You are taking delta intervals from a point
#help-28
graceful loom
ionic zinc
Whats a delta interval
graceful loom
And if every point within that interval is less than or equal to the min or max
torn jolt
open interval
graceful loom
Yeah
ionic zinc
oh ok
so what if a cubic function has two stationary points
both of equal level
like, (-2,2) and (2,2)
graceful loom
Right
torn jolt
thats not happening
torn jolt
cant be equal
torn jolt
ye
ionic zinc
torn jolt
i gtg
ionic zinc
oh
i understood everything uptil the first part
the second part is where everything went to shit
like, second image
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ionic zinc
<@&286206848099549185>
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<@&286206848099549185>
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ionic zinc
uhuh
whats the point tho
only one derivative value is applicable anyways
uhuh
yes
yes
ohh
but like
is there any case that
even if we do find a value
through sigle derivatio
n
it may not be the max?
ionic zinc
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true dagger
I've answered ai), how do I go about answering aii)? I don't really understand what it's asking tbh
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ember shadow
is it supposed to equal ey? not just e
wheat seal
There's a rectangle with these values:
area=3y
Perimeter=y
Lenght=3x
Width=x+2
I need to find the perimeter using systems of equations (highschool level). Would it be 50?
jolly flint
There's a rectangle with these values:
area=3y
Perimeter=y
Lenght=3x
Width=x+...
Lemme check
im getting ≈57 units
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ember shadow
I got 56.84
wheat seal
wait it was actually:
area=3y
Perimeter=y
Lenght=3x
Width=x+5
I put the wrong width. I get to this step but idk where to go from here:
- (8x + 10 = y)
- (y = x^2 + 5x)
viral jasper
wait it was actually:
area=3y
Perimeter=y
Lenght=3x
Width=x+5
I put the wrong...
Looks good so far. Both 8x+10 and x²+5x are equal to y. In algebra, if two things (8x+10 and x²+5x) are equal to the same thing (y), then they are equal to each other. That is, 8x+10 and x²+5x must be equal to each other since they are both equal to y.
wheat seal
8x+10=x^2+5x
3x+10=x^2
=x^2-3x-10
(x-5)(x+2)
so x=5? And then y=50?
ember shadow
yup
jolly flint
I got 56.84
yep
jolly flint
8x+10=x^2+5x
3x+10=x^2
=x^2-3x-10
(x-5)(x+2)
so x=5? And then y=50?
yep
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serene hazel
can anyone help me with vectors
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can anyone help me with vectors
buoyant epoch
sure
serene hazel
nova sigil
Post your question
buoyant epoch
I don't get the notation
nova sigil
To learn vectors use youtube, to go through questions or understand something specific ask away
serene hazel
here
serene hazel
To learn vectors use youtube, to go through questions or understand something sp...
I don't get the language what they're asking
where do i start?
buoyant epoch
ohh you have to look at it from the top
serene hazel
yeah I have read the question but still don't know how do I start
do i need to label the number on given diagram?
does the image look blurry to see or not
buoyant epoch
Can you draw a line where 80 degrees is
I don't really see where the wind is coming from
buoyant epoch
That looks more like 90 degrees
serene hazel
why?
buoyant epoch
Let's try to put this angle in vectors first
serene hazel
ok
also im kinda not sure which side they're asking for
right from the last sentence
buoyant epoch
From the N line, the angle is like 170 degrees
serene hazel
how
buoyant epoch
because it's 80 degrees from the east line
If I'm looking at it correctly
80+90=170
serene hazel
so you're saying its 90 instead of 80?
buoyant epoch
No no no
serene hazel
I don't get where the 90 is coming from
buoyant epoch
I'm not exactly sure but I'm assuming this is the 80 degree angle we're talking about right?
or it should be around there
correct?
