shouldn't the x be zero?
#help-19
solar burrow
lavish kite
...why would it be 0?
solar burrow
because if i am using x=0 for the function
lavish kite
...well you are looking at the value and derivatives of the function at 0, why would that mean that x is 0
(also a formula that just tells you the value of the function at 0 would not be very useful given that one of the things you're putting in is its value at 0, and then the rest of the terms would all be powers of 0 and therefore evaluate to 0)
the basic idea with a taylor series is that even if you just have information at 0 you can use that to get a pretty good approximation of the function around 0
solar burrow
indeed that must be wrong
i think i got confused anyway, now that i look at it again it makes sense
but not necessarily 0
right?
even thought i understan that it shift the function near zero
lavish kite
oh right yes you can use it around any a
just in this case they're doing it with a=0
blazing gyro
∀x(A∨B) → (∀xA ∨ ∀xB)
How do i know if this is true or false
odd edgeBOT
∀x(A∨B) → (∀xA ∨ ∀xB)
How do i know if this is true or false
@blazing gyro Has your question been resolved?
blazing gyro
@plain lagoon
random girder
Khan academy?
random girder
∀x(A∨B) → (∀xA ∨ ∀xB)
How do i know if this is true or false
Substitute by assigning each set 2 or 3 different values with 1 or 2 common ones
blazing gyro
what do you mean
odd edgeBOT
@blazing gyro Has your question been resolved?
karmic zealot
Im new here, Am i able to share a photo of my question ?
tight crescent
Im new here, Am i able to share a photo of my question ?
Yes, of course.
karmic zealot
karmic zealot
Can anyone explain this to me? Why does it equal 1?
Oh i forgot to mention the premise is that A and B and C are the angles of a triangle
upbeat drum
Oh i forgot to mention the premise is that A and B and C are the angles of a tri...
this means $A+B+C=180, C=180-(A+B)$
$\implies \tan(C)=\tan(180-(A+B))=-\tan(A+B)$
upbeat drum
using that and simplifying will give you 1
karmic zealot
So i should convert Cs in both numerator and denominator into A+B, and then simplify it?
upbeat drum
yes so you're only working with 2 letters
manic wren
quick question, is f(x)=x^2 + 1 injective, surjective or neither?
manic wren
mapped from R -> R*
i understand that it isnt surjective
as not all of the values on the image are hit
so im thinking it may be injective, but im not sure as f(-2)=f(2)
does that make it neither?
mystic saffron
f(-2)=f(2) means the function is even not injective
manic wren
so for it to be injective each value on the domain must map to exactly one value of the codomain?
tight crescent
so for it to be injective each value on the domain must map to exactly one value...
To at most one*
manic wren
To at most one*
i thought an injective function has to be mapped one-to-one
oh wait i see
tight crescent
Not all values in the codomain have to be represented in order for a function to be injective
manic wren
and then surjective is each element in the domain must match to 1 or more elements in the codomain?
wait no i worded that wrong
tight crescent
No
manic wren
i mean each element in the domain must match to 1 element in the codomain and multiple elements in the domain can be mapped to one element in the codomain?
is what i meant to say haha
tight crescent
Yes, "if each element of the codomain is mapped to by at least one element of the domain"
And it's injective if there exist no such distinct $x_1$ and $x_2$ that $f(x_1) = f(x_2)$
clever fjordBOT
USS-Enterprise
odd edgeBOT
tight crescent
You can graphically check whether a function is injective by drawing a parallel line to the x -axis. If any intersect the graph twice (or more), it is not injective
odd edgeBOT
Available help channel!
grave cairn
hi, I'd appreciate if anyone could answer this #calculus message thanks
grave cairn
wait why is this autoly pined
wooden python
wait why is this autoly pined
that's what happens to every first message in help channels
the intended use is that you post your question and then helpers can check pins to refer to it
grave cairn
I'm guessing for these types of line integrals $\int f ds$, reverting the starting and ending point wouldnt change the result, am I correct? if so I cant seem the articulate the reason
clever fjordBOT
Mwalls
grave cairn
ds means the tiny curves along the curve, and is treated as "neutral", only the symbol of f on that tiny curve counts towards the final result, which is the net sum of all those tiny curves
grave cairn
well I totally forgot electromagnetics now but work done seems simply enough
but I still couldnt find my mistake in that derivation
mystic saffron
work done isn't line integral mb
grave cairn
well, the intution, like, you'd spend the same amount of work pushing something along some curve whether from A to B or B to A
mystic saffron
thermodynamics will murder you for saying this lol
work done isn't just mechanics
grave cairn
what I mean is no other force is working on that object
like pushing something on a flat table
mystic saffron
like pushing something on a flat table
yeah it's unchanged in this situation
grave cairn
this at least gives me simple intuition but my question is a methematical one so...
