlier to do
20k - 1^523
so then do 19 x 424, which last digit wouild be 6
warm canopy
lol you are free to choose your own number system, work over mod 424 and then its just 0
i have no idea what you're doing
acoustic parrot
idek what that number system is called
LMAO
someone told me earlier thats a method of doing it
i know anjother method where its like
19^1 = 9(ends in 9)
19^2 = 1(ends in 1)
19^3 = 9(ends in 9)
19^4 = 1(ends in 1)
so because its odd
restive jungle
lol you are free to choose your own number system, work over mod 424 and then it...
you are a genius
acoustic parrot
then its just 9 x 4
warm canopy
19^1 = 9(ends in 9)
19^2 = 1(ends in 1)
19^3 = 9(ends in 9)
19^4 = 1(ends in 1...
i mean yeah this is fine
acoustic parrot
idk i hope my teacher doesnt thhink thats the noob way
warm canopy
who cares
acoustic parrot
as long as i get points tbh
plus
he makes us do problems super weirdly sometimes
like
idk if you have ever counted puppies before
for these type of questions
cause i try proving combinatorially for this and i get like
your friend has n+5 puppies
n red puppies
5 blue puppies
so the way to count them would either be like
count (n+5) puppies (left side)
or way 2:
count red puppies (n)
count blue puppies (5)
or count a mix (n x 5)
but idk if that proves its equal to n+5
.close
ornate sky
if somebody could walk me through it that would be great
<@&286206848099549185>
anyone?
tight hatch
first paper do cos inverse of 2/3 to find theta, then sub theta back into sin and sin2
obtuse pebbleBOT
@ornate sky Has your question been resolved?
ornate sky
.close
coral shale
Hello
coral shale
I need help
A tangent and a secant is drawn from an external point P of circle O with radius 4.5 units. The secant passes through the center of the circle at point O. if the tangent segment has length 2 more than the external segment of the secant, what is the length of the tangent segment?
obtuse pebbleBOT
@coral shale Has your question been resolved?
dark stirrup
A tangent and a secant is drawn from an external point P of circle O with radius...
what have you tried?
coral shale
what have you tried?
I haven't
coral shale
what have you tried?
can you help me visualize it?
dark stirrup
What can you draw on your own, and where do you get lost?
coral shale
What can you draw on your own, and where do you get lost?
Let me show you
Idk if its right tho
dark stirrup
You drew it perfectly
Students seem to forget "power of a point" theorem.
Looking it up may really benefit you
coral shale
You drew it perfectly
so is it x(9 + x) = (2 + x)^2?
coral shale
so is it x(9 + x) = (2 + x)^2?
Can the answer be less than 1?
dark stirrup
yeah why not?
coral shale
yeah why not?
Is the answer 0.4?
dark stirrup
Is the answer 0.4?
!show
obtuse pebbleBOT
Is the answer 0.4?
Show your work, and if possible, explain where you are stuck.
dark stirrup
$(a+b)^2\ne a^2+b^2$
warm shaleBOT
SWR
dark stirrup
coral shale
https://en.wikipedia.org/wiki/Freshman%27s_dream
forgot (x + 2)^2 = to x^2 + 4x + 4
the order made me confused
so its 0.8?
Lets goooo I got it!!
Thank you good sir @dark stirrup !
.close
wicked stream
obtuse pebbleBOT
dark stirrup
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
wicked stream
I follow the formula for integral
a^2=4; a = 2
u^2=9x^2; u=3x
Then I plug in u and a
and idk where does the 1/3 in the answer comes from
uneven palm
Something they don’t always tell you is that you’re doing a u-sub when using that identity
uneven palm
u = 3x
1/3 du = x dx
red surge
so 1/3 outside the integral
dark stirrup
a^2=4; a = 2
u^2=9x^2; u=3x
Then I plug in u and a
You did u=3x, but did not consider du and dx
obtuse pebbleBOT
uneven palm
gl on the exam tmr
wicked stream
thank you!
obtuse pebbleBOT
Available help channel!
hoary jolt
am i missing something or is this the exact same question
obtuse pebbleBOT
am i missing something or is this the exact same question
trail musk
Almost, but there's a subtle difference
Notice how c has an x component of -9, a y component of -5, and a z component of 1
But d has an x component of -9, a y component of -5, and a z component of 1 instead
hoary jolt
Almost, but there's a subtle difference
they both have a z component of 1 do they not
timid silo
obtuse pebbleBOT
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
1
nocturne minnow
You can form an equation, based on <1, <2, and the overall angle, do you see that?
nocturne minnow
.close if you are done
timid silo
.close
lavish drum
send help lol
obtuse pebbleBOT
send help lol
fervent nexus
A fundamental period is the smallest positive period of the function
warm shaleBOT
nocturne minnow
One, we aren't here to give out answers.
Two, if you know it's not math, why are you asking a non math related question?
You can ask in a stem server
fathom bridge
nocturne minnow
Look them up
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
mellow crest
obtuse pebbleBOT
@mellow crest Has your question been resolved?
half crown
@royal basin
royal basin
???
half crown
u know how to solve it?
obtuse pebbleBOT