Why cant it be simple
#help-10
junior pebble
timid silo
I'm quite tired right now so I cannot really explain.
junior pebble
If you want to convert then just subtract by90 right ?
timid silo
Subtract from 90, yeah.
dreamy scroll
why did this become like this haha
obtuse pebbleBOT
why did this become like this haha
dreamy scroll
also how to indentify which y's will be given respect to
where did the 2 in the denominator come from haha
fervent cradle
ok so
on the left you're differentiating (y + x)^0.5
so you get a 0.5 out of it after differentiating
which is a 2
what else are you confused about?
dreamy scroll
.reopen
obtuse pebbleBOT
✅
dreamy scroll
what else are you confused about?
my bad i fell asleep a bit ;-;
wait what
im sorry i can visualize what you jkust said
devout sable
im sorry i can visualize what you jkust said
because derivative of f(x)^0.5
,w derivative of x^0.5
warm shaleBOT
devout sable
power rule
dreamy scroll
the derivative of sqrt of x is 1/2sqrt of x?
devout sable
np 
dreamy scroll
why did it become y prime plus 1 ;-;
obtuse pebbleBOT
@dreamy scroll Has your question been resolved?
brisk matrix
the derivative of y+x is y’+1
so when you do the chain rule on sqrt(y+x) you get $\frac{y’+1}{2\sqrt{y+x}}$
warm shaleBOT
maximo
dreamy scroll
chain rule ?
warm shaleBOT
maximo
dreamy scroll
ouch my brain
brisk matrix
in your example this yields: $$\frac{d}{dx}\sqrt{y+x}=\frac{1}{2\sqrt{y+x}}\cdot \frac{d}{dx}(y+x)$$
warm shaleBOT
maximo
brisk matrix
which is exactly what you had above
obtuse pebbleBOT
@dreamy scroll Has your question been resolved?
wicked shuttle
Can anyone explain to me how to write > and <, I keep forgetting which one means what
obtuse pebbleBOT
Can anyone explain to me how to write > and <, I keep forgetting which one means...
wicked shuttle
I have the function f(x)=x^2-7x+12
We know that the function is positive when x is bigger than 4 or less than 3
I keep forgetting which > < means less than and which means more than and how to write it
kindred oasis
The sign points towards the smaller value
Bigger>smaller
Smaller<bigger
Is that what you're asking?
wicked shuttle
Yes
kindred oasis
I keep forgetting which > < means less than and which means more than and how to...
And what do you mean by "how you write it"?
wicked shuttle
If we know that the function f(x) is positive when bigger or equal to 4, and positive when less or equal to 3, how do I write it as a difference with x in the middle
Like f(x) = 3<x>4?
wicked shuttle
Oh
kindred oasis
"V" means "or"
wicked shuttle
So I can’t merge it into one function?
kindred oasis
No
wicked shuttle
Why not?
kindred oasis
It makes no sense to write 3<x>4
It does if x is between 3 and 4, in which case you would write 3<x<4
kindred oasis
It makes no sense to write 3<x>4
But that's just not correct
kindred oasis
Yes
wicked shuttle
And if the clams? change direction, the values need to switch sides?
kindred oasis
And if the clams? change direction, the values need to switch sides?
Wdym?
wicked shuttle
Like, 1 is always less than 4, so 1<4, but if the clam(?) points the other way, like >, then the values switch sides so 4>1
kindred oasis
Yes
wicked shuttle
Is it called a clam?
kindred oasis
No idea
wicked shuttle
Or what’s the technical term in English?
kindred oasis
It probably doesn't have a name, I'm not from an English speaking country though, so I'm not sure
kindred oasis
We don't really give it a name, but sometimes teachers might do it with their students to help them memorize it
timid silo
obtuse pebbleBOT
timid silo
hmm how can i prove the 1/4 part? i was only able to prove that it is inferior or equal to 1 but not 1/4 (m and n are natural numbers greater than zero btw)
icy drum
Can I get help here?
Make ur own channel
magic finch
oh
kindred oasis
icy drum
hmm how can i prove the 1/4 part? i was only able to prove that it is inferior o...
