notice that the differential term 'dt' cancels out
#help-0
tight locust
gaunt moat
hey
gaunt moat
so i have
ln(760/x) = 1.1696
and i know that the final answer is 269
but idk how to do that without like a google calculator
how do i use a regular calculator do to that ?
well atleast i think its 1.1696 i simplfied the right side as much as i could
the full problem is
ln(760/x)=22.1*1000/8.314 * (1/309-1/357)
inner sentinel
gaunt moat
<@&286206848099549185>
wary stream
<@&286206848099549185>
You have to wait at least 15 minutes before pinging helpers
gaunt moat
yea but i did it cause 2 people in here now lol
wary stream
Still, you need to wait
gaunt moat
okay
wary stream
and i know that the final answer is 269
No it's not
Do you know how to get rid of the ln to find x?
gaunt moat
ln(760/x)=22.1x1000/8.314 (1/309-1/357) well for this the answer is 269 lol
wait
no
239****
and nope
i dont
i was doing the math on my phones calculator but on the test i will have to use a regular one so ima need to know how to cancel it lol
wary stream
So how did you get 239 without knowing what to do?
gaunt moat
well online calculator kinda just solves it for me
i just gota make sure i enter the correct info in the right spot and do the conversions
simple turtle
ln(760/x) = 1.1696
can you e bothside?
gaunt moat
well thats what the calculator did but it got really complicated
like it had it as x= 760/e^8991591sqrte^1408409
mild ivy
do you still need help pancake
gaunt moat
yes
simple turtle
well thats what the calculator did but it got really complicated
e^lnx=x
mild ivy
yeah have you learned that you can raise both sides as the power to "e"
gaunt moat
not really
simple turtle
agree with kody. you can e bothside and solve for x
mild ivy
yeah I cannot really find the proof for it, but think of it like this, the base of ln is e, this is really just log base e
mild ivy
=tex e^ln(\frac{760}{x}) = e^1.1696
mild ivy
nothing is going correctly
mild ivy
760/x = e^(1.1696)
multiply by x to the other side, divide by the e^1.1696, that is a number, 760 over that number should be 269
simple turtle
i do that get the number
yes 760/e^1.1696, but the answer you said is not equal
gaunt moat
hmm i get 236 which is close to the answer
i gues 1.1696 is wrong lol but its close to the correctr answer which is 239 lol
thanks for the help
simple turtle
i gues 1.1696 is wrong lol but its close to the correctr answer which is 239 lol
good
gaunt moat
.close
stoic quail
Hi! I'm struggling with a Laplace transform, and I think I'm on the right track. I've got to s^2Y(s) + 6sY(s) + 10Y(s) = G(s), but I'm not sure where to go from here.
naive valley
try factoring out the common Y(s) on the left hand side
stoic quail
try factoring out the common Y(s) on the left hand side
Ohhhhhh
I just saw it now 😭 tysm
naive valley
sure
stoic quail
.close
pale grail
This is for a practice test - I'm not exactly sure what I'm supposed to do here
pale grail
Am I just finding the definite integral from pi/3 and pi/6? The question is looking for max and min so I don't think that's what it is
is it possible to find a max and min of a definite integral? is that what it's asking for?
alpine sable
is it possible to find a max and min of a definite integral? is that what it's a...
What do they mean by comparision property
I googled it
Didn't got anything relevant
Oh
I got it
pale grail
Something like this - I don't really understand how this helps me though
<@&286206848099549185> sorry to bother
I don't really know how to word my question better
hello
last ether
This is for a practice test - I'm not exactly sure what I'm supposed to do here
It's basically asking you to find bounds of an integral
That's the area comparison rule or soemthing I forgot
tacit arch
Something like this - I don't really understand how this helps me though
Calculate everything in equation 4.4.24
last ether
But the founder of the sums themselves is here so
ocean sealBOT
riemann
pale grail
i'm guessing thats (3^1/2)/3 and 3^1/2?
ocean sealBOT
riemann
pale grail
so the two values are ((3^1/2)/3)(pi/3 - pi/6) (3^1/2)(pi/3 - pi/6) ?
(pi(3^1/2))/18 min
(pi(3^1/2))/6 max
I think?
idk how to use the fancy formatting
I hope that's it
.close
hard timber
Help on
hard timber
.close
lone heartBOT
naive valley
what is (*)
hard patio
Hey, can someone help me with proving the following as true or false:
hard patio
where p is the nth prime
ocean sealBOT
Deol
hard patio
$\frac{(p)^2}{(p^2)-1}\le (2)^{(\frac{1}{2^n})}$
ocean sealBOT
Deol
hard patio
where p is the nth prime
slender gull
So, for example, if we had n=2, p would be 3?
hard patio
yes
lone heartBOT
@hard patio Has your question been resolved?
hard patio
<@&286206848099549185> sorry for the ping, but it would be great if anyone can help
lone heartBOT
@hard patio Has your question been resolved?
drifting hull
@hard patio Are you sure, that its correct? the 16th prime is 53. And i get:
,w 2^(1/(2^16))-(53^2/(53^2-1))
ocean sealBOT
weak ravine
Hello
weak ravine
could anyone help me?
