yh
#help-33
pallid pine
paper venture
dense grail
marsh citrusBOT
dense grail
Any help appreciated
runic temple
use the formula for the area of a triangle: (1/2)(a)(b)(sinC)
balmy coral
So
The first step
Is to calculate the longer side of parallelogram
Then what shall you do to find it out
balmy coral
use the formula for the area of a triangle: (1/2)(a)(b)(sinC)
What is this
marsh citrusBOT
@dense grail Has your question been resolved?
dense grail
Idkk
balmy coral
1/2 ×4x7sin100?
Try to figure out the area of the triangle using this first
But change sin(100) to sin(100°)
balmy coral
Try to figure out the area of the triangle using this first
Then there's another one triangle which is congruent to this triangle right?
Then you need to multiply the area of triangle by 2
You finish this first and then @ me
dense grail
Aa
balmy coral
But remember that you haven't finished to calculate the whole area
You have done 100° one
But for the 80° one
You haven't
To calculate their area is also using the same logic.
marsh citrusBOT
@dense grail Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
short wadi
how is 12) infinite?
marsh citrusBOT
how is 12) infinite?
stoic saddle
it's +∞ from both sides, while #11 is +∞ from one side and -∞ from the other
short wadi
makes sense
do you plug in values to see what it is approaching
i mean you can do it in your hea
head
stoic saddle
was that generic-you or was that me in particular
marsh citrusBOT
marsh citrusBOT
Available help channel!
mystic karma
it's +∞ from both sides, while #11 is +∞ from one side and -∞ from the other
Can you please try to explain differently, I have the same question as him, how is 12) Infinite ?
marsh citrusBOT
Can you please try to explain differently, I have the same question as him, how ...
crystal wraith
Can you please try to explain differently, I have the same question as him, how ...
Do you believe it should be + infinite from one side and - infinite from the other.
OR
You totally have no clue how infinity is making an entrance here?
mystic karma
I believe that when we replace x by 3, it becomes (3-3)^2 which is 0 and 1/0 doesn't exist just like the 11), unless it counts as 1/0^+ which is +infinity ?
or is it when (3-3)^2 = 0^2 and thus 1/(0^2) equals +infinity?
still temple
or is it when (3-3)^2 = 0^2 and thus 1/(0^2) equals +infinity?
Take the limit as 3+ and 3-
Both converge to 1/0 which tends to infinity
LHL=RHL so the limit exists.
And it tends towards infinity
crystal wraith
@still temple
I think the confusion is different.
Generally when you have infinity, you say the limit does not exist.
still temple
I think the confusion is different.
Oh lmao
still temple
Generally when you have infinity, you say the limit does not exist.
Wasn't the condition to determine whether a limit exists LHL=RHL?
crystal wraith
Well. A limit is said to exist if it gives you a finite number.
Not infinity.
So op is actually right about the limit not existing.
But the point of that other question was not that. In this particular case, the point was that even if it's infinity, it's not the same infinity each time.
still temple
Oh yea true
crystal wraith
Assuming you are considering limit to infinity acceptable.
If that's acceptable then b is valid.
But a is still not valid.
still temple
Yes
still temple
in this proof why is the x dropped
marsh citrusBOT
in this proof why is the x dropped
still temple
glass silo
As in how did they go from $x(x-1) \geq 0$ to $x - 1 \geq 0$?
elfin berryBOT
@glass silo
still temple
yes
glass silo
As they basically assumed, x is strictly positive, so you can divide through by it and it won't change the order of the inequality
still temple
are there other ways to prove this
like i would have just factored as above
and then have said even if x was negative, 2 negtaive real numbers multiplied by eachother is positive
glass silo
Hmm, what was the original statement to prove?
still temple
because its a disjunction we only need to prove that one of them is true
but if we rearrange, we can have x^2 - x \geq 0
glass silo
and then have said even if x was negative, 2 negtaive real numbers multiplied by...