Try using induction. First prove it works when m is 1, then prove it with m increasing
timid silo
Try using induction. First prove it works when m is 1, then prove it with m incr...
yeah that should be it , i will see if i can prove it
i'm struggling trying to prove the p(n+1) , i can't seem to make good use out of assuming that p(n) is correct
its easy to prove that mn/(m+n+1)^2 < 1/4 but the + n/(m+n+1)^2 is giving me a headache
obtuse pebbleBOT
@timid silo Has your question been resolved?
candid stirrup
hmm i think there is potential looking at the sign of (mn)/(m+n)² - 1/4
if you find it's negative gg
it works for me
@timid silo
timid silo
hmm i think there is potential looking at the sign of (mn)/(m+n)² - 1/4
great find , and it worked for me aswell! thanks alot
.close
fickle orbit
obtuse pebbleBOT
fickle orbit
where has two come from (7.a )
bro i wont be able to sleep unless i get this shit done
im actually pissed
obtuse pebbleBOT
@fickle orbit Has your question been resolved?
fickle orbit
pretty sure they just added 2
so u factorise to get equation below and +2 and it makes sense
obtuse pebbleBOT
@fickle orbit Has your question been resolved?
tardy epoch
.close
timid silo
last question partial fraction and then binomial expansion how do I do it? pls and thank you <@&286206848099549185>
obtuse pebbleBOT
last question partial fraction and then binomial expansion how do I do it? pls a...
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
real prawn
last question partial fraction and then binomial expansion how do I do it? pls a...
well for partial fractions you can do this:
$$ \dfrac{x}{(1+x)(1-2x)} = \dfrac{A(x)}{1+x} + \dfrac{B(x)}{1-2x} $$
after this you can merge those two fractions on the RHS, and then equate the numerators on both LHS and RHS, solve that and find A and B.
warm shaleBOT
agilepotato
timid silo
I've obtained values that could be A or b
one is -1 and 3/4 and other set is
-1\3 and 1\3
obtuse pebbleBOT
@timid silo Has your question been resolved?
eternal cloud
obtuse pebbleBOT
simple stone
obtuse pebbleBOT
cedar lichen
What have you tried
obtuse pebbleBOT
@simple stone Has your question been resolved?
simple stone
What have you tried
i tried to calculator no work
cedar lichen
What does (f - g)(x) mean?
simple stone
What does (f - g)(x) mean?
idk its from my gr 10 friend
cedar lichen
Why are you asking it in their stead
cedar lichen
(f - g)(x) is another way to write f(x) - g(x)
simple stone
ok
cedar lichen
So what's f(x) - g(x)?
obsidian atlas
obtuse pebbleBOT
obtuse pebbleBOT
@obsidian atlas Has your question been resolved?
obsidian atlas
.close
exotic palm
obtuse pebbleBOT
exotic palm
I don’t know how to continue from here
twin sapphire
what are you supposed to do?
wooden cipher
find dy/dx i think
exotic palm
yeah
wooden cipher
you have to clear the denominator and then you can isolate dy/dx
twin sapphire
you could also add (x² dy/dx )/(x+y)² on both sides
basically replace dy/dx by A
and solve for A
if its confusing
exotic palm
hmm
alright
??
my numerator is wrong somehow , hmm
nvm , i didnt subtract 2x^2 - x^2
ty
.close
sterile bluff
hey
sterile bluff
quick question
if a matrix
a b c
d e f
g h k
had a det of 5
what would the det be
if the matrix was
a b c
d-a e-b f-c
g h k
is it just 5
unborn sonnet
Well, we dont know for sure
Unless we work it out
As long as d-a e-b f-c is not a multiple of a b c, then yes
Otherwise the determinant would be 0
unborn sonnet
Well then its just a case of painstakingly working out the question
I dont see a shortcut here
next dagger
not really, no
work out the determinant symbolically, set that to the specified value, and then solve for unknowns
however
next dagger
in the second case, where it's $\begin{vmatrix}
a& b & c\
d-a&b-e &f-c \
g &h &k
\end{vmatrix}$, that'll be the same as $\begin{vmatrix}
a& b & c\
d&b &f \
g &h &k
\end{vmatrix}$
warm shaleBOT
rome of oxtrot
sterile bluff
if there was a row swap it would be negative 5
next dagger
the row operation that changes the middle row is invariant in the determinant
subtracting row 1 from row 2 does not change the determinant
unborn sonnet
Ow right, i see, i was missing that the index of matrices starts uneven (programmed like 5mins ago)
next dagger
the determinant is independent of choice of basis, and so a row operation that is equivalent to a change of basis does not change the determinant
unborn sonnet
True
sterile bluff
the only row operations that effect the determinant
next dagger
and adding a scalar multiple of one row to another row is equivalent to a change of basis
next dagger
yes, row swap flips the sign and scalar multiples scale the determinant
sterile bluff
okay sweet thank yo
obtuse pebbleBOT
Available help channel!
pastel jackal
obtuse pebbleBOT
pastel jackal
is the equilibrium point the value of t when s(t) = 0?