I just want to know whether the wind is coming from that quadrant
buoyant epoch
assuming that's right, we need to add the 90 degrees from where the 85 degree line is so we can think of it like the intersection point is the middle and then we can convert the angle to 90+80=170
which allows us to get a vector
buoyant epoch
That would correspond to a vector of (x, y) = (-0.17; -0.98) approximately and we need to flip the vector because the wind is coming from there. so (x, y) = (0.17; 0.98)
The vector of an angle is (x, y) = (cos(x), sin(x))
serene hazel
how did you get these "-0.17; -0.98" numbers from?
it doesn't show anything from there
buoyant epoch
cos(170) and sin(170)
serene hazel
oh ok
buoyant epoch
The vector of an angle is (x, y) = (cos(x), sin(x))
serene hazel
yea I see it now
buoyant epoch
if the angle is x
because the vector is going in the opposite direction, we need to flip the vector
also, we can convert the 60 degree angle and reverse it so we go the long way to get a 300 degree angle
serene hazel
oh ok
buoyant epoch
so we're taking the long angle
serene hazel
the long angle says 380
buoyant epoch
serene hazel
hmm
buoyant epoch
the long angle says 380
that would be more than a full rotation
buoyant epoch
so for the plane's vector, it'd be (x, y) = (cos(300), sin(300)) = (0.866, -0.5)
serene hazel
ok
buoyant epoch
can we use sine law or cosine law?
I don't think it's needed
serene hazel
can you point me what is the question asking
buoyant epoch
We can use the speeds and weigh it out
serene hazel
🫠
buoyant epoch
The plane is going 380 km/h and the wind is 85km/h
I'm gonna try this
What if we multiply 380 by the planes vector and 85 by the winds vector
buoyant epoch
no no no
380 times the vector
and add that to 85 times the vector
but wait actually lemme write it out on paper
serene hazel
use latex instead but sure
buoyant epoch
im kinda stuck myself
buoyant wadi
More help needed in here?
serene hazel
yes
buoyant wadi
Okay I'm skimming
So you were trying to translate 380 km/h N60W and 85km/h S80E into cartesian coordinates?
serene hazel
yep
buoyant wadi
So S80E is 80 degrees counter-clockwise from direct south, yeah?
serene hazel
ye
buoyant wadi
Hmm, so I guess to start we should unify the angles, make N60W and S80E both based on the same axis
Were you treating due north as 0 degrees? My instinct is to use east since that's pointing right, but it shouldn't matter which one so long as you're consistent
serene hazel
alright
but still wondering what side they're asking for
is there anything to use
my teacher usually only shows us something like sine and cosine law but I don't have any side except for 380
buoyant wadi
What do you mean by side?
Well if we treat due north as 0 degrees and we work counter-clockwise, then N60W becomes 60 degrees right?
serene hazel
in 380
serene hazel
Well if we treat due north as 0 degrees and we work counter-clockwise, then N60W...
yeah
buoyant wadi
Ah okay I think I see what you mean
Well anyway, still having due north be 0, what angle is due south?
And from there, what angle is S80E?
buoyant wadi
Actually it would be 80+180
Since south is 180 degrees from north, and S80E is 80 degrees from south
serene hazel
I see
buoyant wadi
But anyway, so we have the desired angle being 60 degrees and the wind going at 260 degrees
serene hazel
where did 260 degrees come from?
buoyant wadi
260 = 180 + 80
serene hazel
oh I thought it was 180+60 mb
buoyant wadi
fair fair
So lets break the desired angle & velocity into north and west components, 380km/h going 60 degrees
This is the same as finding the side lengths of a right-angle triangle with hypotenuse 380 and angle 60
The adjacent side being north and opposite side being west
Do you think you can figure that out?
buoyant wadi
No problem!
serene hazel
.close
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flat tinsel
I need help with this
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I need help with this
flat tinsel
I’m plugging my phone in then I’m going to be back to get some help
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fleet gulch
hi can someone check my answers plz
fleet gulch
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somber niche
fleet gulch
sorry im like a nube when it comes to discord
i use this like once a month max...
i was hoping if someone could check my answers & see if i did it right
that way im not jus studying wrong matieral
ember shadow
I think the first one is wrong. shouldn't N(B) = N(A' n B) + N(A n B)?
the second page is closer, but N(B) is wrong again
you wrote N(A' n B)
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thick plinth
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wary lodge
U have 3 possible cards and then 2 possible spins, so $3/times2=6$
glossy valveBOT
°Jason Parker°
dim violet
no its 4 possible sums because 5+4 = 6+3 etc
thick plinth
?