I mean, yea you could do signs as you've said, that works too
still temple
and then we can factor out
like so it would be x(x - 1) correct
however
what if x = 0
technically this would prove that both x \geq 1 and x \leq 0
so can you do it this way
glass silo
That would be a fine way to do it, I would say [it would show that both x>=1 and x<=0 are possible yes]
to have the product x(x-1) >=0, you either need both x and x-1 negative (so then x<=0) or both x and x-1 positive (so then x>=1)
still temple
so for inequalities with disjunctions, you can prove either both situations are true, or just that one is true
also for this, i dont get how you can just get rid of the -1 for x-1 > eq 0
glass silo
also for this, i dont get how you can just get rid of the -1 for x-1 > eq 0
as in this here?
still temple
yeah sorry
glass silo
"if you're at least 1, you're at least zero"
glass silo
Well if you assume $x\geq 1$, you already know that $1 \geq 0$, and therefore $x \geq 1 \geq 0$, in other words, $x \geq 0$
elfin berryBOT
@glass silo
still temple
OHH
marsh citrusBOT
@still temple Has your question been resolved?
still temple
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
queen fjord
hi im confused on the explicit formula of functions
marsh citrusBOT
hi im confused on the explicit formula of functions
queen fjord
i understand recursive
but explicit is strange
i get cnofused of where tpo put the common difference and the primary numbner
marsh citrusBOT
@queen fjord Has your question been resolved?
broken forum
i get cnofused of where tpo put the common difference and the primary numbner
the whole point is that it doesnt just go there
its more complicated
if a(n) = a(n-1)*3
then a(n) = (3^n)(a(0))
does that make sense
twin dome
I am currently working on a question about normal distribution and I am having some trouble calculating the probability. I was wondering if anyone could help me out?
The question is as follows:
The weight of bicycles in a certain shop is normally distributed with a standard deviation of $2.2 \mathrm{~kg}$ and a mean weight of $15 \mathrm{~kg}$. Calculate the probability that a randomly selected bicycle from the shop weighs over $20 \mathrm{~kg}$.
Here is my attempt at solving the question:
Let X be the weight of a randomly selected bicycle from the shop. We know that X follows a normal distribution with a mean of $\mu = 15 \mathrm{~kg}$ and a standard deviation of $\sigma = 2.2 \mathrm{~kg}$.
We are interested in finding $P(X > 20)$. To calculate this, we need to standardize X using the formula:
$z = \frac{X - \mu}{\sigma}$
Substituting the given values, we get:
$z = \frac{20 - 15}{2.2} \approx 2.27$
Now we need to find the probability that a standard normal random variable Z is greater than 2.27. Using a table or a calculator, we find that this probability is approximately $0.011$.
Therefore, the probability that a randomly selected bicycle from the shop weighs over $20 \mathrm{~kg}$ is approximately $0.011$.
Any help or feedback would be greatly appreciated. Thank you!
marsh citrusBOT
I am currently working on a question about normal distribution and I am having s...
elfin berryBOT
dgh
queen fjord
does that make sense
yes thx sm
vague ocean
I am currently working on a question about normal distribution and I am having s...
your answer makes sense to me. If the mean is 15 and sd is 2.2, then a value 20 should be a little over two standard deviations away
This ties in with the low probability that you calculated
marsh citrusBOT
@twin dome Has your question been resolved?
fickle sable
can someone help with part b of question 13?
marsh citrusBOT
can someone help with part b of question 13?
trim pulsar
if the col A = 3R
marsh citrusBOT
if the col A = 3R
marsh citrusBOT
@trim pulsar Has your question been resolved?
long cape
marsh citrusBOT
long cape
How would I change log base 3 to ln?
Can’t remember if I need to combine arguments as division first
proper zodiac
doesnt matter
still temple
How would I change log base 3 to ln?
change of base
[
\map{\log_{a}}b = \f{\map {\log_c}b}{\map {\log_c}a}
]
elfin berryBOT
long cape
long cape
change of base
Like this?
elfin berryBOT
long cape
I thought it was a in attic, b in basement
still temple
Like this?
yes
long cape
I thought it was a in attic, b in basement
I guess if we consider base as basement, argument as attic, that works
still temple
what?
flat raft
lixera, didn't you ask for proofs of the log rules a while ago LOL
still temple
lixera, didn't you ask for proofs of the log rules a while ago LOL
learn and improvise 😎
actually got all of them into my head thankfully
marsh citrusBOT
@long cape Has your question been resolved?
proper zodiac
the fact you've had to specifically change lixeras letters to make a mneumonic should tell you its not a good way to remember
proper zodiac
if someone now hands you $\log_{a}(b)$ you're likely going to confuse yourself
elfin berryBOT
ΣAC
proper zodiac
"oh i thought i put a on top because of attic??"