or when velocity = 0
<@&286206848099549185>
obtuse pebbleBOT
@pastel jackal Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
near meteor
obtuse pebbleBOT
sterile bluff
well
if you do
-6^2
the answer is -65
and
(-6)^2 = 36
so therefore would be 7
near meteor
yea i figured that out but now im confused on this
would u be able to help
this is the function
this is the question
im confused on what i would do
how would i substitute radical 6 for x?
sterile bluff
im confused on what i would do
like this
obtuse pebbleBOT
@near meteor Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
runic thunder
obtuse pebbleBOT
runic thunder
How do i solve this
so f(x) = (1/27(x)^5)+(2/27(x)^3)
and f’(x) = (5/27(x)^4)+(6/27(x)^2
then i got lost trying to find the inverse
runic thunder
f(f^-1(x)) = x
f^-1(f(x)) = x
and if f(x) = (a,b)
then f^-1(x) = (b,a)
the a value is -11?
so
f(x) = (-11,b)
f^-1(x) = (b,-11)
to find the "b" i can plug i can plug the x/a (-11) in the f(x) equation
f(x) = 1/27(-11^5 + 2(-11)^3)
so f(x) = (1/27(-11)^5)+(2/27(-11)^3)
so y = (1/27(-11)^5)+(2/27(-11)^3)
i domt think our teacher would want us to mentally do (-11)^5 so this way isn’t correct
Also how is this correct
Wouldnt that mean
f(x) = f^-1(x)
obtuse pebbleBOT
@runic thunder Has your question been resolved?
fossil crag
I think the picture you took meant f^-1(y) = x
Actually the picture is really confusing I'll admit, using color to represent different variables is very bad
fossil crag
Not easy
fossil crag
If you have P a polynomial such that P(a) = 0, then the polynomial (x-a) divides P
fossil crag
But you want f^-1'(-11), not f^-1(-11)
eager kiln
-297 = x^5 + 2x^3
Use a smart calculator to solve it for you. There must be a better way tho out there
fossil crag
Use a smart calculator to solve it for you. There must be a better way tho out t...
That... defeats the purpose of the exercice
fossil crag
You want to prove that x1 exists, not its actual value
runic thunder
Which is where i end up getting to
-297 = (x1)^5 + 2(x1)^3
(The 1/2 are just subscript)
fossil crag
If you do want an exact value, you just got it, it's -3
runic thunder
Ya but in this case it was easy to guess it
And there was probably another way i was meant to get to that
fossil crag
If you stubbornly want to proove that it's the only one, use the Intermediate value theorem
And its corollary
runic thunder
Am i even solving this the right way?
runic thunder
.
fossil crag
You dont need f^-1(-11) to get to [f^-1]'(-11)
You just want to know that f^-1(-11) exists
runic thunder
so i derive f(x) first
fossil crag
Yes
runic thunder
That would be f’(x) =5/27(x)^4 + 2/9(x)^2
fossil crag
Then you get the expression for [f^-1]'(a)
Oh actually nevermind you do need the value for f^-1(a) xd
You need it because of 1/f'(f^-1(a))
runic thunder
Which is where i end up getting to
-297 = (x1)^5 + 2(x1)^3
ya f^-1(x) would be what i was doing?
fossil crag
After you plug in f^-1(a) = -3, you get [f^-1]'(a) = 1/f'(-3) = ...
fossil crag
ya f^-1(x) would be what i was doing?
You already got -3. If you want to verify it's the only one use intermediate value theorem or solve the remaining polynomial factoring by (x+3) and plugging y = x²
runic thunder
then i plug in -3 as the x in
f^-1(x)= 5/27 (x) ^4 + 2/9 (x) ^2
f^-1(x)= 15 + 2
1/0 so DNe?
fossil crag
Lemme check
runic thunder
ok
fossil crag
Remember to put parentheses
runic thunder
Not easy
Ima just ask my teacher tmr if I could get to -3 without needing to guess and check tmr
fossil crag
1/[27(-3)⁴ + 2/9*(-3)²] = 1/2189
runic thunder
Remember to put parentheses
Oh did i miss some?
fossil crag
What is f' ?
runic thunder
then i plug in -3 as the x in
f^-1(x)= 5/27 (x) ^4 + 2/9 (x) ^2
Wait the first term didnt even = -1 here
fossil crag
Lemme check
runic thunder
f = 1/27(x^5+2x^3)
fossil crag
f'(-3) = 5/27*81 + 2 = 17
runic thunder
f = 1/27(x^5+2x^3)
1/27(x)^5 + 2/27(x)^3
fossil crag
So (f^-1)'(-11) = 1/17
runic thunder
f^-1(x)= 15 + 2
.
