nope
#help-36
cold gorge
Learn exponent rules.
cold gorge
If you learn exponent rules now, you'll surely be able ti simplify this.
cold gorge
i just asked for help
I just told you what you might wanna learn to be able to solve the problem.
It's the right way to study.
fringe root
i asked for help doe
like
i want the stes
steps
so i can study them
but yea u right
cold gorge
If you know the rules and still stuck, I'd give you the steps.
But it's kind of meaningless rn.
fringe root
but i know the exponent rules
im stuck at this
i never said i dont know the rules
u just assumed i dont know them
are u not gonna help?
narrow chasm
Can someone give me a hint on how to approach this?
final saddleBOT
Can someone give me a hint on how to approach this?
narrow chasm
It seems that the fact that they're deg n and that the relation holds for n+1 numbers is supposed to help but I cannot find a way to utlilise it.
scarlet sequoia
let f = a0 + ... + anx^n
suppose that g = 0 for now
and big hint: try to show that $\int_0^1f^2(x)dx = 0$
celest plaza
B
soft zealotBOT
rafilou2003
celest plaza
person is seated on a Ferris wheel with a radius of 90 feet. The center of the Ferris wheel is 97 feet above the ground, and it completes one revolution every 98 seconds. Assume the person is at the 3 o'clock position and the wheel is moving clockwise. Create an equation to represent this situation as a function of time F(t).
scarlet sequoia
person is seated on a Ferris wheel with a radius of 90 feet. The center of the F...
!occupied
final saddleBOT
person is seated on a Ferris wheel with a radius of 90 feet. The center of the F...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
scarlet sequoia
Can someone give me a hint on how to approach this?
if you need more help on this question ping me or helpers
final saddleBOT
@narrow chasm Has your question been resolved?
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tulip coyote
There are 601 integers from 200 to 800, if you're including 200
While 800 - 200 = 600, you'd be missing out on counting the 200 if you didn't add one
For an easier example, try out how many integers there are from 5 to 10: {5, 6, 7, 8, 9, 10}
You can see that there are six numbers there, yet 10 - 5 = 5, so you've missed one there...
trail crest
How i look at it. There are n numbers from 1...n and there are k numbers from 1...k so n - k are numbers from k + 1 to n (you removed first k numbers ) . Add 1 for k and thats numbers from k to n inclusive (n - k + 1)
final saddleBOT
@tranquil pine Has your question been resolved?
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@tranquil pine Has your question been resolved?
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Available help channel!
tranquil pine
Does there exist the word "linear bijection" or is the linear unnecessary
tiny gorge
yes it exists
and there are bijections that are not linear, so if you mean linear bijection then "linear" is necessary
bijection just means a map (function) that is one-to-one and onto
topaz yacht
final saddleBOT
topaz yacht
is this a valid solution for this question
final saddleBOT
@topaz yacht Has your question been resolved?
final saddleBOT
@topaz yacht Has your question been resolved?
rancid idol
try #linear-algebra
final saddleBOT
@topaz yacht Has your question been resolved?
topaz yacht
try <#540211747613704221>
took your suggestion, however no response yet
final saddleBOT
@topaz yacht Has your question been resolved?
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gray trench
I understand that delta x would turn out to be 1, so it'd be 1/3, but what would I use for the other values?
final saddleBOT
I understand that delta x would turn out to be 1, so it'd be 1/3, but what would...
gray trench
Would it be the y-values at every 1 interval?
celest crane
Yes.
gray trench
Yes.
Thanks, I realize these are probably really obvious things to discern, but I'm not very confident in the realm of calculus like this...
Lemme go get to work
For the y-values that aren't super exact, would I estimate?
celest crane
Yes.
You could probably round them to within 0.5's.
Or even keep them as integers.
gray trench
Or even keep them as integers.
Alright, I ended up solving it for 38, which was correct!
I have another question on a more conceptual one I think?