These are my questions
I am in high school and this was a take home test and I have like no idea what to do or what to put down. As I was suffering from covid.
Its 1:28 am and I have 6 hours until school starts!
its due in 6 hours! so need like fast help
oak perch
COVID might make you cough, but it doesn’t effect your problem solving ability or make your own homework others
oak perch
So you better select just one question then ask it
weak ravine
only 1 okay.
ill come back
What is this type of math called?
Im gonna watch YouTube tutorials
Alright this is the question I need help with.
oak perch
I don’t know what it’s called, I just know how to solve this problem
3y+x-6=0 letting x or y be zero respectively you can find two points on it:(6,0) and (0,2) draw the line connecting those two points on your diagram, call it L1
weak ravine
Line 1?
weak ravine
Whats this type of math called?
oak perch
I don’t know. I didn’t learn elementary math in English. Then the region you are asked to find is (below or on L1) intersection (above L2)
oak perch
Yeah, English is my foreign language
weak ravine
I understand okay.
oak perch
And I don’t think it even worth a name…
weak ravine
is there some sort of calculator that could solve this?
oak perch
? I don’t see any calculation going on here
weak ravine
Yeh nvm im brain dead
tight kayak
lone heartBOT
tight kayak
anyone know how to do this?
oak perch
Do it by definition
lone heartBOT
@tight kayak Has your question been resolved?
rustic crest
can someone help me with this question?
lone heartBOT
can someone help me with this question?
prime badge
so you're looking for "1st is not defiective and 2nd is not defective and 3rd is not defective"
there's no alternative order that you'd miss with this calculation
selecting 3 random items is always equivalent to pulling one item at a time
(without placing it back of course)
or you can divide accepted 3-choices by total 3-choices, or you can treat it as taking 3 "top cards" and count permutations of the deck that would make you avoid the defective one
rustic crest
Can you provide the working? I am still not quite sure
prime badge
no sorry
lone heartBOT
@rustic crest Has your question been resolved?
tardy rapids
Can you provide the working? I am still not quite sure
Consider 3 slots
— — —
You have to pick the items in a way such that none of them are defective
Meaning the first one you pick must not be defective (9/10)
Second one you pick must not be defective (8/9)
Third one you pick must not be defective (7/8)
Got it?
rustic crest
Consider 3 slots
— — —
You have to pick the items in a way such that none of t...
Oh I got it now, thanks
lone heartBOT
lone heartBOT
Available help channel!
reef pivot
Does a definite integral always equal some area? Also, if a definite integral tells me area, what does an indefinite integral tell me?
weary wyvern
Does a definite integral always equal some area? Also, if a definite integral te...
- yes 2. the antiderivative
lone heartBOT
@reef pivot Has your question been resolved?
reef pivot
Yes
rocky pendant
lone heartBOT
rocky pendant
another quick question
the graph is obviously vertically compressed, and i got the answer just fine but
why don't we just do something like -1/3 to represent the stretch?
uncut plank
Because -1/3 not only represents the stretch, but also flip horizontally because of the negative sign.
turbid marlin
🙃 completely stuck on this one
lone heartBOT
🙃 completely stuck on this one
turbid marlin
seems to be homogeneous, positive, and satisfy the triangle inequality
alpine sable
seems to be homogeneous, positive, and satisfy the triangle inequality
Yes
where is the problem
you also missed one requirement
turbid marlin
did I?
turbid marlin
ok, I've never heard of that xD
alpine sable
haha
turbid marlin
the lecture notes for this course give this as the requirements for a norm
alpine sable
the lecture notes for this course give this as the requirements for a norm
it's the second part in (i)
turbid marlin
I always just grouped them into the 1 thing
alpine sable
I always just grouped them into the 1 thing
it's fine to do that. but you shouldn't forget to prove the second part
turbid marlin
nonetheless, I'm struggling to get a function with ||f || = 0 but f =/= 0
alpine sable
nonetheless, I'm struggling to get a function with \||f || = 0 but f =/= 0
I don't think there is one in this case
because the norm is indeed positive definite
you should just prove that | |f| |=0 implies f=0
turbid marlin
so there's a function for which f = 0 but | | f | | =/= 0?
alpine sable
so there's a function for which f = 0 but | | f | | =/= 0?
no the negation of positive definiteness is | |f| |=0 but f != 0
alpine sable
so there's a function for which f = 0 but | | f | | =/= 0?
there is none
alpine sable
ok, so a non-zero function with | | f | | = 0
Yep there are functions like this
turbid marlin
only thing I could think of for that was like f = 0 for all x except x = 0.5, where f(x) = 1 or smth
but then that's not regulated, right?
alpine sable
do you mean here by regulated continuous ?
because regulated has a very complicated definition
turbid marlin
regulated = a series of step functions uniformly converge to it, right?
turbid marlin
do you mean here by regulated continuous ?
no, the question says R[0,1] which is regulated functions
alpine sable
regulated = a series of step functions uniformly converge to it, right?