still temple
just like
long cape
still temple
...thanks for highlighting that i suppose
glass lake
marsh citrusBOT
glass lake
so
i know the chain rule is used
im not sure how to start
on this probloem
i think something is supposed to be plugged in into x^9
but
im not sure what
can someone give me a hint
sage gale
no, just use chain rule on f(x^9)
glass lake
f'(g(x))g'(x)
glass lake
why do we do that tho
because it says f(x^9)
and i dont see a g in that
so im not sure where that came from
sage gale
g is just a placeholder for some random function
sage gale
yes
glass lake
and f'(g(x))g'(x) has g(x) inside of it which makes it the same thing?
or is there another reason why that is g(x)
sage gale
no you had it the first time, its just because f(x^9) has x^9 inside f(x)
sage gale
then plug in a
sage gale
you got the 8 part right, but not x^9
glass lake
but g(x) = x^9 because f'(g(x)) is where g(x) is inside f'(x) tho?
thats how i gto that
sage gale
wait are you solving F'(a) or G'(a)
glass lake
G'(a)
sage gale
b r u h
glass lake
wait
if g(x) is in f'(x) in the chain rule
doesnt that mean 8 = g(x)
because its inside
which means
the derivative of 8 is 0
so g'(x) = 0
sage gale
no
lets start over
we want the derivative of F(x)
F(x) = f(x^9)
using chain rule...
F'(x) = f'(x^9) * (derivative of x^9)
that is all chain rule tells us
you plugged in a...
glass lake
oh
glass lake
so g(x) is x^9
sage gale
yes
glass lake
f'(x^9) * x^9 and the reason that it's x^9 is because x^9 is in the f'(x)
just making sure i understand
which means
F(x) = 8 * x^9
glass lake
8* 9x^8?
sage gale
yes
glass lake
72x^8 = F(x)
sage gale
continue
glass lake
so to find G'(a)
we need to first find G(x)
and then after we find that
we take the derivative?
sage gale
sure
sage gale
do you see how we have (f(x))^9 and not just f(x)
that means we have to do something about ^9
sage gale
yes you did the outside stuff correctly, but now we have to worry about the inside again
G(x) = f^9 so G'(x) = 9f^8 f'
f(x) stays the same inside but now we want the derivative of f outside
glass lake
9f^8 f'
whats this from
oh
chain rukle
g'(f(x)*f(x)?
i think?
not sure if thats how u got that part
sage gale
yeah except f'(x) on the right
glass lake
actually
wait
so thats just the chain rule
written without the (x)
uh
how do i proceed
i looked at it for a minute
but
im not sure
wait
f^9 * 72x^9/
because we found F'(x)
so we plug that in
okay
so
i think i figured it out
give me a sec
.close
languid willow
i need help
marsh citrusBOT
i need help
sturdy bear
Ok so if we look at the 8 feet long for one side of the office, how many cm is that?
languid willow
uhh idk can u please explain how i'd find that
im a little slow 😭
wait
is it 2?
im so confused
sturdy bear
So you have an 8 ft by 16ft room, I would recommend drawing that first
Then draw another rectangle right beside it but label it with 4 cm and 8 cm
marsh citrusBOT
@languid willow Has your question been resolved?
languid willow
Wait like the final answer you got is 2?
no 😭 idek how to do this
im so confused 😢
sturdy bear
Have you drawn the rooms like I said above?
marsh citrusBOT
@languid willow Has your question been resolved?
quick orchid
can anyone explain to me how these are equal? ¬(¬p ∨ ¬¬q) ≡ p ∧ q.
marsh citrusBOT
can anyone explain to me how these are equal? ¬(¬p ∨ ¬¬q) ≡ p ∧ q.
bright jay
I'm assuming the q is a typo
quick orchid
nah it isnt
bright jay
But apply de Morgan's
quick orchid
why would q be a typo?
bright jay
The double negate symbols
quick orchid
The double negate symbols
im not sure i understand how id apply de morgans here
bright jay
First, I'm asking if it's a typo that you have double negate symbols
¬(¬p ∨ ¬q) ≡ p ∧ q
Two, if it's that, apply de Morgan's
quick orchid
no the double negate symbols are meant to be there
¬(p → ¬q) this was the original
i added the double negate symbols cause i thought itd be easier to simpify
marsh citrusBOT
@quick orchid Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
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
lean gulch
I took geometry last year and I think i can help out
So what do we know about angles on a straight line
This to be exact
You actually don’t need to do worry about that here
Before that what don’t you understand about the fact that angles on a straight line add up to 180? You said it perfectly right here
Im not sure what you mean
Why?