Should I try working the problem out with what info I have first? Or is there something I should know that makes this problem easier to answer?
celest crane
Dusting off my hat on this one. Error approximations for numerical evaluations was one of my Achille's Heels. 🙂
gray trench
Dusting off my hat on this one. Error approximations for numerical evaluations ...
No problemo! I always had trouble with conceptual stuff.
celest crane
You are given M so to speak.
Yes, you are given M.
You are also given a and b as well as |E_s|.
This should just be straighforward substitution and mathing.
gray trench
So, it should work out to be
.00001 = 1/180n M
... What's M? I forgot what M stands for in regards to error approximations. I know there's a way of determining it from the base function, but my teacher didn't really explain it very well.
celest crane
For Simpson's Rule, M is the maximum value of |f^(4)|.
gray trench
For Simpson's Rule, **M** is the maximum value of **|f^(4)|**.
The absolute value of the derivative of f at 4?
2xe^x^2?
gray trench
Oh.
Goodness gracious I need to pay more attention to what the problem gives me
.00001 = 1/180n (76e)
celest crane
It's not necessarily paying attention. I found it always comes down to understanding, or lack of understanding, the information that is given. The only thing that fixes that is practice. Come back to this problem in a day or two and see if you remember how to solve it.
gray trench
I think I'm struggling with having that time to process and understand with the pace my class is going at... I don't mean to deflect blame since I knew what I was signing up for, but still, tough.
celest crane
For the Trapezoidal Rule, M = f''(x), and for Simpson's Rule, M = f^(4)(x).
College calculus?
Or high school?
celest crane
Yeah, college-level Calculus, in particular engineering, tends to be fast paced.
My only recommendation is to solve and understand the practice problems, if any, several times.
gray trench
Understood.
I think part of my frustration also comes from the fact that, I'm a Bio major.
And I really don't understand how this'll come in handy later, buuuut I shall do it nonetheless.
For .00001 = 1/180n (76e) however, by the way
I divide by 76e on both sides and then multiply by 180n right?
celest crane
For problems you find especially difficult, write notes as you are trying to solve it.
Literally, every single thought process.
This is what I often did.
Never erase your mistakes. Write notes in red that explains what you did wrong.
Here I showed what I did wrong and explained in blue what the mistake I made was and what I should have done.
gray trench
I used to write a lot of notes and whatever the instructor would say last semester on harder problems I found difficult to understand
celest crane
That way when I look back on it, I don't have to guess what I did.
gray trench
But there isn't much my professor currently says that I do understand that would help me if I wrote it down, so uh, I've been pretty reliant on myself.
gray trench
That way when I look back on it, I don't have to guess what I did.
I'll definitely start considering doing this though, it would help to remember my line of thinking in certain things...
celest crane
If you look back on an old math problem and you have no clue what you did, you need to add notes to it.
Preferably using different colored pens.
gray trench
I can usually understand what I did without notes, but it would help with the clarity if I did start adding them.
celest crane
I always used orange for things like identities and formulas; blue for comments and references; and red for mistakes,
gray trench
I always used orange for things like identities and formulas; blue for comments ...
My girlfriend does similar for other things actually, haha, I suppose I'll follow suit too.
celest crane
It helps out a lot.
gray trench
Also, in regard to the .00001 = 1/180n (76e), i got something that didn't make much sense.
I divided by 76e first, and then after that I multiplied both sides by 180n.
I got I think a six digit figure in the end
celest crane
76e is a relatively large number.
gray trench
Isn't that the value for M though?
celest crane
Yes.
gray trench
And it says I need the value for n, and n ended up as that aforementioned six digit number.
celest crane
If I were a betting man, I would say this problem is there to highlight the occasional drawback to using Simpson's Rule.
gray trench
Is it the fact that n has to be even?
... I don't know many drawbacks to using Simpson's, my professor only highlighted its usefulness over Trapezoidal approximation.
The only thing she said was that "Simpson's is a bit more difficult but garners a closer answer"
celest crane
I don't know if Calculus textbooks still mention this, it was just a single two sentence paragraph in my old textbook, but many occasions in the real world in which you will need to integrate an expression are not suitable for evaluating an anti-derivative. The problems in your textbook are intentionally easily integrable.