Yep I think so
If this is the case then f as you define it above may be regulated
turbid marlin
and a series of step functions can't uniformly converge to f(x) = 0, f(0.5) = 1
alpine sable
and a series of step functions can't uniformly converge to f(x) = 0, f(0.5) = 1
why not
turbid marlin
because at x = 0.5, the difference between the step function and the actual function is gonna be 1
so it doesn't satisfy this
marsh fog
Isnt your norm an integral? So a function that is symmetric about 1/2 will do the trick?
Sorry, antisymmetric
alpine sable
Ah I see, but maybe there is trickier choice of the step function. I know for a fact that a regulated function can have as much as a countable set of discontinuities
analysis is tricky
turbid marlin
oh hmmmm
turbid marlin
Isnt your norm an integral? So a function that is symmetric about 1/2 will do th...
integral of the absolute value of the function
marsh fog
Yeah true
turbid marlin
if it were just integral tho, you'd be right
turbid marlin
Ah I see, but maybe there is trickier choice of the step function. I know for a ...
aight fair enough lol
turbid marlin
but isn't that f_n
I don't get their proof
they're changing their function to make it less than epsilon
alpine sable
they're changing their function to make it less than epsilon
which function u mean
turbid marlin
f
alpine sable
but it's still 1/n, we just need a N after which we have 1/n < epsilon
archimedian property or something
turbid marlin
hmmm
I don't get why it's ok to just change f to make some converge to it
like surely f needs to be fixed
alpine sable
f isn't fixed tho, cuz it relies on n
no we defined f(n) as equal to 1/n for every natural number n. That's the fixed definition of f
I guess
turbid marlin
oooooh
alpine sable
tricky example they have here
turbid marlin
ty 🙃
alpine sable
U welcome 
turbid marlin
.close
thick lynx
For a stake of 1€ you can spin the wheel of fortune twice.
If the yellow field appears both times, you get paid 2€. If the red field appears once and the yellow field appears once, you get 1€. Otherwise nothing is paid out.
thick lynx
For the wheel it's:
1/4 chance it's yellow
3/4 chance it's red
Now what's the chance that you lose 1€?
(3/4)^2, no?
that would give 9/16
but if you go with P("lose 1€") = 1 - P("winning 1€") - P("winning 0€") that gives 11/16
thick lynx
1 - 1/16 - 6/16 = 9/16
P("Yellow, Yellow") = (1/4)² = 1/16
P("Yellow, Red or Red, Yellow") = (1/2) * (1/4) * 2 = 1/4 = 4/16
onyx mist
I have this system(z transform difference equation) where I'm doing a step response on the difference equation y(n) = x(n-1) +2x(n-2)+0.2y(n-1) - 4y(n-2), since it's n-2, I have to go back twice and use that older value. Since that value is basically 0, this should be correct for 10 samples right?
lone heartBOT
I have this system(z transform difference equation) where I'm doing a step respo...
@onyx mist Has your question been resolved?
lethal dock
lone heartBOT
oak chasm
The first light flashes on every multiple of 22 seconds.
The second light flashes on every multiple of 16 seconds.
lethal dock
Ohh so the common multiple
oak chasm
Yes, that's right.
lethal dock
So
22 -> 2×11
16 -> 2⁴
Lcm = 2⁴×11 = 176
oak chasm
Yes, that's right.
You take the highest of the two powers of each prime factor.
GCD is the lowest of the two powers of each prime factor.
And LCM times GCD is their product.
Since the lowest plus the highest power for a prime is the same as one of the powers plus the other that you get in the product.
lethal dock
Wait what 
oak chasm
Well, for the LCM:
2¹ · 11¹
2⁴ · 11⁰
LCM = 2⁴ · 11¹
For the GCD:
2¹ · 11¹
2⁴ · 11⁰
GCD = 2¹ · 11⁰
For the product:
2¹ · 11¹ · 2⁴ · 11⁰
Which is just the rearranged version of the LCM times the GCD:
2⁴ · 11¹ · 2¹ · 11⁰
The reason why is because LCM takes the highest power for each factor and GCD takes the lowest power for each factor, and the highest and the lowest will include the first and the second powers for each factor.
lethal dock
Well, for the LCM:
2¹ · 11**¹**
2**⁴** · 11⁰
LCM = 2⁴ · 11¹
For the GCD:
2**¹...
GCD will be 2¹ × 11⁰?
oak chasm
Yes.
lethal dock
Oh ok
lethal dock
Well, for the LCM:
2¹ · 11**¹**
2**⁴** · 11⁰
LCM = 2⁴ · 11¹
For the GCD:
2**¹...
First and second power for each factor?
oak chasm
Yes, the power from the first and second numbers.
So, LCM will get one power, GCD the other.
And when you multiply the LCM and GCD, you get both powers multiplied together just like you'd get in the product of the first and second numbers.
lethal dock
So LCM×GCD=1ST-NUMBER×2-NUMBER
lethal dock
Woah that works
oak chasm
Yeah, it's like this. The product of the two is:
(2⁴ · 11⁰) · (2¹ · 11¹)
Then, the LCM gets the highest power and the GCD gets the lowest power:
[2⁴ · 11¹] and [2¹ · 11⁰]
Notice that that just rearranged the factors.