mystic saffron
yeah proof by intuition doesn't work here
grave cairn
yeah my example actually arent of this type
clearly the starting and ending points would change the sign of the integral
which is a basic property
mystic saffron
but it's a line integral
grave cairn
oh well..
grave cairn
no, it's the one that already converted into a normal integral
the $\int_{\theta_1}^{\theta_2} r(\theta) d\theta$ one
mystic saffron
bot dead?
clever fjordBOT
Mwalls
grave cairn
not sure how but inserting space before the second $ seems to fail today
mystic saffron
$it fails every time $
mystic saffron
**Mwalls**
well if it's a normal integral, sign will change on exchanging the limits
grave cairn
anyway if I revert the curve, then theta 2 would switch place with 1 and the result would be the negative of the original result
unless there's another thing compensating or my method casting the original problem into this is incorrect
could you try finding the mistakes I'll type them again here
$x=R\cos\theta , y=R\sin\theta$ , then $\int_{L}yds=\int_{\frac{3\pi}{4}}^{0}R\sin\theta\sqrt{(dx)^2+(dy)^2}= \int_{\frac{3\pi}{4}}^{0}R\sin\theta\sqrt{(dx/d\theta)^2+(dy/d\theta)^2}d\theta=\int_{\frac{3\pi}{4}}^{0}R\sin\theta\sqrt{(-R\sin\theta)^2+(R\cos\theta)^2}d\theta=\int_{\frac{3\pi}{4}}^{0}R\sin\theta*Rd \theta=\text{something minus but it's supposed to be postive}$
mystic saffron
anyway if I revert the curve, then theta 2 would switch place with 1 and the res...
yes, I don't see anything g wrong hwre
I'm not sure about this
I have not reached here in calculus yet
clever fjordBOT
Mwalls
grave cairn
thanks, it's a little annoying to have encountered this mistake consider I've been learning calculus for quite a while. it means I've probably got some very basic things wrong
mystic saffron
it also means you have got more things to learn
odd edgeBOT
@grave cairn Has your question been resolved?
odd edgeBOT
@grave cairn Has your question been resolved?
odd edgeBOT
@grave cairn Has your question been resolved?
low locust
1+1= <@&268886789983436800>
formal coyote
1+32 = 33
fair token
.close
odd edgeBOT
odd edgeBOT
Available help channel!
sour heron
is this geometric series convergence calculation correct?
low locust
a geometric series usually starts at 0
sour heron
a geometric series usually starts at 0
My series is this currently which has to start from n=1. It should sum to 1 which wolfram says it does but I am not sure how. Been a while.
sour heron
move one factor of 1/3 out of the sum
sorry had to go for a moment, so the formula basically becomes (a/(1-r))-a?
or rather: (2/(1-(1/3)))-2=1
low locust
or you can also do it that way, yes
fiery sentinel
Can someone explain this to me?
odd edgeBOT
Can someone explain this to me?
low locust
n=7n-6n
fiery sentinel
Okay now how would you do A={6a+10b:a,b in Z}
odd edgeBOT
Available help channel!
winged condor
hey I have this equation y = 3 (x - 2)^2 + 2 (z + 1)^2 - 5 that I want to plot but I have no idea what this curve is
winged condor
any help?
winged condor
more like 3
sand night
is that even possible to graph
winged condor
the shape is in R^3
winged condor
thanks :)
candid crag
I don’t understand what this is asking me to do. where did the Y come from? What is going on
stark coyote
its testing your knowledge on solving a system of equations using back-substitution.
each "hotspot" is a system, and it gives the substitution. you gotta decide whether the substitution is correct.
crimson hamlet
I know the answer is B but can anyone explain the process
royal herald
,w graph x(sqrt(4-x^2))
clever fjordBOT
royal herald
See what that is in the first quadrant?