marsh citrusBOT
lean gulch
Up to you man
It’s a fairy simple question so if you aren’t sure I can explain it to you but all good
marsh citrusBOT
Available help channel!
wheat ice
Suppose there's a spherical cap of a certain beta angle to the z axis(figure a) and a vector V on the zy plane with angle theta to the z axis(figure b). Is there a way to find that angle alpha (in terms theta and beta) that delimits the end of the spherical cap (in x direction) in the position of the vector V (refer to figure c).
This question is mainly a curiosity of mine and that's the reason of the shitty pic, but i tried my best on paint.
Edit: V is on the spherical cap, that is, V is the same size as the radius of the spherical cap. (just to be make sure this is known)
marsh citrusBOT
Suppose there's a spherical cap of a certain beta angle to the z axis(figure a) ...
@wheat ice Has your question been resolved?
wheat ice
<@&286206848099549185>
marsh citrusBOT
@wheat ice Has your question been resolved?
marsh citrusBOT
@wheat ice Has your question been resolved?
wheat ice
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
wind mural
Hello! I'm confused on how to solve the integral ∫sqrt(1-x) * x * dx. I've tried u-substitution by setting u equal to 1-x and thus du equal to -dx but I have no idea where to go from there since I can't further manipulate du to substitute out all x.
marsh citrusBOT
Hello! I'm confused on how to solve the integral ∫sqrt(1-x) * x * dx. I've tried...
nocturne fiber
I mean that's the right substitution
are you sure you're still stuck?
u=1-x means x = 1-u
you're really close
marsh citrusBOT
marsh citrusBOT
Available help channel!
glass slate
marsh citrusBOT
glass slate
I dont get this
crisp lion
geometrically speaking, you are given a square starting at (a, a) and ending at (b, b)
and your function is a line on that square; given the above conditions this line (i.e. function) must intersect the square’s diagonal at least once
leaden monolith
A visual aid to help
If your function is continuous in that square in the middle
glass slate
so this means it has to have a root?
leaden monolith
It MUST pass through the diagonal at some point
glass slate
ok i think i got it
thx
it has to intersect y=x to have a solution
and if its continuous, it does
.close
fickle whale
that's the answer apparently
swift olive
I don't understand the question. Are you asking how the equation could be simplified? The handwriting is hard to read could you try rewriting with latex?
marsh citrusBOT
swift olive
.reopen
fickle whale
I don't understand the question. Are you asking how the equation could be simpli...
yeah like how do I simplify it to
fickle whale
or did I go wrong somewhere?
swift olive
deleting the first message made the bot try and close but I think its ok
fickle whale
:o
swift olive
how can you make them have a common denominator?
fickle whale
multiply first function's numerator by (10x-6) ?
swift olive
Multiplying the numerator and denominator by the same number is equivalent to multiplying by 1
marsh citrusBOT
Available help channel!
white brook
This is the question I'm slightly confused on
marsh citrusBOT
This is the question I'm slightly confused on
elfin berryBOT
white brook
As far as I can tell I need a particular solution for y, since there's stuff on the right side
But I've not quite done particular solutions in terms of another variable
Since it's an x^2 term, do I use y_p=Ax^2+Bx+C?
Something like this?
marsh citrusBOT
@white brook Has your question been resolved?
marsh citrusBOT
white brook
.reopen
marsh citrusBOT
✅
white brook
Still a little confused on this. I got this as the answer but it's saying I'm wrong
marsh citrusBOT
@white brook Has your question been resolved?
lofty gyro
be careful! the x is outside the squareroot!
lofty gyro
Still a little confused on this. I got this as the answer but it's saying I'm wr...
otherwise, it should be correct
furthermore, shouldn't it need you to find c1 and c2 too?
marsh citrusBOT
marsh citrusBOT
Available help channel!
sick quiver
Hi! I was wondering how I am supposed to clarify this question. I do know how to solve it, but I was wondering if someone could walk me through the steps!
marsh citrusBOT
Hi! I was wondering how I am supposed to clarify this question. I do know how to...