but what about 7+3 and 6+4
those both euqal
10
<@&286206848099549185>
@scenic thistle
dim violet
yes
spice orchid
yeah so go through every card+spinner options and see how many different ones there are
dim violet
5 + 3 = 8
5 + 4 = 9
6 + 3 = 9
6 + 4 = 10
7 + 3 = 10
7 + 4 = 11
you have 8, 9, 10 and 11 therefore 4 possible sums
thick plinth
ok thank you so much
dim violet
you can also calculate it with $possible sums = possible cards + possible spins - 1$
glossy valveBOT
MinecraftJoe09
autumn sparrow
“In how many ways can you arrange 4 books in math and 3 books in physics in a single shelf so that no two books in physics are next to each other (all the books are different)?”
noble dew
okay lets try and think about it visually
one moment please
we have 7 different spots for our books to occupy
lets start by fixing our physics books in these specific spots
how many ways can we arrange these physics books?
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autumn sparrow
3!
noble dew
yep
and how many ways can we arrange the math books if we placed them in between the physics books?
autumn sparrow
4!
noble dew
so your answer is
noble dew
its not
autumn sparrow
damn
noble dew
notice how i emphasized and earlier
when dealing with combinatorics, hearing the words and/or should mean something
autumn sparrow
i have no idea
i know the formula is supposed to be 3! x 4! x (4c2 + 4c1)
someone explained it but i dont understand why
i mean why isnt the answer just 144
autumn sparrow
4!
noble dew
not quite
hold on let me think for a second
So when you were figuring out how many ways were possible to arrange the physics books, you said it was 3! right?
autumn sparrow
yes
noble dew
do you know why it is?
autumn sparrow
if we put one book in a specific spot then theres only two spots left where we can put a different book etc etc
noble dew
yep, so we have 3 choices for one spot, and 2 choices for the next spot, and 1 choice for the last spot
aka $3\times 2\times 1 = 3!$
glossy valveBOT
Cyphercrit
noble dew
whenever you hear and, you should think about multiplication
on the contrary, whenever you hear or, you should think addition
noble dew
“In how many ways can you arrange 4 books in math and 3 books in physics in a si...
if look back at the original question, you can see why we aren't adding 3! and 4!
autumn sparrow
i understand
so why isnt it 3! x 4!
wait wait
nvm i still dont get why thats not it
noble dew
do you remember how at the start, i chose where we were going to put the physics books?
autumn sparrow
yes
noble dew
we also need to factor in the possibility of other spots being chosen, since the only requirement is that all of the physics books aren't together
autumn sparrow
how should i do that
noble dew
one second
basically, you need to think about the possible arrangements of the physics books such that no one of them is directly next to the other
first, you can start by arranging the 4 math books, depending on how you arranged them, there would be 5 possible gaps
one of them being before the first math book, 3 of them being in between consecutive math books, and one of them being after the last math book
does that make sense?
autumn sparrow
i dont understand how there are 5 gaps
noble dew
PMPMPMP is one where you have one before the first math book and after the last math book
autumn sparrow
shouldnt there be 3 since there are 7 books total
noble dew
not neccesarily
MPMPMPM is one where you have 3 gaps in between each math book
so we have three scenarios really, one where we have an arrangement of some books PMPMPMM, one where we have the arrangement of some books MPMPMPM, and one where have an arrangement of some books MMPMPMP
if so lets line up these scenarios
PMPMPMM
MPMPMPM
MMPMPMP
if we don't double count gaps, how many gaps are there with physics books?
noble dew
so the possible gaps are: one gap before the first math book, one gap after the last math book, one gap in between the first two math books, one gap in between the second and third math book, and one gap in between the third and fourth math book
for a total of 5 gaps
noble dew
well, we only have 3 physics books, right?
so we need to choose only 3 gaps, not 5 of course
which means we need to choose 3 gaps from 5 possible gaps
so we need to count the number of ways to choose 3 gaps
autumn sparrow
so 5x4x3
noble dew
not quite
how many ways can we choose 3 elements (gaps) from a set of 5 elements (gaps)?
autumn sparrow
well i thought it was 5x4x3
not sure but shouldnt it be just: for the first gap (1/3) i have 5 gaps to choose from, for the second gap (2/3) i have four and for the last gap(3/3) i have three
noble dew
$n\choose k$
glossy valveBOT
Cyphercrit
autumn sparrow
no idea what this is
noble dew
not sure but shouldnt it be just: for the first gap (1/3) i have 5 gaps to choos...