U wanna integrate from 0 to 2
And you’ll get ur answer
Is that what ur question was?
crimson hamlet
Is that what ur question was?
i know that that is what i have to do, question is how do i integrate that? ive tried trig sub, but i suck at it
i just need a walk through
royal herald
U sub is only necessary
$\int_0^2 x\sqrt {4-x^2} ,dx \newline u = 4-x^2 \newline ,du = -2x ,dx \newline \therefore -\frac 12 ,du = x dx \newline -\frac 12 \int_{u(0)}^{u(2)} \sqrt u , du$
stark coyote
-1/2du = xdx
royal herald
Would you know how to go from there @crimson hamlet
stark coyote
forgot the -1/2 constant outside the resulting integral
royal herald
Oml thx lol
crimson hamlet
Would you know how to go from there <@413399965881335808>
no lol
clever fjordBOT
Stephen
stark coyote
no lol
integration takes a ton of practice. u-sub is one of the easier ones. if you are struggling i suggest putting in a lot of time to understand it, so trig sub will be easier to get.
crimson hamlet
U don’t remember how to integrate sqrt(u)?
yt aint tell me yet. learning through youtube till i actually have to take the class
thanks a lot though. im sure i can figure it out from here
stark coyote
you're trying to run before you walk, man. gotta learn antiderivatives first.
crimson hamlet
i did
stark coyote
if you knew them then you would know how to integrate sqrt(u)
crimson hamlet
fair
royal herald
yt aint tell me yet. learning through youtube till i actually have to take the c...
Ah ok I see, good job taking initiative
royal herald
you're trying to run before you walk, man. gotta learn antiderivatives first.
But yea this is it, try taking some more time doing some simpler integration before you move onto subs
odd edgeBOT
@crimson hamlet Has your question been resolved?
fringe sail
odd edgeBOT
feral solar
hi
fringe sail
and what did they do after i am pretty lost
feral solar
i can attempt to help
fringe sail
sure
fringe sail
ok
feral solar
ok
so apply reverse synthetic division
and if you do that, you can find the same polynomial
feral solar
OHHH
fringe sail
cause this is the solution sheet
feral solar
ax+b is the polynomial
wait what
no
im lost dude
im only in precalc
im not like these math genies
manic sleet
Whenever we divide a polynomial by a quadratic i.e. (x-r1)(x-r2) the remainder is of the form ax+b :)
ax+b is your remainder
Q(x) is the quotient
feral solar
ok
fringe sail
Whenever we divide a polynomial by a quadratic i.e. (x-r1)(x-r2) the remainder i...
why is it in that form
isnt it just a constant
- y or something
feral solar
ohhhhh
manic sleet
you can do out the math but after doing Polynomial Long Division you will get something of the form ax+b
feral solar
ok i understand
manic sleet
if you divide by some (x-r1) you'll a constant remainder
feral solar
thank you
fringe sail
bro this isnt ur question lmao
feral solar
i know
manic sleet
also I saw you @lavish osprey 👀
fringe sail
you can do out the math but after doing Polynomial Long Division you will get so...
ok
from there
what did the teacher do
the constant can be represented by ax+b
manic sleet
we divided by x-1 and x+3, correct?
fringe sail
into ax+b ohh
manic sleet
we know we get f(1) which is 2
fringe sail
cause its the remainder
manic sleet
and the quotient will cancel out to 0 :)
we simply just get a system!
$
[
\begin{cases}
a+b=2\
-3a+b=6
\end{cases}
]
$
fringe sail
so from the 2 we can find a and b but how does tihs relate to getting the remainder when the same polynomial is divided by (x-1)(x+3)
clever fjordBOT
FancyBredFries
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
manic sleet
so from the 2 we can find a and b but how does tihs relate to getting the remain...
(ax+b) is the remainder
finding a,b gives you the remainder :)
fringe sail
wauit whaaat
why is it specific to (x-1)(x+3)
what if its f(x)=q(x)(x+21)(x-4) + ax+b
like
wouldnt the remainder be different
oh wiat
im
dumb
mb
cause it sets the things multipled by each other to 0
ohh
ok
ty
.close
vale grove
I have a doubt in the next statistics question, because i don't know which statistics test i have to use). The security department of a factory wants to know if the true average time it takes for the night guard to complete his round is 30 minutes. In a random sample of 32 rounds, the guard averaged 30.8 minutes with a standard deviation of 1.5 minutes. Determine if this evidence is sufficient to reject the null hypothesis that the average time per round is 30 minutes or not. Use a 0.01 significance level.
vale grove
<@&286206848099549185>
neat dirge
I have a doubt in the next statistics question, because i don't know which stati...
here you would assume normal distribution. since the standard deviation is known, you find the z value from a table.
also since there is more than 30 samples, i dont think a t test can be used
honestly my stats is rusty tho i might need to double check this
i think this is a t test with known standard deviation
since the standard deviation is known, i think you can just use the table value
then get your critical value from t using the table for that
actually no
get your critical value from the z table, get your test statistic from the formula
@vale grove last line, ignore the rest
its a z test
odd edgeBOT
@vale grove Has your question been resolved?
neat dirge
I have a doubt in the next statistics question, because i don't know which stati...
since the sample size is large ( greater than 30, sometimes 20 depends on your syllabus) and the standard deviation is known (meaning an estimation is not needed), then you use a z test.