@sick quiver Has your question been resolved?
marsh citrusBOT
@sick quiver Has your question been resolved?
marsh citrusBOT
@sick quiver Has your question been resolved?
broken forum
Hi! I was wondering how I am supposed to clarify this question. I do know how to...
did you get the right answer
and did you show your work
if you did then theres nothing else to say
sick quiver
I checked the back to get the answer cause I couldn’t quite understand it, but I think I need more clarification on why 6/12 turns to 1/2 instead of just being 6/12 = 0.5
broken forum
I checked the back to get the answer cause I couldn’t quite understand it, but I...
are you asking why is 6/12 equal to 1/2?
sick quiver
No, but rather do I always have to simplify fractions all the time?
broken forum
no ofc not
you can do however
its just usually easier to deal with fractions when they get messy
like 3/7
and you dont lose precison by rounding either
junior geode
How can I find the variance of an arrival time conditioned on a counting process?
marsh citrusBOT
How can I find the variance of an arrival time conditioned on a counting process...
junior geode
For example we want to find $Var(T_4 | N(1) = 2)$ where $(N(t))_{t \geq 0} \sim PP(\lambda)$
marsh citrusBOT
@junior geode Has your question been resolved?
junior geode
<@&286206848099549185>
marsh citrusBOT
@junior geode Has your question been resolved?
marsh citrusBOT
@junior geode Has your question been resolved?
junior geode
I know how to find [E(T_k | N(t) = n)], but I'm quite sure how to find E(T_k^2 | N(t) = n) either
marsh citrusBOT
@junior geode Has your question been resolved?
azure trench
Stuck on part b
marsh citrusBOT
Stuck on part b
stoic saddle
simplify 1/(tan^2(θ)+1)
azure trench
Oh so ur working backwards ? Subbing in x and then manipulating until u get cos squared?
Yeah that works
Thx
.close
marsh citrusBOT
pallid pine
Stuck on part b
you could also just automatically recognise that
tan^2 + 1 = sec^2
cos^2 = 1/(tan^2 + 1)
marsh citrusBOT
Available help channel!
still temple
guidance on this
marsh citrusBOT
guidance on this
cunning jackal
What angle does a tangent make with the radius
still temple
Ohh so
desert socket
yes
still temple
90-62
cunning jackal
Angles in the same segment subtended by the same arc on the circle
Look at arc AB
still temple
yeah
cunning jackal
It is subtending two angles on the major arc
One of them is y
And the other is 62
still temple
wht's subtending? 😭
cunning jackal
wht's subtending? 😭
Like the end points of the chord AB are joined to a point
On the circumference
still temple
Oh okay okay
still temple
Ohh okay okay
cunning jackal
Use that
cunning jackal
Angles subtended by same arc in the same segment are equal
Do you want a proof of this?
Like a justification
I can explain if you want
still temple
Oh okay
still temple
I can explain if you want
Yeah 🥺
cunning jackal
Alright to prove it, we need another property which says angle subtended by an arc on the circumference is half of that subtended at the center
still temple
Yeah ik that one
cunning jackal
Great
Now by that logic
But angle y and angle 62°
Should be half of the same angle at the center right?
still temple
Yep yep
cunning jackal
So that means?
cunning jackal
No
still temple
(y + 62 )/ 2 = angle in center
still temple
Ohh oky oky
still temple
Oh its alrr
cunning jackal
still temple
angle O is the double of angle A?
cunning jackal
Yep
still temple
Yeahh okayyy
cunning jackal
And O is double of B as well
still temple
Yeah
cunning jackal
Now think, doesn't that just mean A is B?
still temple
So A and B are equal
cunning jackal
Yep
still temple
Yeahhh
cunning jackal
Now see your problem figure
still temple
cunning jackal
Look at the two angles subtended by AB
still temple
Yeah
still temple
Uhh why?
cunning jackal
Rotate the figure
And just observe carefully
Lines from A and B
Meet at y
The same way angle B was made in the example figure I sent
still temple
62
cunning jackal
Great
still temple
And so now z left
cunning jackal
Alright so AC is given to be our diameter
still temple
Oh i get how to solve z
still temple
Alright so AC is given to be our diameter
Yeah
cunning jackal
Oh i get how to solve z
Sure go ahead and try it
still temple
I did it
What is did is:
Angle E = 180 - 70 (cyclic quadrilateral )
we alr know what y is
so 110 - 62
cunning jackal
Nice
desert socket
wait is a quadrilateral concylic if its in a semicircle?
still temple
that equals to 48
cunning jackal
so 110 - 62
Good job
still temple
wait is a quadrilateral concylic if its in a semicircle?