And if you multiply some things, you're allowed to rearrange them and get the same answer.
oak chasm
It's kind of a tangent, sorry.
If you're good at getting GCDs from reducing fractions, you can get the LCM from the GCD.
oak chasm
No problem.
lone heartBOT
@lethal dock Has your question been resolved?
lone heartBOT
@lethal dock Has your question been resolved?
vale wigeon
peak lodge
Can someone please help?
lone heartBOT
Can someone please help?
lone heartBOT
@peak lodge Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
sweet dune
Does anyone have experience with angled kinematics? I'm making a launcher that launches a ball in the air & has to reach a target. I need help modelling an equation that can calculate what angle the projector has to shoot to reach target knowing that the distance to target can be different to the previous launch, i know its al SUVAT equations, but it involves angles which i'm not too sure about, so any help would be appreciated, i have a fully drawn model, so its easy to understand what i need help with.
Ball weight is 0.35kg
tacit arch
This is a good start
https://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic-formulas/a/what-are-the-kinematic-formulas
or if you prefer video https://www.youtube.com/watch?v=8NLzuURxFwY
sweet dune
Oooo that is perfect!!! Thank you!!
Also If my weight is 0.3kg , how do i find the initial velocity, i'm guessing it starts with f=ma , but i'm not sure if i need to take into account angles & g etc.
Reason i ask is because most projectile motion videos tell you the initial velocity of ball, wheres i only know the initial force that the launcher acts onto the ball for it to fly + i know the ball weight
@tacit arch
lone heartBOT
@sweet dune Has your question been resolved?
real solar
Oooo that is perfect!!! Thank you!!
Also If my weight is 0.3kg , how do i find...
you could use momentum-impulse if you know the time the force is being applied
because its difficult to say if you only have force, we know its not a continuous force, so there needs to be some time frame where it is applied, the longer its applied the higher the velocity
sweet dune
what if we assumed time = 0 ?
real solar
what if we assumed time = 0 ?
that is impossible, bc if time of force applied is 0 then there was no force applied
lone heartBOT
@sweet dune Has your question been resolved?
odd viper
You have 300 people with disease X, which causes a 100% chance of death. Of the 300, half have genetic marker A and half have genetic marker B. You have 100 doses of a drug. For people with marker A it cuts the risk of death to 10%. For people with marker B it only cuts it to 50%.
How many of the 100 doses do you give to people with genetic marker B? Give reasons
lone heartBOT
You have 300 people with disease X, which causes a 100% chance of death. Of the ...
@odd viper Has your question been resolved?
lone heartBOT
@odd viper Has your question been resolved?
tacit arch
tried using probability but m stuck with this question now
what are you supposed to do? minimize deaths? maximize deaths?
odd viper
what are you supposed to do? minimize deaths? maximize deaths?
It's a bit related to ethical reasoning too
Depends upon you how many you give to B and how many left would you give to A but you have to give ethical reasons for your choice of number of doses you'd give to A and B respectively
odd viper
👍
lone heartBOT
Available help channel!
bitter stirrup
Hi, trying to understand how to graph the rest of the points here, can someone help me please?
bitter stirrup
(I am solving the first problem
remote heron
Hi, trying to understand how to graph the rest of the points here, can someone h...
the rest?
how do you mean
remote heron
normall if you have the vertex, and intercepts
you just draw these
i mean and then fill in the rest
but it should be clear
you dont have to be careful about the other points i mean
lone heartBOT
lone heartBOT
✅
bitter stirrup
.close
alpine sable
Can anybody explain what this means? I generally do not struggle with summation notation, but for this example I'm having trouble.
worn fox
What is giving you trouble with this particular example?
alpine sable
So if x = 3, then
1
+
1 + (2)
+
1 + (3) + (3)^2
I'm trying to understand what LHS of the equation is saying
worn fox
You give it a number, x, and it adds together the powers of that number from 0 to n-1
alpine sable
Sorry maybe it might have been more appropriate to say the middle of the equation, although they're linked.
worn fox
The left hand side is just shorthand notation for the middle
worn fox
You give it a number, x, and it adds together the powers of that number from 0 t...
This also describes the middle
alpine sable
So if x = 3, then
1
+
1 + (2)
+
1 + (3) + (3)^2
Yes but I'm not completely sure if I know how it turns out, I've given my example for the summation upto 3, and if this is correct then I understand it.
ocean sealBOT
iCaird
worn fox
Literally just replace x with 3 everywhere
alpine sable
That seems a bit unworkable for me. How would I evaluate any case?
Sorry all the induction questiosn I've came across so far have been much simpler
I can't really evaluate something with the exponent n-1
worn fox
You can also pick your n
alpine sable
So for whatever n I choose?
So if I were to pick x = 3, the summation is simply considering the sums of the base 3 and upto an arbitrary exponent?
And this is unlike something like $ \sum_{i=1 }^{n }x^2 = \frac{(k+1)(k+2)}{2} $ where it considers all the natural numbers
Well that didn't work well
alpine sable
So if I were to pick x = 3, the summation is simply considering the sums of the ...