In reality, you would almost always rely on software to do the calculations for you though.
But if you had to do some math by hand, you would likely rely on Simpson's Rule to do the calculation.
gray trench
I suppose that makes sense, but then why have you solve for n then?
I feel like they could've made the problem a word one if they wanted to convey that.
Especially since I'm still stuck on that one equation still lol.
celest crane
It's to develop your understanding of how to approach this type of problem. One of the major differences between job classes is that you either don't need to solve any problems and just do tasks, the job requires some knowledge that is well-established and you just need to familiarize yourself with that information, and jobs that require you to know how to solve a problem on your own. The pay scale for each type of job increases exponentially in the respective order.
gray trench
Fair enough I suppose. It's why I'm here after all, to push forward my understanding!
Is my equation still correct though?
celest crane
To the best of knowledge, n is a large number.
celest crane
I got the same.
gray trench
Wow, that's a gross number. Let's see if it's correct
celest crane
Round it.
gray trench
so 114772
celest crane
Yes.
gray trench
Wow, it said it was wrong
celest crane
Hmm.
gray trench
Rough, that was my last attempt for the problem too. Ah well.
I'll ask my professor in person about it.
There's one more I need to do and then I'm done for today.
... I need to find out what n would be again
celest crane
I think it was the (b-a)^3.
gray trench
I think it was the (b-a)^3.
Really? Weird.
celest crane
Well, n divides the interval into equal-sized partitions.
Hmm, nevermind.
I was thinking incorrectly about that.
gray trench
I assume I use Simpson's for this next one, yes?
celest crane
Yes.
celest crane
Ahh, I know what we did wrong. It was supposed to be h^4, not h^2.
gray trench
Ahh, I know what we did wrong. It was supposed to be h^4, not h^2.
Oh, that's frustrating.
celest crane
And I forgot to raise n to a power.
Which would result in n = 18.4 or 19.
Which makes a lot more sense.
gray trench
... Oh, that's what it represents.
So it'd end up being
8-4 = 4
4/12
turns into 1/3 / 3
celest crane
Yes.
gray trench
1/9 (1/4^5 +1 + 4(1/(13/12)^2 +1 ... etc
.. That's a lot of partitions
I wish there was a more easier way of writing them all down
I might save this one for later, I'm getting sleepy and it seems like a much longer problem.
celest crane
I don't think you need to write out the entire function, just write f(4), f(4 1/3), ...
gray trench
I don't think you need to write out the entire function, just write f(4), f(4 1/...
Oh, I meant to compute it into my calculator
celest crane
Yeah, with Calculus you'll find there is a lot of gruntwork.
gray trench
Yeah, with Calculus you'll find there is a lot of gruntwork.
I don't think I have a single calculus or math related class again until third year at least
my second and fourth year are free
But yeah, this is rough
past nebula
final saddleBOT
past nebula
pls ping me when you reply
inland kettle
!done
final saddleBOT
If you are done with this channel, please mark your problem as solved by typing .close
past nebula
wait how
inland kettle
??
past nebula
can you explain how to do it
inland kettle
a is 3^1001 + 4^1002
and b is 3^1001 - 4^1002
@past nebula the identity of a^b - b^2?
inland kettle
sighs
past nebula
😭
past nebula
yeah
past nebula
(a+b)(a-b)
inland kettle
yes
past nebula
oh ok
inland kettle
also one more thing
(x + y)^2 + (x - y)^2 can be expanded, you can use that too
if you want
tranquil pine
guys how do I calculate the uncertainty of the average value of the three values
$$x \pm \Delta x$$
$$y \pm \Delta y$$
$$z \pm \Delta z$$
final saddleBOT
guys how do I calculate the uncertainty of the average value of the three values...
soft zealotBOT
Alison Burgers
signal vector
Their uncertainty will also be averaged
tranquil pine
are you sure?
signal vector
Yes
tranquil pine
A solution I found online said something different actually
they said that I should be adding up the fractional uncertainties/percentage uncertainties
as in:
$$\frac{\Delta x}{x} + \frac{\Delta y}{y} + ...$$
and then divide that by 3
and then multiply with the average
soft zealotBOT
Alison Burgers
signal vector
When you add two values, how do you get the uncertainty of their sum?