No if the four sides touch the circumference of the circle
cunning jackal
wait is a quadrilateral concylic if its in a semicircle?
Cyclic quadrilateral means all 4 vertices lie on the same circle
cunning jackal
No if the four sides touch the circumference of the circle
Not 'touch' actually
still temple
U helped a lot @cunning jackal
cunning jackal
Touch is a word used for tangents
still temple
Ohh okay okayyy
cunning jackal
Thankuuuuu
You're welcome
still temple
Umm can i get help with another?
cunning jackal
Uhh actually I got some work to do
still temple
Oh it's alr
cunning jackal
Just open another channel if you want
still temple
Okayy
cunning jackal
Thanks again
😄
desert socket
Cyclic quadrilateral means all 4 vertices lie on the same circle
which quadrilateral are you considering?
cunning jackal
Beard is here I guess
still temple
❤️
cunning jackal
which quadrilateral are you considering?
ACDE
cunning jackal
it was this
When can you say a point will lie inside this triangle? Like, what can you say about that point's position with respect to the lines
still temple
Umm i didnt get it
cunning jackal
For example, I ask about line AC. And if I mention any point lies inside the triangle ACB, doesn't that mean the point is to the right of AC?
Because the triangle is in the right side of AC
still temple
Yeah yeah
cunning jackal
Yep, what does that mean
still temple
x greater than 3
cunning jackal
Nice
still temple
cuz its on the right side
still temple
it would be y is less than 6?
cunning jackal
Yep
still temple
cuz the point would be under BC
cunning jackal
That's the second one
still temple
Ohh iccc
cunning jackal
Now AB is a little tricky
still temple
Yeah
cunning jackal
Well if you notice what we did for AC and AB, we essentially assigned a certain sign to the value of x-3 and y-6 respectively
still temple
Yeah
still temple
Yeah
cunning jackal
Now what I want you to notice is we're essentially assigning specific signs to the value of the expression which we get on putting the point in the equation of the line
still temple
yeahh
cunning jackal
Like I say if x's value is 5, 5-3>0 so it lies to the right
Now for the line y=x+1/2
still temple
Yeah
cunning jackal
We'll do the same thing, assign signs
still temple
okay yeah
cunning jackal
One way to do it is identify a clear point which we know lies on one side of the line and then see what sign it gives
For example can you tell me where the origin i.e. (0,0) lies with respect to AB?
still temple
it lies on the left side?
cunning jackal
Use the y intercept of the line
To decide whether the origin is above it or below it
By above, I mean the side in which the triangle is
still temple
Use the y intercept of the line
Uhh i didn't get that
cunning jackal
Uhh i didn't get that
Where does this line AB cut the y axis?
still temple
On 0
still temple
yeah yeah
still temple
M = gradient?
cunning jackal
Which axis?
still temple
the y axis
still temple
Oh icc
cunning jackal
okay so the line cuts y axis at 0.5?
Yes, better to list both coordinates
Now then
still temple
Okay
cunning jackal
That means the origin is on the opposite side of the triangle right?
still temple
Yep
cunning jackal
Great
cunning jackal
One way to do it is identify a clear point which we know lies on one side of the...
Back to this thing now
We want to identify what sign a point lying above AB would give when it's plugged into the equation of AB
Well we know the origin lies below it
still temple
Yeah
cunning jackal
So essentially if you can find what sign putting the origin in will give you
The sign we require is the opposite one
Get my point?
still temple
Uh?
cunning jackal
When you plug in the origin's coordinates into the expression of AB, what do you get
cunning jackal
Yep, we get a positive value
still temple
Oh okay
cunning jackal
if I put 0,0 in x-y+1/2 what I will get
And we're getting 1/2 as you said
Which is positive
still temple
yes
cunning jackal
Now we know that all the points lying below the line satisfy x-y+1/2>0
But the triangle lies above it
cunning jackal
yep
There you go
That's your third inequality
Now actually I want to explain it in a simpler way
still temple
Ohh yeahh
cunning jackal
The y co-ordinate at any point on the line is given by x+1/2
Now we want a point 'above' it
Which means we want a higher y co-ordinate
still temple
Yeah
cunning jackal
So we want a y which is greater than x+1/2
still temple
Yep
cunning jackal
That's a way shorter way to get to the answer but I wanted to explain the other one to you as well
cunning jackal
You're welcome
cunning jackal
Gl
still temple
thanku sm
cunning jackal
You can .close
still temple
.close
short wadi
Do we need to do product nd chain rule to compute this?