fossil crag
That's not correct. What is even x ?
runic thunder
-3?
fossil crag
Look
Let's start over
You found f^-1(-11) = -3
You also calculated that f'(x) = 5x⁴/27 + 2x²/9
So f'(-3) = 5 × 81/27 + 2 × 9/9 = 15 + 2 = 17
So [f^-1]'(-11) = ?
fossil crag
Yes 1/17
runic thunder
f^-1(x)= 15 + 2
So i didnt seperate the term
I just divded the coefficient by 27 instead the x aswell
runic thunder
then i plug in -3 as the x in
f^-1(x)= 5/27 (x) ^4 + 2/9 (x) ^2
.
Oh i see i added the numerator instead of multiplying
obtuse pebbleBOT
@runic thunder Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lunar rover
Hey, im trying to figure out trigonometry, for example to calculate sinus, cosinus and tangens (I hope this is correct as im not used to do math in english), as an example they are showing this picture, and the second picture how to calculate it.
obtuse pebbleBOT
Hey, im trying to figure out trigonometry, for example to calculate sinus, cosin...
lunar rover
In the example they get this, but they dont explain how the cos48 = 0,6691, any help with that?
random depot
Sinus
Cosinus
Tangens
Sorry
lunar rover
?
timid silo
In the example they get this, but they dont explain how the cos48 = 0,6691, any ...
yeah
cos is the adjacent line ÷ hyp
which is b ÷ 5.9
lunar rover
Yea I know the formula, but where did they get the 0,6691 from?
timid silo
you can do it on a calculator :))
lunar rover
I mean that is literally what I am asking, how do you get that number/How to calculate it
timid silo
it has something to do with the radians
im not too educated about that part
but for now, adjacent line ÷ hyp
high lily
chuck cos48 into a calculator
lunar rover
Again, I know the formula, they are multiplying the hypotenusa with the 48 angle
to get b
high lily
,w cos(48deg)
lunar rover
the cos-1 ?
warm shaleBOT
lunar rover
I got error domain lol
high lily
what exactly are you chucking into the calc
lunar rover
oh my bad I was doing cos -1
when I did cos(48) on the calculator I got -.6401443395
high lily
make sure the calc is set in degrees
lunar rover
let me look it up then I dont know how to do that
lunar rover
yah
high lily
what brand calculator are you using
lunar rover
Ok i got it
TI-83
I got the correct answer
It also has a second button for cos^-1 whats what used for?
simple viper
open
proven zephyr
sesame
simple viper
No no
sorry
image is
idk why
sorry
one sec
there we go
ill show my working too hold on
scarlet osprey
typical trigo question
scarlet osprey
the question does have few typo for sure
simple viper
hmm?
simple viper
maybe we doing wrong
scarlet osprey
maybe the question is ill-framed. if it was BC instead of CB, all the mentioned can be proved
But since it's CB, we'll surely assume that the question creator meant that CQ:QB::1:2
simple viper
So we assumed ratio wrong?
scarlet osprey
the question's having an error
simple viper
the question's having an error
I mean BC and CB is same tbh
scarlet osprey
Well, order of points would matter when you say that you're dividing it in unequal parts
timid silo
how do i integrate this
obtuse pebbleBOT
how do i integrate this
sage geode
Yes but don't forget to divide by 3
du = 3dx, dx = du/3
And later you'll have to convert u back into x
sage geode
Yes you have to divide it by 3
timid silo
so this
sage geode
You can also simplify 6/0.5
sage geode
Yeah
glass mason
Hello
glass mason
Identify the horizontal and vertical asymptotes of the graph of the function. Then state the domain and range.
short yarrow
4(3x+1)^0.5 <@917799892833927219>
hmm
glass mason
<@&286206848099549185>
short yarrow
domain:
R - {-1/3}
range:
R - {2/3}
and idk what are are asymptotes so....
sed
glass mason
.reopen
obtuse pebbleBOT
✅
glass mason
💀 *
tulip kestrel
what is your question?
glass mason
Identify the horizontal and vertical asymptotes of the graph of the function. Th...