also seen as nCk
noble dew
not sure but shouldnt it be just: for the first gap (1/3) i have 5 gaps to choos...
this implies that the order in which we select the gaps matters, but it doesn't
autumn sparrow
just a sec
noble dew
noble dew
yeah, or just 5 choose 3 or $5\choose 3$
glossy valveBOT
Cyphercrit
noble dew
so, we have $5\choose 3$ ways to select the gaps, and $3!$ ways to order the physics books, and $4!$ ways to order the math books
glossy valveBOT
Cyphercrit
noble dew
i know the formula is supposed to be 3! x 4! x (4c2 + 4c1)
if you're confused about this, 5 choose 3 = 4 choose 2 + 4 choose 1
noble dew
whats the final answer?
autumn sparrow
1440
noble dew
,w 3! * 4! * (5 choose 3)
noble dew
yep
your teacher would probably prefer that you keep it as 5c3 * 3! * 4! though
as long as you have the above in it though, it shouldn't matter
i.e. dont just write down 1440 as an answer and call it a day
autumn sparrow
your teacher would probably prefer that you keep it as 5c3 * 3! * 4! though
im writing it out in my notebook rn i just didnt know how to write this out in text
thank you so much tho
noble dew
no problem
autumn sparrow
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wraith river
is my diagram correct?
what exactly is a resultant ground velocity
@knief
@lime ether
lime ether
what exactly is a resultant ground velocity
if observed from the ground
it’s the velocity relative to the ground
lime ether
no that looks fine
lime ether
like why do i see a right angle
they are just drawing that in to determine the other angles
wraith river
It doesnt matter if i draw it like this?
lime ether
that looks fine
wraith river
i drew mine straight
lime ether
the wind pushes it to have that resultant ground velocity
oh no
the 430 is greater so it should be higher
wraith river
oh
lime ether
the magnitude of the 430 is obviously greater than the 400 so the vector should be longer thus it won’t be a straight line
wraith river
oh ok
whole compass
help pls
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hard mango
hi can someone help me get started on this. i don’t exactly understand how the graph should look
hard mango
inland trellis
!status
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1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1 definitely
inland trellis
What subject is this?
hard mango
pre-calculus
craggy tapir
start by graphing f(x) first
inland trellis
^^
craggy tapir
the question is asking for the area from x = 1 to x = 7, so we are going to consider that portion of the graph
"with 12 rectangles" means that you need to divide that graph into 12 sections, and draw 12 rectangles side by side, each tangent to that graph
somewhat like this
and you need to calculate area of each rectangle for an approximation of the area under that curve
in more rigorous terms, you are to compute a riemann sum of that curve with 12 terms
hard mango
thank you!!
craggy tapir
somewhat like this
just for clarification, this is not the graph of your function, this is just a doodle
hard mango
🤭👍
winged jungle
hello i am needing to review entire algebra one, i apologize as my english is not too good
astral sinew
winged jungle
yess
very hard haha
i do know some things, having trouble remembering
i am doing state test, they are making me do it for american school credits
very hard 😆
torn jolt
idk abt american things so can u tell the portions of algebra one
winged jungle
i will get my teacher's curriculm quickly please wait
torn jolt
ok
winged jungle
Quarter 1
Unit 1: Expressions and Linear Equations
Unit 2: Linear Functions
Quarter 3
Unit 4: Exponents and Radicals
Unit 5: Polynomial Operations
Quarter 2
Unit 2: (continued) Linear Functions
Unit 3: Linear Inequalities
Quarter 4
Unit 6: Investigating Quadratic Functions
Unit 7: Representing and Interpreting Bi-Variate Data
winged jungle
i believe so
torn jolt
i believe so
which topics do u know best?
winged jungle
functions , linear equations, expressions, rules, factoring, graphing, exponents, radicals,
plotting points
torn jolt
do everything other than those
torn jolt
so like
its algebra
hence its connected
so if u do smth udk
also
u get practice on it
winged jungle
okay!😆
torn jolt
which class r u in?
winged jungle
i do not understand i am sorry
torn jolt
which class?
winged jungle
i am in the ninth grade
i am in algebra one math class
winged jungle
that is okay i am learning as well
torn jolt
lol
winged jungle
i moved to us 8 months ago 😆
winged jungle
how to graph inequality?
i am confused on how to take from equation to proper graph
tribal heron
Hi guys I just wanted someone to double check if my steps are correct in finding the partial derivative dz/dx
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raven mauve
Can someone help please
raven mauve
raven mauve
307.57 approx
flint crane
yeah
flint crane
ok
raven mauve
I done a
For b is it just Pythagoras?