marsh citrusBOT
Do we need to do product nd chain rule to compute this?
proper zodiac
You will yes
marsh citrusBOT
proper zodiac
Is it best to do the chain rule first and then do the product rule?
You would not be able to do the chain rule without first doing the product rule
marsh citrusBOT
Available help channel!
oak void
marsh citrusBOT
elfin berryBOT
yomiko
oak void
$\int f(x) f'(x) dx$ \ $ y = [f(x)]^{+1}$
elfin berryBOT
yomiko
oak void
then?
main idol
even so its y = e^sinx it would be sinx e^sinx tho
what is "it" in this sentence
oak void
dy/dx
main idol
no
oak void
of e^sinx
elfin berryBOT
main idol
,tex .diff rules
elfin berryBOT
riemann
main idol
y=e^sin(x) is of the form f(g(x)) where g(x) = sin(x) and f(x) = ?
oak void
e^x ?
main idol
correct
use one of the bottom two rows to find dy/dx
whichever notation you're more comfortable with
oak void
wait so you don't use f(x) ^n+1 ?
elfin berryBOT
main idol
can you see that those are different?
main idol
you would do y = ln|(x^2 + x + 5)^-1/2| right?
differentiate and check
main idol
i did it and checked the answer but they didin't do ln|f(x)|
show the answer
main idol
i did it and checked the answer but they didin't do ln|f(x)|
and show your derivative
elfin berryBOT
riemann
main idol
$h(x) = x^2+x+5, g(x) = \sqrt{x}, f(x) = \log(x)$
elfin berryBOT
riemann
oak void
I've never done chain rule up to 3 function
main idol
I've never done chain rule up to 3 function
good time to practice
main idol
but you also don't need to if this is all you're asked to find
you do use power rule here to differentiate
$y = f(g(x)) = \sqrt{g(x)}$
elfin berryBOT
riemann
main idol
can you find f(x) =? and g(x)=?
oak void
you do use power rule here to differentiate
I would times it by half and also times it by dy/dx of whats in the bracket
wait
i don't get it, i tried to apply the answer's method to other question but i get it without ln|f(x)| but they've got ln|f(x)| as their answer
main idol
i don't get it, i tried to apply the answer's method to other question but i get...
am i supposed to know the other question?
main idol
surely not this one right?
oak void
like for example $\int \frac {e^{2x}}{e^{2x}+3} dx$ i get $\frac {2e^{2x}}{e^{2x}+3}$
elfin berryBOT
yomiko
main idol
well that's because the derivative works
main idol
you didn't use chain rule properly so your derivative doesn't work out
oak void
you didn't use chain rule properly so your derivative doesn't work out
right, but sometimes the answer use chain rule and other times it doesn't
its confusing
main idol
you need to be able to identify function compositions correctly
tulip folio
I am looking for someone who is very good with writing calculus proofs.
tulip folio
I know how the entire thing works. Just don't know how to write it formally using theorems such as the EVT to show there is a global minimum on the closed interval [c1,c2] and so on...
main idol
have you ever written an epsilon delta proof?
tulip folio
Yes but that has nothing to do with this lol.
tulip folio
No
I just gave a suggestion
That is why i'm here. I'm asking how you would formally prove this.
main idol
Yes but that has nothing to do with this lol.
sounds like you know what you want
tulip folio
f is continuous on [c1,c2] , so f must attain its minimum and maximum on [c1,c2]. And the minimum cannot be attained at c1 and c2 since they are local maximums. So the minimum is attained in (c1,c2), which becomes a local minimum of f on [a,b].