I guess my main question would be, do I have to consider the sum of the other integers alongside with this?
Like if I pick x = 3 then do I have to have $1 + 3 + 3^2 + 3^3 + 3^4 + \cdots + 3^{n-2} + 3^{n-1}$ + x =2 + x = 1?
ocean sealBOT
bonaparte
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Okay to try and use what I've read, the i is the index, n-1 is the upper limit of the summation, so the i goes all the way through 0 to n-1, so the powers start from 0 and ends up to n-1.
I am able to choose the upper limit of the summation, since the upper limit is n-1, I will choose n=4 to get the upper limit I want to evaluate, which is 3.
If the upper limit is 3, then it becomes 1 + x + x^2 + .... + x^{n-1}
+ 1 + 2 + 2^2 + ... + 2^{n-1}
+ 1 + 3 + 3^2 + ... + 3^{n-1}
because my understanding of the upper limit tells me I have to repeat the process the amount of times the upper limit's value is
However this is just wrong, I'm guessing.
worn fox
There is no repeating of the process
The upper and lower limit are just telling you how many things we will add together
If the lower limit is 0 and the upper limit is 3, we will add 4 things together
In the example you gave we would the 4 things added together be $1+x+x^2+x^3$
ocean sealBOT
iCaird
worn fox
And we are free to pick what x we want to evaluate this sum at
alpine sable
Is there any relationship between the upper limit and the x I want to pick?
worn fox
No
alpine sable
Okay
n is the number of terms in your summation . x is the base of all the terms
So it's saying that
$1+x+x^2+x^3+.... +n times$ = $\frac {x^n-1}{x-1}$ isn't that all
ocean sealBOT
Frustrated Cat
worn fox
There could be, but they don't have to be(I wouldn't worry about that)
If you're still confused here's a short Khan academy video
alpine sable
Why is the summation limit n-1? It seems a little pointless
(Sorry the question is a bit off topic)
worn fox
It's convention for that formula, so that the identity on the right hand side looks nicer
It's a good question
We often label things a certain way to make equations and identities neater
alpine sable
Okay I think I've gotten it, can you ask me a question to make sure?
worn fox
Sure, try writing out $\sum_{i=1}^{6} ix$
ocean sealBOT
iCaird
alpine sable
i_x? i'm thinking is what you wanted to write
worn fox
No I changed it
worn fox
This is a specific case
alpine sable
Okay my attempt would be $ i_1 x + i_2 x + i_3 x + ... + i_6 x$
alpine sable
Like how else can you write that?
worn fox
$x + 2x + 3x + 4x + 5x + 6x$
ocean sealBOT
iCaird
alpine sable
Oh okay, that should have been obvious.
I think I'll just try deal with this another time, when I'm a bit more clear headed. Thank you for your help. @worn fox
I'll be closing the channel now.
.close
tropic veldt
Please can someone
lone heartBOT
Please can someone
tropic veldt
Tell me if I solved for the correct Cartesian equation
8i-7j+k
This is my answer. Thanks
marsh fog
That's the cross product, you're on the way there but there are more things you need to do.
Try to use the equation $\vec{r}\cdot \vec{n} = d$
ocean sealBOT
Kimbomanjaro
marsh fog
You have just found $\vec{n}$
ocean sealBOT
Kimbomanjaro
marsh fog
Do you know what a dot product of two real vectors is?
tropic veldt
It is when you multiply their components
marsh fog
Yeah, and add them together. So if $\vec{r}=\begin{pmatrix} x\y\z \end{pmatrix}$ then $\vec{r}\cdot\vec{n}=8x-7y+z$
ocean sealBOT
Kimbomanjaro
marsh fog
Plugging in any point on the plane will give you d, which finishes your cartesian equation for the plane.
lone heartBOT
@tropic veldt Has your question been resolved?
tropic veldt
Yeah, and add them together. So if $\vec{r}=\begin{pmatrix} x\\y\\z \end{pmatrix...
I multiply them add them together? Please explain further, I am confused
alpine sable
I multiply them add them together? Please explain further, I am confused
v1=[1, 2,3]
v2=[4, 5,6]
v1.v2=1* 4+2* 5 +3* 6
tropic veldt
Ohh thank you
I see now
So I find the dot product of u and v then is that the Cartesian equation?
marsh fog
No, try taking the vector you found earlier, 8i-7j+k, and finding the dot product with both u and v. You may notice something.
So for $n=8i-7j+k$, compute $n\cdot u$ and $n\cdot v$
ocean sealBOT
Kimbomanjaro
tropic veldt
Thank you, I’ll try that and get back to you
tropic veldt
I got 0 for both of them so cross product of vectors times a vector equals 0
How do I then find the Cartesian equation please?
Do I times it by (x,y,z)?
tropic veldt
<@&286206848099549185>
lone heartBOT
@tropic veldt Has your question been resolved?
lone heartBOT
lone heartBOT
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rough stirrup
If in matrix A the basis is comprised of 2 vectors (v1, v2)
And the question asks if V is a subspace of R4 spanned by column vectors of A, choose a basis of V among v1 v2 v3 v4.
how would we go about answering this?
lone heartBOT
If in matrix A the basis is comprised of 2 vectors (v1, v2)
And the question as...