neat dirge
yea this is the formula
neat dirge
rlly helped a lot
np
odd edgeBOT
odd edgeBOT
Available help channel!
frosty gorge
odd edgeBOT
frosty gorge
Can anyone explain how I would do 1.2.6 b? I’m very confused at what the hint is suggesting I do. I also attached the answer to b
odd edgeBOT
@frosty gorge Has your question been resolved?
odd edgeBOT
@frosty gorge Has your question been resolved?
odd edgeBOT
@frosty gorge Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
junior ether
does x³ increase at x=0?
odd edgeBOT
does x³ increase at x=0?
steep cliff
x=0 is the inflation point of x^3. It neither increase or decrease at x=0
I hope that answers your question
junior ether
x=0 is the inflation point of x^3. It neither increase or decrease at x=0
so the increasing intervals would be (-∞,0)∪(0,∞)?
steep cliff
yes
south citrus
odd edgeBOT
south citrus
Part B and C are correct but how would I find A?
odd edgeBOT
Available help channel!
mystic saffron
.open
odd edgeBOT
fast ivy
This question killin gme 😭
odd edgeBOT
fast ivy
Graph peice wise function
piece
I show work
i try my beat to graph
I guess what is hard for me is the part it say x<-1
and x>/= -1
odd edgeBOT
Available help channel!
lone glacier
Is this possible?
odd edgeBOT
Is this possible?
lone glacier
,rotate
clever fjordBOT
proud ibex
Sorry, you can't do that with integrals
lone glacier
Damn
proud ibex
(assuming you're integrating with respect to x, of course)
main creek
trig sub will work i think
lone glacier
My brother said to bring the sprt (x^8 +25) to up and do integral by parts
lone glacier
trig sub will work i think
I don’t think we learned that yet
merry finch
That’s probably the best way I think
clever fjordBOT
merry finch
Yeah
lone glacier
Ok
merry finch
Then spam differentiate the x³
Use tabular IBP if you know it
If you don’t know it now’s a good time to learn it
lone glacier
This stuff?
lone glacier
I don’t think I know what
odd edgeBOT
@lone glacier Has your question been resolved?
gritty fjord
what is the derivative of this function?
odd edgeBOT
what is the derivative of this function?
gritty fjord
?
proud ibex
Applying the chain rule, if we are given a function of a function, h(x) = f(g(x)) the derivative is $$h'(x) = f'(g(x))g'(x)$$
mystic saffron
Applying the chain rule, if we are given a function of a function, h(x) = f(g(x)...
!nosols
odd edgeBOT
Applying the chain rule, if we are given a function of a function, h(x) = f(g(x)...
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.
clever fjordBOT
thedude365
gritty fjord
**thedude365**
I can't understand
odd edgeBOT
@gritty fjord Has your question been resolved?
icy bough
Assuming you have Line 1, which equates to y = 2x - 3, and Line 2, which is y = -(1/2)x + (19/2), how would you find their intersection point?
noble forge
Well, if they intersect, then at at least one point both x and y co-ordinates of the point on both lines are the same
So, you can assume both y and x are some constant
This would transform into a system of linear equations in two variables
icy bough
This would transform into a system of linear equations in two variables
Actually, I don't think a system is necessary here
noble forge
well, both are the same
mystic saffron
beard was explaining the in depth concept
icy bough
.close
odd edgeBOT
icy bough
.reopen
odd edgeBOT
✅
icy bough
@noble forge If you don't mind actually, could you explain your approach to me more deeply?
I already got the answer, but I'm curious about your method
tight crescent
this did the trick.
That's a system of 2 linear equations with 2 unknowns. You just already had y on a silver platter
if y = something and y = something else, then logically, something and something else are equal
icy bough
if y = something and y = something else, then logically, something and something...
Transverse property.
Is that all it is then?
tight crescent
In this case yes. But it's called solving by substitution
We had this:
$y = 2x - 3 \ y = -\frac{1}{2}x + \frac{19}{2}$
clever fjordBOT
USS-Enterprise
tight crescent
This is a system of two equations with 2 unknowns
icy bough
so you just subbed it in
tight crescent
We can use substitution and sub one y into the other
icy bough
$2x -3 = -\frac{1}{2}x + \frac{19}{2}$
clever fjordBOT
Ralph
tight crescent
Yes, and you solve for x, then solve for y
noble forge
$y=-\frac{1}{2}x+\frac{19}{2}$\$y=2x-3$\$2x-3=-\frac{1}{2}x+\frac{19}{2}$\$\$
Since we had coefficients of y same in both the equations, we just equated the RHSs. Had it been that the coefficient of x was same in both the equations, then we would isolate x and equate the other side of both the equations
tight crescent
In this case this is the transitive property yes
clever fjordBOT
B-eard
tight crescent
But using substitution doesn't always necessarily mean that
If we have something like
$y = 2x \ x - y = 0$
clever fjordBOT
USS-Enterprise
icy bough
then you would solve for one of the variables and plug it into the other
tight crescent
You can again use substitution and switch y for 2x. This is in no way the transitive property though
and you get $x - 2x = 0$
clever fjordBOT
USS-Enterprise
icy bough
Cool, thanks.