So b is 1.7
I don’t know how to do c tho
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cobalt spruce
When it comes to sinusodial functions how does a cercle affect the horizontal translation (H)
cobalt spruce
If the equation at a is 16sin(10(x)) + 19
At b why isn’t it (x-90)
It’s (x-27)
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hardy magnet
i am a little confused but if am correct is it 7/12, can someone inform me?
robust slate
,w 210/360
glossy valveBOT
robust slate
i am a little confused but if am correct is it 7/12, can someone inform me?
Yeah
hardy magnet
oh
its my calculator giving me a different input than others really weird
thanks
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fluid prawn
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fluid prawn
How do I do this
lofty vine
since they dont ask for a rigorous method, you can reduce the numerator and denominator to the highest power term
lime ether
yea sqrt (9x^2+… is going to about 3x
fluid prawn
since they dont ask for a rigorous method, you can reduce the numerator and deno...
Don’t u cancel out all insignicant terms
lime ether
then just compare coefficients
lofty vine
Don’t u cancel out all insignicant terms
same thing
fluid prawn
Ok so I have 4x/sqrt9x^2
lofty vine
yep
fluid prawn
And if I plug in infinite it’s infinite/infinite
lime ether
lhopital
fluid prawn
Answer is 1/2
fluid prawn
just by inspection i can see it is 1/2
How
lofty vine
$e^x=1+x+\frac{x^2}{2!}+...$
glossy valveBOT
Obotron
lofty vine
replace e^x with it's taylor series and evaluate
fluid prawn
Idk that
lofty vine
but you know lhopital's rule?
fluid prawn
Yes I got 1/2
lofty vine
that's so weird. L'hopital's rule should definitely be taught after Taylor series
but ok
lofty vine
l'hopital is the way
static forge
no need for l'hopital, just divide and multiply by 2 to get the square root inside
fluid prawn
no need for l'hopital, just divide and multiply by 2 to get the square root insi...
After deriving?
It looks like it goes on forever
static forge
no like without using l'hopital
just divide and multiply by 2
youll get 2ln(sqrt(x))/sqrt(x)
fluid prawn
youll get 2ln(sqrt(x))/sqrt(x)
I don’t understand
static forge
ln(x)/sqrt(x) is just 2 * 1/2 * ln(x)/sqrt(x)
lofty vine
youll get 2ln(sqrt(x))/sqrt(x)
yes but that requires you to somehow prove that ln(f(x)) grows slower than f(x) for all f(x)
i know its something that we take for granted
but it's kinda hard to prove
static forge
yes but that requires you to somehow prove that ln(f(x)) grows slower than f(x) ...
i think thats something thats already taught
fluid prawn
I still don’t get it
lofty vine
its true, but i cant just assume it and give the answer
fluid prawn
ln(x)/sqrt(x) is just 2 * 1/2 * ln(x)/sqrt(x)
Why did you multiply by 2 and 1/2
static forge
well you cant assume l'hopital either
lofty vine
well you cant assume l'hopital either
not the same thing
static forge
Why did you multiply by 2 and 1/2
to get the square root inside ln
static forge
not the same thing
why not
lofty vine
l'hopital is a formula thats explicitly given, most calc courses dont explicitly state the relative growth rates of functions
they might tell you that e^x grows faster than x etc but that's not an explicit formula
static forge
l'hopital is given in high school?