@rough stirrup Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
Idk how to find the length of OA without knowing the angle of O
I've tried
But the methods I thought don't work
So I'm asking now...
ember dust
we don't need angle O
we know the relation between the circle formed from CD and the circle formed from AB
alpine sable
we know the relation between the circle formed from CD and the circle formed fro...
AD?
alpine sable
Ok
ember dust
do you recall the circumference of a circle formula?
^
alpine sable
2 pi radius?
alpine sable
I don't understand.. a linear graph?
ember dust
yeah
what this means is
if the radius is doubled (i.e. goes from 2 -> 4)
the answer that you will get is also doubled
so let's say f(r) = 2 * pi * r
the reason I'm saying this is because we know the relation between radius and circumference in this question
alpine sable
(I haven't learned f)
ember dust
okay forget that part then
focus on this
that means the reverse is true
if the cirumference (the answer) is doubled, that means the radius is also doubled
does that make sense?
alpine sable
Yes
ember dust
so what do you think we would do from here
alpine sable
So AB is like the circumference of CD?
ember dust
think of it as a circle segment
alpine sable
U mean sector?
ember dust
terrible drawing but something like this
ember dust
U mean sector?
sure
so if the circumference has doubled, what has happened to the radius?
ember dust
no no youre right
thats perfect
so from here, we know that OC is half of OA, right?
alpine sable
Yea
ember dust
so do you know what OC is, assuming CA is 9?
ember dust
exactly
ember dust
great job
alpine sable
Thank u so much
ember dust
that was all you
alpine sable
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fathom karma
I think this is not true for non-finite measures but can't seem to find a counterexample
fathom karma
Is the measure $\lambda = \left(\frac{1}{x}\right)\mu$ an example for $E = (0,\delta)$?
ocean sealBOT
allmight
lone heartBOT
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fallow zealot
If anyone can solve 24b, he/she is certified high IQ
lone heartBOT
If anyone can solve 24b, he/she is certified high IQ
fallow zealot
<@&286206848099549185>
limpid spade
why ping
alpine sable
What have you tried?
drowsy lagoon
ACF is 90
buoyant kayak
i can see why you're having trouble with math
limpid spade
^
buoyant kayak
yeah what have you tried
fallow zealot
I tried all types of angles in every single shape
I still can’t find the approach to it
buoyant kayak
what
fallow zealot
Prop of rectangle
Any prop of triangle is possible
Ffs it’s a difficult question and I can’t grasp where the hell I can even start to figure it out
fallow zealot
Of the triangle
Yes I do but If I can’t even guess where I can get the solution, no properties will help
Shit not even the helpers know how to solve it 😭😭😭
uncut plank
So ABCD and CEFG are congruent rectangles, does that mean CF = CA? And why?
@fallow zealot
fallow zealot
CF = CA because they both have the same angles and same length therefore they are congruent triangle?
harsh swallow
iz easy
uncut plank
Yes. CF = CA because of congruent triangles
harsh swallow
think of equalateral triangle
fallow zealot
Well it wasn’t easy until I though of congruent triangle
uncut plank
think of equalateral triangle
Look at the question
harsh swallow
?
harsh swallow
?????
fallow zealot
Its like I have been learning multiplications and suddenly there’s a question that requires division to solve
uncut plank
Alright, so you know congruent triangles.
∠ACF = ∠FCB + ∠BCA
The question is what is the sum of ∠FCB and ∠BCA? (in degrees)
harsh swallow
actually i forgot if equilateral triangle means all 3 sides are equal or just 2
i mean the just 2
fallow zealot
Alright, so you know congruent triangles.
∠ACF = ∠FCB + ∠BCA
The question is wha...
90
fallow zealot
👍
uncut plank
What type of triangle of ∆ACF? Is it isosceles, equilateral, or scalene? @fallow zealot
slender gull
Good. And we have ∆ACF where CA = CF. This means that ∆ACF is an ... triangle
You already wrote an.
👀
uncut plank
You already wrote an.
That is the biggest clue ever, wait.... Equilateral starts with "e"
So, what the hell am √(-1) doing here?
fallow zealot
What type of triangle of ∆ACF? Is it isosceles, equilateral, or scalene? <@89135...
Isosceles
uncut plank
Isosceles
Great. Because ∆ACF is isosceles, ∠CFA = ∠FAC. And remember that the sum of angles of a triangle is 180°. And that's it
turbid prairie
hi, i'm trying to get the cross product of these two vectors and i keep screwing it up. i've checked my algebra loads of times and i'm almost 100% sure it's correct:
turbid prairie
i've got the x and z components, just keep getting the wrong y component
these are the two vectors i'm cross producting
<@&286206848099549185>
lone heartBOT
@turbid prairie Has your question been resolved?
lone heartBOT
@turbid prairie Has your question been resolved?
sour ridge
If anyone can solve 24b, he/she is certified high IQ
is its answer 45 degrees?
angle CAF
fallow zealot
is its answer 45 degrees?