@tulip kestrel this
tulip kestrel
<@477880016869523456> this
but what is your question about it?
tulip kestrel
i'm just asking how can i help , what steps are you stuck on
and show me your work if you have any
tulip kestrel
sry
no problem and pls don't laugh anymore at other people in this server
we try to encourage people to ask not discourage
short yarrow
no problem and pls don't laugh anymore at other people in this server
i just laughed at ur question sed
anyways fine
👍
🤝
obtuse pebbleBOT
@glass mason Has your question been resolved?
radiant merlin
if you have 4 box, and 2 ball. how many different way can you put the ball?
glass mason
i'm just asking how can i help , what steps are you stuck on
I just need the domain and range
lean trail
if you have 4 box, and 2 ball. how many different way can you put the ball?
2*(4C2)ways
radiant merlin
2*(4C2)ways
C?
radiant merlin
So 12 ways
the answer should be 6 tho, since the ball is the same
lean trail
4!/((4-2)!*2!)
manic wigeon
Laplace inverse, how do i solve this one? tried applying the property but didnt work
obtuse pebbleBOT
Laplace inverse, how do i solve this one? tried applying the property but didnt ...
manic wigeon
having trouble visualizing how does that translate to f(t)
id probably go for b-a/(s+a)(s+b)
short skiff
It'd be preferable to decompose this function into simpler functions so that you can use the inverse Laplace transforms on each of them.
Are you familiar with partial fraction decomposition?
manic wigeon
oh thats probably why im having trouble, im not familiar
short skiff
May I solve the example in the picture I showed to explain the idea?
short skiff
Let's try to expand $\frac{7x - 23}{(x - 2)(x - 5)}$ into $\frac{A}{x - 2} + \frac{B}{x - 5}$: $\$
First, we'll modify the right-hand-side such that it has the denominator $(x - 2)(x - 5)$ as well:$ $\$
$\frac{A(x - 5) + B(x - 2)}{(x - 2)(x - 5)} = \frac{(A + B)x + (-5A - 2B)}{(x - 2)(x - 5)}$. $\$
Now, in order for the transformation to be valid, the two sides have to be equivalent. This means that the two terms in the numerators, which are $7x - 23$ on the left-hand-side and $(A + B)x + (-5A - 2B)$ on the right-hand-side would be the same. This means the coefficients should be the same, so we get: $\$
$\begin{cases} A + B = 7 \ -5A - 2B = -23 \end{cases} $\$
And this should tell you what $A$ and $B$ should be.
warm shaleBOT
RoiKadmon
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
manic wigeon
🤔 gonna work on it
short skiff
I'll isolate the equation which got messed up: $\frac{A}{x - 2} + \frac{B}{x - 5} = \frac{A(x - 5) + B(x - 2)}{(x - 2)(x - 5)} = \frac{(A + B)x + (-5A - 2B)}{(x - 2)(x - 5)}$
warm shaleBOT
RoiKadmon
manic wigeon
**RoiKadmon**
i understand it
so in my case it would be something like s/s+1 and 5/s+4
and then i can solve it
short skiff
You'll have to separate the functions to know exactly what the numerators of the $s + 1$ and $s + 4$ fractions will be, but at the end, it's going to look something like: $\$
$\frac{A}{s + 1} + \frac{B}{s + 4}$ $\$
where $A$ and $B$ are real numbers, and then you can apply the inverse transformation on each of these.
warm shaleBOT
RoiKadmon
short skiff
Good luck! Let me know if you get stuck.
short skiff
Let's try to do the same thing as last time: $\$
$\frac{s + 5}{(s + 1)(s + 4)} = \frac{A}{s + 1} + \frac{B}{s + 4}$ $\$
Now, we rewrite the right-hand-side such that the numerator will be $(s + 1)(s + 4)$ as well: $\$
$\frac{A}{s + 1} + \frac{B}{s + 4} = \frac{A(s + 4) + B(s + 1)}{(s + 1)(s + 4)} = \frac{As + 4A + Bs + B}{(s + 1)(s + 4)} = \frac{(A + B)s + (4A + B)}{(s + 1)(s + 4)}$ $\$
Now, we say that the two expressions in the numerator must be equivalent: $\$
$s + 5 \equiv (A + B)s + (4A + B)$ $\$
And thus, the respective coefficients are the same: $\$
$\begin{cases} 1 = A + B \ 5 = 4A + B \end{cases}$
warm shaleBOT
RoiKadmon
manic wigeon
oh i think i see where i got it wrong
i was assuming s = a and 5 = b
gonna try again 🙂
ok understood that
but what after i find that (a+b)*s + (4A+B) / (s+1) (s+4) = s+5/ (s+1) (s+4)
im having trouble finding the property that i should use for this one
the next step would be to redo the fraction decomp assuming a 1 and b 5?
manic wigeon
the next step would be to redo the fraction decomp assuming a 1 and b 5?
i found 6s+9 / (s+1) (s+4)
got it!!!!!!
tyvm 🙂
i was messing up on the frac decomp
short skiff
I'm sorry for responding late.