You just add their uncertainties
Same goes for 3 values
tranquil pine
OH i see
signal vector
The average of the three values is the sum of the three values divided by 3, so their uncertainty will also just be averaged
tranquil pine
gotcha
signal vector
I have no clue why you'd take this fractional thing
tranquil pine
I think I was confusing it with multiplication of values with uncertainties 😓
Really sorry
thanks for the help btw
signal vector
Nah nah all good
final saddleBOT
final saddleBOT
Available help channel!
oak scarab
Not sure how to begin
final saddleBOT
Not sure how to begin
cyan kayak
@oak scarab hint, take (x - r)(x - s) and expand it out. This should give you two coefficients. You'll have x^2 + bx + c. Where b is something involving the sum of r and s, and c being something involving the product.
If we set 0 = x^2 + bx + c, and we multiply it by some value a we get 0 = ax^2 + abx + acx
For this question you have a and r as givens, additionally, you know ab = -5 and ac = 1.
oak scarab
<@931522315739594792> hint, take (x - r)(x - s) and expand it out. This should g...
Sorry, I'm a bit confused by what you mean r & s
cyan kayak
If you have (x-r)(x-s) = 0 then your roots are r and s
You know r, one of the roots. And you can find s using the coefficients.
oak scarab
I think the method my teacher taught was a bit different. I was taught that let Alpha and Beta be the roots. Then Alpha + Beta = -b/a and Alpha x Beta = c/a .
cyan kayak
Then using s you can find a
cyan kayak
I think the method my teacher taught was a bit different. I was taught that let ...
It's equivalent.
final saddleBOT
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valid anvil
Can anyone help me prove this
final saddleBOT
Can anyone help me prove this
final saddleBOT
@valid anvil Has your question been resolved?
tranquil pine
hi i have an issue with volume of a parallelopiped
final saddleBOT
hi i have an issue with volume of a parallelopiped
tranquil pine
my teacher said that it was vector A cross vector B dot vector C
i'm not sure if it makes sense to me
errant dawn
i'm not sure if it makes sense to me
Your teacher is referring to the fact that the volume of a parallelepiped can indeed be calculated using the scalar triple product of three vectors
errant dawn
i'm not sure if it makes sense to me
If you have three vectors representing the edges of the parallelepiped (let's call them A, B, and C)
then the volume V is given by the absolute value of the scalar triple product |A ⨯ B ⋅ C|.
This method is based on vector algebra and is an alternative approach to calculating the volume of a parallelepiped.
tranquil pine
but why is it that, i dont understand where it comes from
errant dawn
but why is it that, i dont understand where it comes from
the formula comes from and how it relates to the concept of volume in the context of vectors
tranquil pine
is there a derivation or something of the sort that i can have a look at
errant dawn
u want video's that I recommend for u?
tranquil pine
u want video's that I recommend for u?
yes please
junior token
but why is it that, i dont understand where it comes from
Do you know what the cross product means geometrically
junior token
yes, the magnitude is the area of the parallelogram enclosed by the vectors
And the direction is
junior token
perpendicular to the plane which cintains the vectors
Yes, and what does the dot product mean
(geometrically)
tranquil pine
product of magnitude of a vector with the projection of another vector along it
junior token
product of magnitude of a vector with the projection of another vector along it
Yes
So you can put all of that together by considering that the dot product projects C onto A x B
Giving the height of the parallelepiped
The base is given by the magnitude of A x B
And the volume of the parallelepiped is the base times the height
final saddleBOT
tranquil pine
.reopen
final saddleBOT
✅
tranquil pine
im sorry were you typing something
junior token
There’s also the determinant
which can also be interpreted as the volume of that parallelepiped
is that why you originally asked?
tranquil pine
is that why you originally asked?
no
tranquil pine
which can also be interpreted as the volume of that parallelepiped
im sorry whats that
junior token
im sorry whats that
What’s what
tranquil pine
interpretation of volume of a parallelopied as a determinant?
junior token
interpretation of volume of a parallelopied as a determinant?