lofty vine
whether it's high school or college is irrelevant. if u are studying limits you will probably learn l'hopitals rule
static forge
youll probably learn ln(x)/x goes to 0 as well when x goes to infinity then
lofty vine
true, but if it's a quesiton asked to u in an exam you wont just write 0 and say that 'x grows faster than lnx'
static forge
if its taught no need to elaborate, you just have to point out that you have a limit that's written in the form ln(X)/X with X -> +infinity
lofty vine
so that means if my teacher does a question in class: $lim_{x \to \infty}\frac{x^2}{x^2+x+1} = 1$ then i get the same question in an exam i can say that my teacher taught me this limit = 1 so i dont need to show it
glossy valveBOT
Obotron
static forge
something as specific as that will not be taught in class by your teacher and will not be in the books as a "proposition" or "corollary" or whatever
ln(X)/X is more general and can be applied to many cases
same as e^X/X
ln(X + 1)/X ln(X)/X-1
etc...
lofty vine
that's fair enough, this example was very specific. But lnx/x at infinity is not as much of a standard limit as say sinx/x at 0. And since it can be so readily proven, why not just do it., instead of risking losing marks for not proving it
static forge
ok this just depends on what type of exam it is in the us, either multiple choice, or free answers, in both cases im still wondering if l'hopital is taught and the standard limits of ln are not?
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lofty vine
ok this just depends on what type of exam it is in the us, either multiple choic...
most calc students have an understanding of relative growth rates that allows them to calculate standard limits like lnx/x, x/e^x etc. However, this does not mean they can assume the values of said limits in exam just because they are intuitive/well-known. The main 'standard' limits that can be taken as given are trig limits whose proofs require methods outside the course (sinx/x requires the squeeze theorem/geometry) etc. In those cases, the limits are explicitly given in questions (at least that's true in the UK)
or for example the limit defintion of e
static forge
that confuses me because ln(X)/X also uses the same principle (squeeze theorem)
or the basic definition of the limit iirc
lofty vine
that confuses me because ln(X)/X also uses the same principle (squeeze theorem)
but u can prove it using L'hopital's rule
u cant prove sinx/x using L'hopitals rule or taylor series without circular reasoning
u cant prove the limit definition of e for the same reasons
static forge
okay thanks for the insight
but where has the original poster of the question gone @fluid prawn
lofty vine
we stole their channel lol
static forge
oops
lofty vine
sorry @fluid prawn
static forge
yeah sorry
swift star
Find the standard deviation and mean for a normally distributed x, if 1.1% of the data are less than 7.84 and 50.8% of the data are less than 17.08
swift star
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void echo
i have done that question but i dont remember rn, i will have to check the book
do you knnow about normal ditribution curve? @swift star
void echo
z=x-(mean)/SD
it says 1.1% of the data are less than 7.84
so the area from 0 to 1.1
is z
void echo
so the area from 0 to 1.1
on normal distribution curve
similarly from 0 to 50.8% area is equal to z
void echo
similarly from 0 to 50.8% area is equal to z
where x is 17.08
@swift star do you understand it?
swift star
yea
but i need the mean and SD
i found them by trail and error but dont know any method that is more mathematical
the equation im stuck at is 17.08-x/SD=0.02
and the other one being 7.84-x/SD=-2.29
i got z by cross referencing a zscore table
swift star
i havent gotten to that in school yet, so im clueless
void echo
i havent gotten to that in school yet, so im clueless
about solving equations?
swift star
about solving equations?
2 variable equations,.. either i didnt do it or i forgot it
void echo
ok so
you find the value of one variable in terms of other from any equation
now you put the value of that variable in other equation ( which will have only one variable)
in this case
multiply both side by sd
you will have have $17.08-x =0.02SD$
and $7.84-x=2.29SD$
glossy valveBOT
Kyanite
void echo
find the value of x from any of the equation that is only x in LHS or RHS and other terms on the other side
and put the value of x in next equation
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past obsidian
Im trying to understand the working out for the integration of this -could someone show theirs
granite torrent
do you m,ind showing
are you familiar with integration by parts
past obsidian
sorry i dont get it
hybrid zephyr
Can't help then
past obsidian
i am getting -lnxcosx + (integrate)cosx/x
past obsidian
sinx differnitates to cosx
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wooden orchid
can anybody see the steps they did here to get to the second matrice?
ivory cairn
-5/2 row2 + row3 -> replace row3
wooden orchid
ahh i thought that the h would also go into a fraction then
but you ignore that oke
thanksss
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calm jewel
if A / 5 has the rest 2 and b/5 has the rest 4 what is a + b /5 rest
calm jewel
rest = remainder
torn jolt
if A / 5 has the rest 2 and b/5 has the rest 4 what is a + b /5 rest
6
because even u can do it simple math
if
A/5 = 2
torn jolt
Where di x come from 😭
torn jolt
ye
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6
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.
torn jolt
!nosols
i was going to explain how
but i think i ddi ti wrong aswell
cuz i thought a/5 = 2
viral jasper
i was going to explain how
you did, but the point is to not give answers in general. Even with explanations.