Best of luck, and keep in mind:
The higher the degree in your numerator and the denominator, the more terms you'll have to break the fraction down to. The general idea is to have a factor for each term and go up in powers, as is the case with x - 3 here:
obtuse pebbleBOT
@manic wigeon Has your question been resolved?
lean trail
.close
pale gulch
hi apparently the x value from O to P is 1/2, im not sure why
obtuse pebbleBOT
hi apparently the x value from O to P is 1/2, im not sure why
pale gulch
like just because theres a right angle between the perpendicular line and the circle line doesnt mean its in the middle
oh nvm
it must have something to do with the perpendicular line having an intercept at 2,0 i assume
not sure why tho
turbid wing
hi apparently the x value from O to P is 1/2, im not sure why
the centre points are (0,0) right?
obtuse pebbleBOT
@pale gulch Has your question been resolved?
pale gulch
the centre points are (0,0) right?
yea
turbid wing
from the equation of the circle, the radius comes out to be 1
so how can the distance be 1/2 from O to P
since OP is the radius
vagrant pine
x3+y3+z3=k
obtuse pebbleBOT
x3+y3+z3=k
vagrant pine
my math teacher told the class whoever solves it right gets 100 precent
royal basin
did your math teacher also give instructions as unclear as you just wrote?
did they just write the equation on the board and nothing else?
vagrant pine
wdym
lean trail
x=y=z=1; k=3
royal basin
there is only an equation that your math teacher decided to write out and refuse to clarify further
also are those threes meant to be exponents
lean trail
x=y=z=1; k=3
Give this one solution to your teacher as an example. There are infinite solutions to this equation as we only have 1 equation involving the 4 variables
timid silo
x3+y3+z3=k
Is k also a variable
royal basin
well "solves it right" could mean "solves the problem i had in mind but refused to write out and will refuse to clarify", so...
lean trail
Maybe the point is that no one gets 100% because there is no problem to solve and the teacher is messing with y'all
royal basin
there is only an equation that your math teacher decided to write out and refuse to clarify further
obtuse pebbleBOT
@vagrant pine Has your question been resolved?
lean trail
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idle slate
Yo
idle slate
I don’t get it guys
dim patio
Don't get what
dim patio
The width should be double that of the radius of a single wire
idle slate
I think the answer is 3.55
Cuz we have to find the radius
And the diameter is half the of the object or what’s ever it is , we did die by 2 then we find the answer so we get the Raduis
14.2/2
Answer /2
Is this correct?
fossil crag
What is the width of a single wire in terms of its radius ?
obtuse pebbleBOT
@idle slate Has your question been resolved?
idle slate
What is the width of a single wire in terms of its radius ?
We gotta divide 14.2 by 10
Then we find the answer then we divide by 2
Then some
Done*
fossil crag
Yes
lilac heart
Hi
fossil crag
So the radius is 14.2mm/20
lilac heart
Could you please help me
pale gazelle
obtuse pebbleBOT
pale gazelle
this statement is false right?
civic zealot
nope, that's true.
timid silo
think about the negation of the statement:
$\exists \epsilon > 0: \forall s \in S: t - \epsilon ≥ s$ or $s>t$
warm shaleBOT
rbit ✨
timid silo
can s > t ever be true?
pale gazelle
oh i see t - eps would imply that is the supremum right?
timid silo
yes
civic zealot
.close
obtuse pebbleBOT
civic zealot
oh... i didn't know I could do that.
viral blade
civic zealot
must be
obtuse pebbleBOT
Available help channel!
lapis oasis
obtuse pebbleBOT
lapis oasis
what equation do u use for this
sage geode
When an object is dropped, then its height can be represented as h - gt^2, where h is the initial height and g is 9.8m/sec^2 (and t is in seconds)
So, since the height of the object got to 0 (because it hit the ground) after 1.5seconds of being dropped
Therefore h - g(1.5)^2 = 0
All you need to do it to solve for h
sage geode
Show your work
lapis oasis
i got 72
sage geode
g is 9.8
sage geode
Is the answer not 72?
lapis oasis
no
sage geode
Are you sure it's in feet?
lapis oasis
yeas
obtuse pebbleBOT
@lapis oasis Has your question been resolved?
dark orchid
obtuse pebbleBOT
https://media.discordapp.net/attachments/903430332324405288/1026920453882789908/...
dark orchid
How to solve number 4?
gray creek
Sry
high lily
you messed up signs when skipping steps
dark orchid
you messed up signs when skipping steps
skipping steps?