icy bough
.close
odd edgeBOT
odd edgeBOT
Available help channel!
solar ether
odd edgeBOT
solar ether
the physics part of this is 1/R = 1/R1 +1/R2
that's what it means to be connected in parallel
but can someone tell me how to find the math part to it
odd edgeBOT
@solar ether Has your question been resolved?
solar ether
<@&286206848099549185>
wraith garnet
Hi mitsuki
solar ether
Hi mitsuki
hello
wraith garnet
I am not math nerd
solar ether
I am not math nerd
then?
solar ether
bruhh
hollow ibex
solar ether
yeah
marsh basin
<@&268886789983436800>
solar ether
error / true value ?
ember mulch
Error
solar ether
x 100
odd edgeBOT
@solar ether Has your question been resolved?
gusty totem
help in channel 21
odd edgeBOT
help in channel 21
gusty totem
no channel 21
someone get me back to channel 21 fast bruh
my text is in there
how do i understand
math
close
.close
random dune
Hello
random dune
Why is 1/lnx undefined at x=0? Since the limit of lnx as x approaches 0+ is negative infinity, doesn’t that mean that 1/lnx is zero at x=0
tall veldt
A limit is not the same thing as the value of a function
ln(x) is not defined at 0, so 1/ln(x) is not defined at zero, regardless of what the limits are
odd edgeBOT
@random dune Has your question been resolved?
shut egret
odd edgeBOT
shut egret
hello
lime root
quadratic formula
lime root
x
odd edgeBOT
odd edgeBOT
✅
odd edgeBOT
shut egret
.reopen
odd edgeBOT
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uncut remnant
quadratics generally have 2 roots, but it may be repeated
uncut remnant
They are repeated iff the discriminant is 0
shut egret
oh what was the rule again?
and do i always have to say it
when doing sums like that
like ... has 0 real roots
or 1 real root
shut egret
They are repeated iff the discriminant is 0
whats that again?
lime root
the discriminant is b^2 - 4ac
lime root
you can just find the roots
idt it's required to show how many roots it has
unless the question asks you to
odd edgeBOT
shut egret
.reopen
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✅
lime root
the q says 1 decimal place
odd edgeBOT
shut egret
.reopen
odd edgeBOT
✅
shut egret
i use y-b=m(x-a) but am i meant to do
anything to the sum above
cos think i am but i forgot
royal herald
The equation is in standard form
shut egret
oh wait im so dumb i just turn the fraction into y=mx+C?
royal herald
No need
odd edgeBOT
odd edgeBOT
Available help channel!
celest monolith
I need help with arithmetic sequence
odd edgeBOT
I need help with arithmetic sequence
celest monolith
Problem
This is the problem
This is the answer
But I don’t know how to get it to that fraction answer
sand night
is it a^10?
celest monolith
Ok
sand night
now rewrite the equation as 3 times (2/5)^9
celest monolith
Got it
sand night
now you have 3 times 2^9/5^9
celest monolith
Ok
celest monolith
1953125 bottom right?
sand night
now you just mutiply like normal
celest monolith
5^9
sand night
idk what 5^9 is
celest monolith
Or should I just solve as I’d
sand night
so probs
sand night
ye np
celest monolith
-close
sand night
.close not -close
trim ember
Don't understand how they further factorised from step 2 to step 3 instead of what I have on the right.
halcyon kite
Don't understand how they further factorised from step 2 to step 3 instead of wh...
ab - 2b = 0
b (a - 2) = 0
(a - 2) b = 0
Let
a = y - x
b = y + x
now try
and uh, idk how you got what you wrote on the right
trim ember
ab - 2b = 0
b (a - 2) = 0
(a - 2) b = 0
Let
a = y - x
b = y + x
oh wait, I thought for some reason that (y-x)-2 was as a multiplication 💀
trim ember
and uh, idk how you got what you wrote on the right
I had (y-x) * a-2a
to (y-x) * a(1-2)
thanks + just realised I broke a law in maths to get what I had on the right
.close
vital crypt
Help please
odd edgeBOT
Help please
vital crypt
Number 8.
swift rock
synthetic division?
vital crypt
How do i even solve it
Long division and ita required
-x/x=-1
What do i do with the 4x³ bro
Man im confused what do i do
swift rock
isnt ur question wrong?
vital crypt
isnt ur question wrong?