Have the student work through the problem themselves and guide them along the way.
torn jolt
problem solving
is it algebra or smtn
calm jewel
i dont really know
becaus i havent gotten forward from just understanding the question
torn jolt
A/5 = x + 2
B/5 = x + 4
A + B/5 = ??
calm jewel
B/5 = another numerical like y + 4
torn jolt
Ye ye
iron cairn
the number a could also be written like 5 * m + 2 and b could be written as 5 * n + 4
calm jewel
yes thank you
iron cairn
if you add them it would be 5m + 2 + 5n +4
calm jewel
yes
iron cairn
which would be the same as 5(m + n + 1) + 1
calm jewel
yes
iron cairn
if you would divide that with 5 what would the remainder be...?
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slender pond
How do I answer this?
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How do I answer this?
shrewd hamlet
What have u tried
slender pond
I tried the log rules
I got log 36 (abc) = 1
To get 36 = abc
But I idk what to do next
@shrewd hamlet
shrewd hamlet
@slender pond why not?
just find a,b,c such that a<b<c and abc = 36
and that u get positive probabilities
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flat prawn
I think its time for me to learn proportionality, anyone know how to do this?
lime ether
nah it’s just an assignment looks like an ap classroom progress check
graceful loom
ap exam ended?
I heard
earnest anvil
guys can you help me understand equations😭
graceful loom
No
flat prawn
Yeah just
flat prawn
Ok so
The rate of change of the salt in the tank is
6-0.02A
With A being the amount currently in it
earnest anvil
Open a new channel
sorry um how
flat prawn
So let me get an initial condition
Oh it says
At 10 mins its 50
So i should do
50 + integral between 10-12 right
Oh but i need to find a tangent line
So y = mx + b
m i can get by plugging in
Which is 5
But what is the y intercept
Poooh
What if i dont need a y intercept
What if I just started from 10
5(x-10)+50
Thats gotta be the answer to the first questiob
Ok i need help again
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zealous wasp
Does anyone have an intuitive way of understanding ODE particular solutions?
zealous wasp
Im a bit confused when he says the growth factor or growth time is t-s
When s in an interval and t is the current time
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dense cove
Help
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
quaint prawn
are you allowed help on this quiz? Also you might want to blur your profs name and class name next time
for privacy
dense cove
Sorry
quaint prawn
no need to apologize
dense cove
It’s after the quize and allowed help with fixing the questions
I just don’t get the -400 how it gets solved
ember shadow
not sure what you're asking, but 400 gets subtracted because that is the monthly payment
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dense cove
I got it sorted out I just didn’t understand how to solve it
torn jolt
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torn jolt
where do i start?
ember shadow
first plug in x = 2, y = -6
devout valley
What do these mean?
[edit: the first one has been done for you, when x = 2, then y = -6, what about the second one?]
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proper summit
Hi, I'm having trouble understanding some examples of a topological manifold, particularly with coordinate charts. The first example are graphs of continuous functions. If $U \subset \mathbb{R}$ is an open subset and $f: U \to \mathbb{R}^k$ is a contiuous function, then the graph of $f$ is defined as the subset of $\mathbb{R}^k \times \mathbb{R}^k$: $$\Gamma(f) := {(x,y) \in \mathbb{R}^n \times \mathbb{R}^k : x \in U \quad \text{and} \quad y = f(x)}$$ on the subspace topology
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neat bay
what does this mean?