high lily
also you should have a few subscripts in the point slope formula
nocturne minnow
Yes, what's x - -6 equal to?
dark orchid
Yes, what's x - -6 equal to?
yeah that always confused me. +6
high lily
you made an algebraic mistake going from
y-9 = -5(x- -6,)
the the following line
dark orchid
so then, -30
high lily
yeh
obtuse pebbleBOT
high lily
$$y - y_1 = m(x - x_1)$$
warm shaleBOT
ℝamonov
dark orchid
.reopen
obtuse pebbleBOT
✅
high lily
those 1s in subscript aren't just for show
dark orchid
brb
high lily
you essentially wrote 0 = m(0)
dark orchid
back
high lily
the subscripts are there to distinguish coordinates of your point(s)
x_1 is the x-coord of the point you're using
y_1 is the y-coord of same point
writing stuff like y-y which is just 0 there is wrong
dark orchid
x_1 is the x-coord of the point you're using
y_1 is the y-coord of same point
w...
so what's the correct thing to write?
y-9=m(x-x1)
what would you have me put in that y-9,
in the y to be specific?
high lily
the formula you should've written in the first line is the image above
dark orchid
the formula you should've written in the first line is the image above
what image?
high lily
$$y - y_1 = m(x - x_1)$$
warm shaleBOT
ℝamonov
warm shaleBOT
ℝamonov
high lily
that's what I've been saying this whole time
dark orchid
but then, i did know that i was putting in the coords in there anyway
laziness
heh.
Thanks thro.
.close
toxic orchid
Hello, i'm stuck with this exercise :
obtuse pebbleBOT
Hello, i'm stuck with this exercise :
toxic orchid
I just cant find how one can derive the fraction from the multivariate gaussian that is proposed
In fact, i can reduce the problem to show that $(X\hat{\beta})_j = y_j$ , but i dont see why would it be true.
warm shaleBOT
Eliaz
toxic orchid
I dont know also how to deal with normalization terms like 1/det(XT*X)^n, since i dont seem dont have it in the setting of question a).
I would also appreciate help with question 3, because i can't get why the posterior means cannot be written explicitely. I presume it is about showing that some operations cant be done analytically, like finding the root of a polynom which degree is more than 5
lament orbit
obtuse pebbleBOT
lament orbit
hello
im stuck with finding the slope
(The last equation on my paper) I’m not sure if I’m doing that correctly and how k can shorten it down
instead of that x would it just be 1?
timid silo
im stuck with finding the slope
try diffrentiation but i dont know if that works
obtuse pebbleBOT
@lament orbit Has your question been resolved?
celest badger
please help
obtuse pebbleBOT
please help
celest badger
how do i find the covariance
nimble ibex
obtuse pebbleBOT
brisk grove
y = mx + b
Let's say the points at which the line is tangent are x = t, and x = s.
You have:
f(t) = mt + b
g(s) = ms + b
f'(t) = m
g'(s) = m
4 equations, 4 variables.
Though it shouldn't be too complicated.
nimble ibex
Okay so that makes sense. And forgive me if I'm just asking a stupid question... but how would I solve that?
plucky zodiac
obtuse pebbleBOT
undone sparrow
It's a rectangle?
undone sparrow
Do you have any givens
undone sparrow
And so are all the other sides
Which are?
obtuse pebbleBOT
@plucky zodiac Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
little sonnet
obtuse pebbleBOT
little sonnet
i need answer for this qestion
tardy epoch
• Show your work, and if possible, explain where you are stuck.
little sonnet
havnt started sadly'
tardy epoch
you should attempt it before asking someone
knotty crow
have you got your textbook
obtuse pebbleBOT
Available help channel!
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.
knotty crow
1 + 2 + 3 = 6
6 * 3 = 18
sum of digits is divisible by 3 and 9
so...
just look at a last digit
if it's even (remember 0 is even as well) then number is also even
if it's odd, number is odd
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
obtuse pebbleBOT
timid silo
Cuz M left
- Caetano made five cards, each with a letter in the
front and a number behind. The letters form the word
𝑂𝐵𝑀𝐸𝑃 and the numbers are 1, 2, 3, 4 and 5. Notice the
comics and answer: what is the number on the back of the card
with the letter 𝑀?