Wdym my question is wrong?
swift rock
on the screen shot its 4x^3 - 12 x^2 - 6x + 9 but on paper its -x^4 + 3x^3 - 5x - 4
vital crypt
Holy shit
I was answering 7
For 30 minutes
WHt the duckity duck
Thank you @swift rock
You are too pro
.close
brisk fulcrum
Inverse functions exist only for bijective functions
A function has to be one one and onto
To have an inverse
wraith ice
If you have multiple values that when put in the function gives you the same value (i.e. f(1) = f(2) = f(3)), then you can't take the inverse. If h(x) is the inverse of f(x), what would h(f(1)) give? 1, 2, or 3? It can't map it back to a single value.
brisk fulcrum
If it's not one one, one value of y will have 2 values of x
wraith ice
No problem, a quick example is the inverse of x^2. what would be the inverse of f(2)? both 2 and -2 give the same answer, 4. So f(2) = f(-2).
sudden forge
odd edgeBOT
sudden forge
i need help finding angle 1
tight crescent
i need help finding angle 1
You've figured out 2, right?
eager prawn
what is the 180-50+42=？
tight crescent
i think 1 is 88
It is. How did you get to 88
tight crescent
i found out 2 is 42
Good
sudden forge
because 50 plus 42 is 92
eager prawn
?
sudden forge
180-92=88
eager prawn
sorry
tight crescent
Yeah
sudden forge
thank you
tight crescent
No problem
sudden forge
.close
tired mulch
can someone pls help with this? i think a is right
odd edgeBOT
can someone pls help with this? i think a is right
tired mulch
but im not sure about b and c
brisk fulcrum
Do you know how the absolute/modulus function works?
tired mulch
Do you know how the absolute/modulus function works?
i dont think im fully familiar with it
tired mulch
When do you think 2-x is less than 0?
when x > 2
tired mulch
So |2-x| is -(2-x) when x>2
so its -(2-x) for b and +(2-x) for c?
brisk fulcrum
That's not the entire function is it?
Oh
Never mind
It's 2-x for a
And -(2-x) for b
For c it's -(2-x)+5x
odd edgeBOT
river summit
hey, im getting 3/4.5 for the answer however the answer is supposed to be 3/2 and i dont know what im doing wrong
mystic saffron
so avg rate of change is just
lavish osprey
hi there. Can you show your work so far?
river summit
i do the math and get the points (-4,-2)(1/2,1)
odd edgeBOT
Show your work, and if possible, explain where you are stuck.
river summit
then i do 1--2 on the top which is 3
then 1/2--4 on the bottom which is 4.5 right?
my work is all over the place kinda i can send it if it would help
main creek
which formula are you using?
river summit
just slope formula
main creek
why 1-(-2) on the top then?
river summit
y2-y1
main creek
that'll be f(b) - f(a)
or in this case a(b) - a(a)
$A(x) = \frac{f(b) - f(a)}{b-a}$
clever fjordBOT
saad
river summit
the professor never taught us that way though the way they taught us is to plug in the -2,1 into the function to get our x1,y1 x2,y2 then use slope formula
river summit
but i have a 1/2 as one of my points
main creek
as one of your y-values, correct
river summit
so how would i get a whole number
main creek
why do you need a whole number
river summit
the answer is 3/2
if i have a 1/2 as one of my points how does it end up the answer being that
river summit
i was never taught this formula
so she cant be expectig us to use it
im trying to solve this using slope formula
main creek
whats your x_1 value
river summit
-2
main creek
x_2?
odd edgeBOT
odd edgeBOT
Available help channel!
hollow olive
does anybody know how to do this?
odd edgeBOT
does anybody know how to do this?
hollow olive
quasi sparrow
Use double angle formula and factor the top maybe?
hollow olive
i used the double angle forumula but how do u factor that 💀
lime root
i used the double angle forumula but how do u factor that 💀
2cos^ - cos - 1 can be factored
hollow olive
2cos^ - cos - 1 can be factored
bruh im still lost it doesn't look factorable
quasi sparrow
,w factor 2x^2-x-1
clever fjordBOT
quasi sparrow
bruh im still lost it doesn't look factorable
Notice that the coefficients sum to 0 so cos=1 must be a root
hollow olive
OHH wait
is it like a normal quadratic
like x to the 2nd power + 2x + 3 or something
alr let me try that thank you so muchhh
what happens after factoring
i got it nvm
.close
lavish laurel
how cna something riased to the power of +infinity be zero?