Yes it is
fallow zealot
I did that in 3rd grade and my teacher said no
sour ridge
I did that in 3rd grade and my teacher said no
which class question was it?
what level?
fallow zealot
Year 10/ form 3
fallow zealot
Well then it’s secondary 3 I guess
fallow zealot
Grade 12?
fallow zealot
Then I am grade 10
fallow zealot
This will be my first time
sour ridge
hmm
fallow zealot
I have HKDSE
By the way good luck for the exam
China and India always neck to neck in everything
sour ridge
true
lone heartBOT
@turbid prairie Has your question been resolved?
naive crystal
sour ridge
Hmm
lone heartBOT
@turbid prairie Has your question been resolved?
lone heartBOT
@turbid prairie Has your question been resolved?
turbid prairie
can anyone help me with this?
i'm trying to get the vector cross product of the two vectors but i ca'nt seem to ge the y component correct
lone heartBOT
@turbid prairie Has your question been resolved?
tight locust
,w (a,b,c) x (d,e,f)
ocean sealBOT
turbid prairie
i'll give this a try, i think it's what i've been doing already but
grand canopy
tacit arch
.close
strange quartz
Answer says 9, wheras i've got 72
lone heartBOT
Answer says 9, wheras i've got 72
merry coral
Show us ur work
ocean sealBOT
proper tangle
,w d/dx 1/6 x^3 + 1/3 x^2 - 4/3 x, x = -4
ocean sealBOT
proper tangle
,w d/dx 1/6 x^3 + 1/3 x^2 - 4/3 x, x = 2
ocean sealBOT
wary stream
,w d/dx 1/6 x^3 + 1/3 x^2 - 4/3 x, x = 2
You can perform these commands in #bots or message the texit bot itself. You don't need to blow up this channel like that
proper tangle
wait how did you can these two lines?
strange quartz
Show us ur work
first factorised f(x) to get roots
then i differentiated and subbed in the roots
to get the gradient
oh the normal
nvm i know what i did wrong i only found the tangent
proper tangle
You can perform these commands in <#488104216678760469> or message the texit bot...
i see your point. in this case, since OP has confused tangent with normal, so the bot's calc results illustrate that OP isn't going the right direction.
wary stream
i see your point. in this case, since OP has confused tangent with normal, so t...
Then provide what was needed instead of blowing up the channel
strange quartz
.close
lone heartBOT
lone heartBOT
Available help channel!
golden sequoia
lone heartBOT
lone heartBOT
marsh fog
.reopen
golden sequoia
.reopen
lone heartBOT
✅
golden sequoia
ok
marsh fog
What do you suspect was wrong?
golden sequoia
since this is a universaly quantified statement, i cant assume for one variable only right
marsh fog
I think your proof holds just fine, your choice of c was arbitrary aside from the hypotheses holding
golden sequoia
okay so for universal i should assume for an arbitrary, for existential i should do proof by example?
just asking because i have an exam tomorrow
marsh fog
Yeah, if you are asked to show something 'for all' then pick an arbitrary one that is in the collection you want (I.e. if you want to show something for all real numbers, you generally will start with 'let $x \in \bR$'). For existence of something, you want to try to construct an example. Often times you may be asked to show 'existence and uniqueness'; to do uniqueness you almost always just assume you have two that do what you want and show they are the same.
ocean sealBOT
Kimbomanjaro
golden sequoia
okay that makes sense thank you. can i show you a proof im unsure how to do its proof by cases for absolute value
marsh fog
Sure, I can give it a look at least.
golden sequoia
it's problem (e)
marsh fog
Think about what the modulus is, it's telling you that a is a distance $|a|$ from the origin (basically by definition). Thus this means that if $|a| \leq b$ then $a\geq -b$. If you have studied open balls, then you could maybe phrase it in terms of those by saying there is an open ball of radius b around x (by definition of 'modulus' as a metric on $\bR$).
ocean sealBOT
Kimbomanjaro
golden sequoia
oh ok i haven't studied open balls yet but you're saying i can just use the definition itself to prove this?
marsh fog
Yeah, perhaps you could take modulus of both sides in the equation $|a| \leq b$, then you know that $|b| \geq |a|$, and apply that to -b and -a.
ocean sealBOT
Kimbomanjaro
golden sequoia
okay that makes sense thanks so much for the help
golden sequoia
yeah im still doing some more ill open another channel if i need help thank you
marsh fog
Sounds good, best of luck :)
jade swift
is this a linear equation?
lone heartBOT
is this a linear equation?
jade swift
If not please explain how I change the subject to h because I have no clue what to do
Been trying for quite a while
rugged sun
I think it will be linear in some variables but not others. But regardless, to change the subject to h, you can multiply both sides by h, then divide both sides by (s - t/3).
storm tundra
ooo help 0
lone heartBOT
ooo help 0
storm tundra
anyways
heres the problem
heres my solutions so far
a) (2x +5)(2x-5)
b)
so i factorized 2x^2 - x - 10 to (2x-10)(x+1)
i then have
(2x+5)(2x-5)
(2x-10)(x+1)
now usually there would be a common numerator and denomenator so you could cancel them out but either my process so far has been wrong and i have got wrong values orrr there is another step i am missing
summer trail
storm tundra
"what you have is 2x^2-8x-10"
what do you mean by this?
i think that 2x^2-x-10 factorizes to (2x-10) (x+1)
from what i got is that where i went wrong
i used pairs 2, -10 (to multiply to -20 but add to 1) instead of 4 and -5
ill remember that its HIGHEST common factor
anyways thx
.clos
.close
deep radish
Can someone help me on the next step to get the the target thing I wrote at the top
deep radish
I’m confused on the factorial part
untold crane
lone heartBOT
@deep radish Has your question been resolved?
lone heartBOT
marsh fog
Looks like you forgot the derivative of x perhaps?