OBE=6
OP=8
<@&286206848099549185> / The blue text is me solving it
But im not correct in this
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
fleet torrent
why is cos x negative instead of sen x?
obtuse pebbleBOT
why is cos x negative instead of sen x?
fleet torrent
I solved it but my answer isn't the same as my teacher's
I got (cos x)^2 - (sen x)^2
royal basin
you screwed up the signs
the derivative of cos is -sin and the derivative of sin is +cos
you did it the opposite way
fleet torrent
that's not my answer
that's my teacher's
that's why I am confused, I don't know why he did that
.close
quaint finch
How do I factor 64x^3 + 1
obtuse pebbleBOT
How do I factor 64x^3 + 1
nova bane
How do I factor 64x^3 + 1
sounds like a sum of two cubes tbh
you know the formula right
nova bane
oh
quaint finch
Help 💀
nova bane
(x ± y)(x² ± xy + y²)
quaint finch
Oh
nova bane
take the cube root of the first term (64x³)
quaint finch
I know that
nova bane
just dont mess up the signs
quaint finch
take the cube root of the first term (64x³)
How do I find the cube root?
nova bane
How do I find the cube root?
what number when multiplied to itself 3 times makes 64?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
hey, this does not exist right?
twin sapphire
it does
obtuse pebbleBOT
@sacred birch Has your question been resolved?
tardy epoch
why does that one exist but not this one?
Calculate both one sided limits
fervent lake
because left and right hand limits are different in it.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dense osprey
consider linear functions q and h such that q(x) >= h(x) when x<=1. if their graphs are perpendicular and q and h has y-intercepts of -7/2 and -1 respectively, find the equations of q and h.
obtuse pebbleBOT
consider linear functions q and h such that q(x) >= h(x) when x<=1. if their gra...
dense osprey
i have no idea how to start
obtuse pebbleBOT
@dense osprey Has your question been resolved?
hexed agate
Try sketching the graph
dense osprey
i can imagine how the graph goes but idk how to get the equation
hexed agate
It says when x<=1, q(x) >= h(x), how will it look like?
dense osprey
It says when x<=1, q(x) >= h(x), how will it look like?
y value of q(x) will be higher than or equal to h(x)'s
when the x value is equal to 1 or less than
so at 0, h(x) has a higher y than q
so im assuming they intersect somewhere around -1 (x)
@hexed agate
hexed agate
Why not at x=1 q(x) = h(x)?
hexed agate
So like q(1)=h(1)?
hexed agate
Why not at x=1 q(x) = h(x)?
.
dense osprey
idk man
hexed agate
Since the lines are perpendicular what does it mean about their slopes ?
dense osprey
negative reciprocal
hexed agate
Yeah
dense osprey
so what do i do about that
q(x) = mx + -7/w
h(x) = (-1/m)x - 1
idk man
what do i do w that
if im even correct
@hexed agate
smh
.close
hexed agate
@dense osprey since they are perpendicular don't you think they meet when y is on the midpoint of -1 and -7/2?
obtuse pebbleBOT
<@386464668488826881> since they are perpendicular don't you think they meet whe...
hexed agate
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
inland bolt
obtuse pebbleBOT
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
north elk
obtuse pebbleBOT
stable rain
whatve u done
obtuse pebbleBOT
@north elk Has your question been resolved?
dense osprey
yo @drowsy cosmos
obtuse pebbleBOT
yo <@511209824470564865>
dense osprey
i got 2 and 1/2 but they arent negative reciprocals anymore
but the lines are perpendicular
drowsy cosmos
2 and 1/2 are two seperate solutions so:
q(x)=-1/2x-7/2 and h(x)=2x-1
q(x)=-2x-7/2 and h(x)=1/2x-1
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
violet mulch
hi
violet mulch
im learning implicit diff. and I have a stupid question
mint tendon
violet mulch
if I were to differentiate an equation
with respect to x
if the one of expressions does'nt involve x,
like g(y)
violet mulch
probably
high lily
doesn't hurt to have d(whatever)/dx
rotund crest
Hey anyone here capable of helping me with some accounting maths questions?
mint tendon
violet mulch
well thats the assignent. the equation is a curve in the plane
mint tendon
oh interesting so its parametric?
violet mulch
there are no specific numbers so I guss in a curve y is function of x
mint tendon
yeah if its implicit differentiation y is prob gonna be a function of x
violet mulch
meaning I have to differentiate with chainrule on the y expressions?
mint tendon
yep
violet mulch
and productrule the middle one
mint tendon
bingo
devout warren
How do you integrate 1/x * sqrt(x^2 - a^2) ?
obtuse pebbleBOT
How do you integrate 1/x * sqrt(x^2 - a^2) ?
devout warren
distant moth
devout warren
Hahah hello again mate
astral mantle
try using a trig sub
devout warren
I tried but they don't work