This is basically how the proof works
Just don't know how I can use theorems/definitions to write the formal proof for it.
flat raft
I think there's an edge case where if the function is constant, then you have a local maximum and minimum at the same point lol
tulip folio
The question says that it is not constant
proper zodiac
the question explicitly rules out constant functions
main idol
f is continuous on [c1,c2] , so f must attain its minimum and maximum on [c1,c2]...
f is continuous on [c1,c2] , so f must attain its minimum and maximum on [c1,c2].
sounds like you proved it with your first line here
just cite EVT
tulip folio
So basically. I can cite EVT to show that there is a global minimum between [c1,c2]. I just don't know how to prove the part where I have to show there must be a local minimum in (c_1, c_2), the open interval.
main idol
So basically. I can cite EVT to show that there is a global minimum between [c1,...
this says (a, b) not (c1, c2)
glass perch
Doesn't EVT just say there's a minimum in [a,b], which is too weak?
flat raft
you have a global minimum over f restricted to [c1, c2], but that translates to being a local minimum
tulip folio
yea
glass perch
What does c1, c2 is a maximum mean for the derivative of f?
glass perch
Like is the derivative positive or negative before and after c?
tulip folio
positive?
glass perch
Before or after the c's?
tulip folio
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
echo mountain
Hey, I can't get the equation below right now, there's a mistake somewhere. Could someone write down the steps for me please? Thanks in advance!
marsh citrusBOT
Hey, I can't get the equation below right now, there's a mistake somewhere. Coul...
@echo mountain Has your question been resolved?
ornate silo
marsh citrusBOT
frozen rover
choose C
frozen rover
The sum of the value of two edges of the triangle is more than the value of the third one
marsh citrusBOT
choose C
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
broken forum
can you write the equation ?
broken forum
13 > c
c is the third side
so c has to be less than 13
do the rest of the equations
ornate silo
oh i have to do all 3 ?
broken forum
ye
broken forum
now what ?
solve for c
ornate silo
c < 13
c > -3
c > 3
ornate silo
so i have to choose the answer that is in range ?
ornate silo
all right got it now
broken forum
they wont show you 6 and 8 for example
ornate silo
ornate silo
i did $\frac{2x^2}{2} = 18$
elfin berryBOT
Bunnings
ornate silo
take 10 min to try to figure it out
i understood it properly dont worry. I remember things easily
broken forum
i understood it properly dont worry. I remember things easily
what
ornate silo
oh i thought you referred to the previous question and said to take 10 mins to better understand
my apologies
ornate silo
**Bunnings**
which led to $x^2 = 18$
elfin berryBOT
Bunnings
ornate silo
$x = 3\sqrt2$
elfin berryBOT
Bunnings
broken forum
**Bunnings**
yeah I get that
wait
chartbit did you solve it already
why are you thumbing up
its wrong
glass silo
**Bunnings**
Justify what you’re representing by x
ornate silo
one side is x so other side has to be 2x
area of triangle is 1/2 * 2x * x
so 1/2 * 2x * x = 18
glass silo
i thought your answer was 3root2
(Of course, that is not the final answer!)
ornate silo
so one side is 2* 3sqrt2 and other is 3sqrt2
now i just have to a^2 + b^2 = c^2 right ?
thanks
i dont know how do i calculate this one
ornate silo
yeah i tried them a while ago. These are the ones i face trouble with
broken forum
oh okay
ornate silo
15*10^m+n right ?
broken forum
yeah
ornate silo
i dont see this as answer
ornate silo
so how do i do ?
glass silo
15*10^m+n right ?
This is the product but it isn’t in scientific notation
broken forum
make 15 less than 10
ornate silo
1.5
broken forum
ye
ornate silo
but what about the rest ?
broken forum
if you divide by 10 you gotta multiply by 10 somewhere else
ornate silo
1.5 * 10^m+n for sure
no ans for that. option b is close
but where does the 1 come from
broken forum
read what i said
ornate silo
yeah so i have to add one to exponent because i divided by 10 ?
broken forum
yes
ornate silo
i solved this and get answer $\frac{1-x}{(x+1)(x-1)}$
elfin berryBOT
Bunnings
broken forum
damn you have a lot of questions
elfin berryBOT
Bunnings
broken forum
yep
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
For this, I got to the point where I had y = 6(x^2-8x+16/6) + 89 - 16, but I'm not sure what should be the next step
marsh citrusBOT
For this, I got to the point where I had y = 6(x^2-8x+16/6) + 89 - 16, but I'm n...
still temple
?
late geode
your manipulation wasn't ideal
still temple
?
late geode
can you show the work that led up to that
still temple
ok