You should still have a +1 on the LHS
After differentiating
marsh fog
Yeah, $\frac{d}{dx} (x)=1$, I cant see a 1 in your working?
ocean sealBOT
Kimbomanjaro
analog swift
Anyone ?
marsh fog
If you would like to ask a question, you can open your own help channel!
analog swift
oh ok
lone heartBOT
@thin urchin Has your question been resolved?
marsh fog
But 1+ something is not itself
copper charm
Can someone help me put this in factored form?
thin urchin
This channel is not open
thin urchin
But 1+ something is not itself
Where am I missing a 1+?
marsh fog
When you differentiate 5sin(x)+4cos(y)-4sin(x)cos(y)+x, I think you get everything you wrote, plus 1, because of the x on the end
runic lava
lone heartBOT
runic lava
can someone help me?
lone heartBOT
@runic lava Has your question been resolved?
solemn juniper
What's giving you issue?
solemn juniper
So for the top one, it looks like the line segment EF is supposed to represent side BC in the original drawing
So you need to scale/translate all sides in the same manner
The second one is also wrong, I think you need to look at how reflections are explained a little more
runic lava
english is not my first language 🥲 but thank u
my prof gave this as an example
like this?
copper charm
Can anyone help me put this in factored form?
alpine sable
Good
Make a channel
Like everyone else
And don’t go demanding factored equations without showing us an equation
copper charm
There is not a equation
alpine sable
That’s a problem we can sort in your own channel
copper charm
How do I make one
runic lava
😄
lone heartBOT
@runic lava Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
wary stream
Did you watch that video? @alpine sable
Because that video applies the concept you need
devout wraith
Yea
lone heartBOT
@alpine sable Has your question been resolved?
fickle kayak
Can i have help
lone heartBOT
Can i have help
wary stream
Can i have help
wary stream
Looks like you did everything
fickle kayak
But i i am pretty sure i am right
Yeah but some of them don’t match
Let me erase the ones
that i’m confused
about
wary stream
A good tip, look at the units
fickle kayak
wary stream
For example, the last one, everything is in terms of inches and miles yet you picked an answer that was in cm
wary stream
Does that make sense to use an answer of cms if you were given inches and miles?
wary stream
2.54 cm in 1 inch
wary stream
Create a proportion, this entire page looks like it's about that concept
wary stream
That's why I was saying look at the units
fickle kayak
Wait what would be the answer for this
If 1 unch = 1.4 miles
Inch*
How many miles would be 1 inch?
So 1.4 into 1.4
@wary stream
wary stream
How many miles would be 1 inch?
1 inch equals 1.4 miles meaning for every inch it's 1.4 miles
fickle kayak
Yes
But how would i solve
1.4 inches
= how many miles
?
@wary stream
Would it be 1.4x1.4
wary stream
Make a ratio
You have 1 inch per 1.4 mile so that's 1 in/1.4 mi
You have 1.4 inches per how many miles
Then you solve it
fickle kayak
i don’t know how to solve it
ocean sealBOT
dldh06
fickle kayak
Yes
wary stream
How would you find x?
wary stream
Cross multiply
wary stream
Yes
wary stream
You can close now
Using .close
fickle kayak
.close
mental fox
Can someone help me with this equation? Im having trouble finding y
lone heartBOT
@mental fox Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
Hello everyone, thanks for taking time to help. The approach mentioned in the book is clear to me, but I don't get what's wrong with my approach... please help
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@456226577798135808> Has your question been resolved?
no, my love.
swift shore
ocean sealBOT
alpine sable
sorry for that :|
alpine sable
<@&286206848099549185>
lone heartBOT
@alpine sable Has your question been resolved?
real glen
K so first of all the question says "AT LEAST" 3 bowlers
Second if you want to do it your way, aka by calculating 3 bowlers, 4 bowlers and then 5 bowlers, it cannot be 12C8
Once you pick 3 bowlers from 5, you cannot pick anymore bowlers so you have to select remaining players from 10 people
So its (5C3 * 10C8)/(15C11) for when 3 bowlers are selected
But you need to consider cases for when you have 4 bowlers and 5 bowlers
so your total probability is actually (5C3 * 10C8)/(15C11) + (5C4 * 10C7)/(15C11) + (5C5 * 10C6)/(15C11) = 12/13
but this is usually way harder to calculate compared to how its done in your book
@alpine sable