upbeat drum
what's t
lavish laurel
the mgf is a function of the dummy variable t
odd edgeBOT
@lavish laurel Has your question been resolved?
lavish laurel
no
lavish laurel
.close
odd edgeBOT
odd edgeBOT
Available help channel!
rugged flame
how do you work out part b
odd edgeBOT
how do you work out part b
rugged flame
<@&286206848099549185>
its such a basic question and is 2 marks but i cant seem to know where i went wrong
i ahve the ms as well but that doesnt make sense to me <@&286206848099549185>
<@&286206848099549185>
odd edgeBOT
@rugged flame Has your question been resolved?
odd edgeBOT
@rugged flame Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
midnight frost
hii! can someone double check if my solutions/answers are correct ? thankss!
odd edgeBOT
@midnight frost Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
fluid kiln
odd edgeBOT
indigo shale
<@&286206848099549185>
Hello! I'd be delighted to review your responses since we share a common topic. 😆
indigo shale
hii! can someone double check if my solutions/answers are correct ? thankss!
Your first 3 items are correct, I'm currently checking the last two. :)
indigo shale
hii! can someone double check if my solutions/answers are correct ? thankss!
Having reviewed your answers, I'm pleased to inform you that they are all correct! 🫰
indigo shale
Hi there! I'll give this problem a shot and drop you a message once I'm done. 😊
fluid kiln
Ok
tepid yacht
Hello! I'd be delighted to review your responses since we share a common topic. ...
If someone else has this channel, please do not assist the previous people that use this channel as you have just stated 3 statements that is not related to the original person who owns this channel. You can see who owns the channel, at the top, where it says help - # | 'name'. And if you look in the occupied list, you can see that person opened a new channel, #help-1
indigo shale
If someone else has this channel, please do not assist the previous people that ...
Oh, my apologies! My bad... 😓 I'll make sure it doesn't happen again. ✌️
odd edgeBOT
@fluid kiln Has your question been resolved?
fluid kiln
gi crosswise na si gojo
Bisaya
low tusk
is it considered piracy of some sort if i want to discuss a proof from an actual text ? via a screenshot from the pdf
low tusk
is it considered piracy of some sort if i want to discuss a proof from an actual...
It's about a proof from Elementary Number Theory, in particular, with quadratic residues.
.close
mystic saffron
Help
mystic saffron
I need help with geometry
tawdry cave
odd edgeBOT
Help
No need to ask "Can I ask...?" or "Does anyone know about...?"—it's faster for everyone if you just ask your question! See https://dontasktoask.com/
mystic saffron
I did ask
tepid yacht
Post your question
mystic saffron
how can i check for option no 3?
odd edgeBOT
how can i check for option no 3?
mystic saffron
how can i check for option no 3?
it means ig in how many places f(x) value becomes 0
yes that i got it
So i need to plot the graph right?
is there any other way to do that
mystic saffron
So i need to plot the graph right?
not necessacry
neccessary*
mhm
sin x becomes 0 at 2npie
n is integer
yes
so between -pie to pie, function may not become 0
odd edgeBOT
mystic saffron
no problem
odd edgeBOT
Available help channel!
broken shale
- Previously, De Anza statistics students estimated that the amount of change daytime statistics students carry is
exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students.
a. In words, Χ = ____________
b. Χ ~ (,_____)
mystic saffron
wait it's decreasing in pi/2 to pi interval
i didnt checked all the options
It's fine
could you check if options 1 and 4 are correct
cause i got them correct now
2 is wrong cause decreasing
broken shale
.close
odd edgeBOT
broken shale
.close
odd edgeBOT
Available help channel!
tepid galleon
If F and G are vector fields, how can i prove that rot(F∇G)= ∇Fx∇G?
mortal trench
What is rot
tepid galleon
its the rotational of the vector field. The context its using the Stokes Theorem to prove that.
Im gonna send a picture
i need to prove that
I was using the Stokes theorem and i need to prove that rot(F∇G)= ∇Fx∇G
odd edgeBOT
@tepid galleon Has your question been resolved?
tepid galleon
<@&286206848099549185>
odd edgeBOT
@tepid galleon Has your question been resolved?
odd edgeBOT
@tepid galleon Has your question been resolved?
odd edgeBOT
@tepid galleon Has your question been resolved?
odd edgeBOT
@tepid galleon Has your question been resolved?
sweet gazelle
Ok let's do this question
Let me see what you did
I'm still working out the question myself
@oak umbra
Your welcome
I think you just had to follow through simplifying the expression as much as possible, and also remember to plug in the values of x and y at the point given
Are you in high school or university?