What gamma
proper summit
What gamma
the projection map
neat bay
Why did you write R^n and R^k
Shouldn’t it all be R^k
I’m confused
Sorry
@proper summit
proper summit
Shouldn’t it all be R^k
one is dimension $n$ and one is dimension $k$. I assume this is so the projective map leaves out the last entry
glossy valveBOT
Zorich
proper summit
But I'm not sure, which is why I am asking
neat bay
The function f is from R -> R^k basically
So its graph should be a subset of R x R^k
Unless you’ve written U subset R wrong
Did you mean U subset R^n
proper summit
no, $U$ is a subset of $\mathbb{R}$
glossy valveBOT
Zorich
proper summit
however, it has a function that maps it to $\mathbb{R}^k$
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Zorich
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neat bay
no, $U$ is a subset of $\mathbb{R}$
Ok, so then the graph should be a subset of R x R^k, not R^k x R^k, and then in the set-builder notation you write R^n x R^k too
Three different things lol
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timber cape
The graph of a continuous function is a common example used to illustrate topological manifolds. Essentially, it's a way of visualizing how the function maps points from one space to another. In this case, given an open subset ( U ) of ( \mathbb{R} ) and a continuous function ( f: U \to \mathbb{R}^k ), the graph of ( f ) is defined as the set of points ( (x, y) ) in ( \mathbb{R}^n \times \mathbb{R}^k ), where ( x ) comes from ( U ) and ( y ) is the output of ( f ) for that input ( x ). This definition allows us to study the properties of the function and its mapping visually. What specific aspect or detail are you having trouble with regarding this example?
glossy valveBOT
ika
tawdry roost
Hi, I would like assistance in using desmos graphing to have a similar graph as to the one above? If any values or numbers are needed I can attempt to provide them
tawdry roost
I'm sorry if the image is blurry, I can't get another screenshot of it
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onyx inlet
Parallel vectors yeah
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onyx inlet
How do I know how to establish the relationship when they are parallel
An example, it says 6i+8j is parallel to vector OP
I know you can do the magnitude of one is directly proportional to the magnitude of another
But when I use the magnitude of 6i+8j = k * magnitude of OP ( 80 )
10 = k * 80
And k = 1/8
It says I'm wrong
And it's 80 = 10 * k
And I = 8
K*
void echo
is there any question?
unborn cliff
void echo
your concept it not wrong but it depends on the context
onyx inlet
your concept it not wrong but it depends on the context
The vector 6i+8j and 8i-6j are parallel to OP and OQ respectively. If the magnitude of OP and OQ are 80 units and 120 units respectively, express
a.) OP and OQ in terms of i and j
void echo
The vector 6i+8j and 8i-6j are parallel to OP and OQ respectively. If the magnit...
you need to calculate OP ini terms of i and j , so you will take magnitude of op directly proportional to 2(3i+4j)
also it is not the magnitude that is proportional
it is the vector
onyx inlet
I was told both
void echo
since it also includes direction
onyx inlet
Huh
void echo
vector a =k times vector b
you dont know the vector OP
but you know that vector 6i+8j is parallel to op
so k times vector (6i+8j) = OP vector
and from this you will equate their mangnitude
void echo
yes because in this question u need that vecrot in terms of i and j, since you will multiply the factor k to them
void echo
like u got 1/8
that is correct but
it is 8i-6j = 1/8(xi+yj)
xi+yj is vector OP
since youdont know the value , i used the variable x and y,
when you will multiply by 8 on the know vector
the factor will become 8
not 1/8
onyx inlet
So if I ever get something around that fraction form all I need to do is express it in the x y form to see if I got the constant correct
past obsidian
Hello, on this quesrtion i was able to expand the first fraction with one on top, but im dont know how to get to the second number - thanks
willow sedge
timtom
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hard mango
hi can someone help me start the equation for the left hand rectangle
hard mango
here’s an example because my teacher makes it so confusing:
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vivid berry
am i doimg this right
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vivid berry
void echo
hi bum chicken
vivid berry
hi
void echo
for intersection
void echo
just equate both the function
vivid berry
so there is multiple points of intersection?
thick hedge
void echo
assume x is a number say 2 or 4 or anything but we are putting x, if for some x in functon f is equal to the same x in g function then they will be equal
so we are equation the two functions
void echo
so there is multiple points of intersection?
it will depend on the roots
void echo
i did this
yes
now to check, you can put these values in both the functions
if they give equal values then they intersect