Ah OK I see
echo light
@oak umbra hey sorry for the ping but do ýou know how to do this as a partial fraction
😭😭
broken panther
Stuck on it and don't know where to proceed, this is on the topic of Interior & Exterior Angles.
manic sleet
the sum of the interior angles of a triangle always adds to 180deg :)
broken panther
However, the only given triangle I have is X, Y, and Z.
untold mist
well
broken panther
The others are 4-sided polygons.
night bone
Untrue
manic sleet
isolate the triangle with angles y, 80, and 55 see if that helps :)
a moderately sized part of Geometry is being to able to see these sort of figures deconstruct so you can get what you need
and this elementary example is actually good practice
broken panther
isolate the triangle with angles y, 80, and 55 see if that helps :)
Do I draw additional triangles to break it down?
manic sleet
if it helps, or you can just outline it
manic sleet
not quite
manic sleet
you're overthinking this lol
broken panther
It's a new topic
Since we only get 1 day to do this then we jump to the next
So I cant quite wrap my head around this
manic sleet
isolate this triangle
cold viper
Ignore the triangle in the middle for a moment and just look at the two big triangles
manic sleet
notice the angles in the red triangle :)
all interior angles in a triangle sum to 180
so this calculation is trivial! 
broken panther
Then the other corner will equal 45 degrees?
manic sleet
y=45deg 
broken panther
broken panther
y=45deg <:catthumbsup:614540188747563008>
Ohhhh I see I was overthinking it afterall
Then I do the same with X?
manic sleet
Ohhhh I see I was overthinking it afterall
sometimes it's easier than you think 
manic sleet
Then I do the same with X?
broken panther
Man I feel stupid now 💀
manic sleet
then finding z is easy, just that middle triangle :)
manic sleet
Man I feel stupid now 💀
no feeling stupid, only getting smarter here!
wow that sounds dystopian asf
broken panther
Good motivator
manic sleet
but you get the idea supposed to be positive lol
broken panther
So now having the measurements of angle x and y, to find z I simply just have to find the Triangle Sum Theorem?
Which is probably a yes
broken panther
but you get the idea supposed to be positive lol
Alrighty got it now, thanks! Also agreed with AP Psychology.
.close
odd edgeBOT
manic sleet
Alrighty got it now, thanks! Also **agreed with AP Psychology.**
AP Psych is a journey for sure
broken panther
I have a C in there 
odd edgeBOT
Available help channel!
icy prairie
icy prairie
<@&286206848099549185>
odd edgeBOT
@icy prairie Has your question been resolved?
odd edgeBOT
@icy prairie Has your question been resolved?
odd edgeBOT
@icy prairie Has your question been resolved?
remote sequoia
how do I find the smallest value of square root of P?
remote sequoia
x > 4
crisp wadi
Did you mean x > 4? There's no smallest value of sqrt(P) if x > 16
crisp wadi
First you could introduce a new variable, say $t = \sqrt{x} - 2$, so that
[ \frac{2x}{\sqrt{x} - 2} = \frac{2(t + 2)^2}t = (t^2 + 2^2 + 2t) \cdot \frac2t ]
Do you see an application of $a^2 + b^2 \geqslant 2ab$ here?
clever fjordBOT
A Lonely Bean
remote sequoia
I have not studied introducing a new variable yet, however, my teacher said to use cauchy which i don't know how
remote sequoia
Cauchy-Schwarz inequality?
yes
odd edgeBOT
@remote sequoia Has your question been resolved?
remote sequoia
<@&286206848099549185>
odd edgeBOT
@remote sequoia Has your question been resolved?
meager monolith
So 2x/{[sqrt (x)]-2} +4={2sqrt(x)sqrt(x)-4[sqrt (x)]-8}/{[sqrt (x)]-2} ={2sqrt(x)[sqrt(x)-2]+8}/{[sqrt (x)]-2}
=2[sqrt(x)] + 8/[sqrt(x)-2]
=> 2x/{[sqrt (x)]-2} =2[sqrt(x)] -4 + 8/[sqrt(x)-2]=2([sqrt(x)]-2) + 8/[sqrt(x)-2]
2([sqrt(x)]-2) + 8/[sqrt(x)-2] > or = sqrt{2([sqrt(x)]-2) *8/[sqrt(x)-2]}=sqrt(16)=4
So the answer is 4
remote sequoia
So 2x/{[sqrt (x)]-2} +4={2sqrt(x)sqrt(x)-4[sqrt (x)]-8}/{[sqrt (x)]-2} ={2sqrt(...
is that cauchy?