Oh
junior token
interpretation of volume of a parallelopied as a determinant?
If you consider the matrix with the 3 vectors making up the parallelepiped as its columns
Then, the determinant of this matrix is the volume of the parallelepiped
tranquil pine
ohhh
i'll keep that one in mind too
thank you so much
enjoy your day:)
.close
final saddleBOT
junior token
enjoy your day:)
Thanks!
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Available help channel!
sterile kestrel
final saddleBOT
sterile kestrel
i dont know what to do this question
static plinth
let’s say x is the amount of time it takes for the smaller one to fill the tank
the time it takes for the larger one to fill the tank would be x-10 right
what can we do with this information to solve for x
sterile kestrel
idk
static plinth
have you done these types of problems before?
sterile kestrel
no
sterile kestrel
i think smaller tap + larger tap=75/8
static plinth
close
sterile kestrel
or 1/smaller + 1/larger
static plinth
yep
sterile kestrel
after reciprocal
static plinth
and we also drew connections between smaller and larger
sterile kestrel
ohk
static plinth
we can solve for x here
sterile kestrel
thx
static plinth
yw
sterile kestrel
.close
final saddleBOT
final saddleBOT
Available help channel!
robust knoll
Can anybody help me understand this calc 3 problem?
Find the line of intersection between the planes 2x + 4y - z = 7 and y + z = 2
I understand how to find the direction of the intersecting line, thats just getting the vectors normal to the planes (coefficients) and taking the cross product
I was mainly trying to understand how to get the shared point that the vector should go through, when i searched it up on the internet it said to plug in a random value z = 0 to get rid of a term and then solve for the x and y points from there, but i don't quite understand if or why that works
final saddleBOT
Can anybody help me understand this calc 3 problem?
``Find the line of intersec...
@robust knoll Has your question been resolved?
ancient monolith
final saddleBOT
ancient monolith
i worked out magnitude by working resultant force of x and y
then doing pyhtagoras
but when doing my triangle
the angle i worked out was the wrong 1
it was the other angle
idk how im suppose to know which it is
ancient monolith
its for a right angle triangle
it works tgho
it is a right
angle
working out the resultant for x and y
then doing pythagoros
weary scaffold
it is a right
which one?
ancient monolith
which one?
the resultnt
dense coral
working out the resultant for x and y
yeah that seems about right
ancient monolith
yeah that seems about right
but i worked out the angles
and i got the correct angle but wrong way
weary scaffold
the resultnt
ohhk i misunderstood
dense coral
and i got the correct angle but wrong way
draw the resultant triangle out
ancient monolith
let me send a picture gimmme a sec
dense coral
i find it it very useful to define a coordinate system, then write down [left/right] and [up/down] for the resultant x and y components
ancient monolith
dense coral
then draw the resultant force triangle using those as legs
can you tell me your resultant x component and y component?
dense coral
can you tell me your resultant x component and y component?
.
dense coral
it's not right actually
you've wrote the resultant x component as the y component and vice versa
30cos30 - 25cos50 = 14.24 N [right]
ancient monolith
you've wrote the resultant x component as the y component and vice versa
oh did i do it the wrong way around
dense coral
yeah you did
final saddleBOT
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Available help channel!
raw flint
find U2 + U1
final saddleBOT
find U2 + U1
raw flint
I will use a simple base to make them vectors
U1: (3,2,1,-4),(1,0,0,-1)
U2: (1,1,1,0),(1,0,-1,2)
what now?
raw flint
I will use a simple base to make them vectors
U1: (3,2,1,-4),(1,0,0,-1)
U2: (1,1...
and is this step ok?
final saddleBOT
@raw flint Has your question been resolved?
raw flint
<@&286206848099549185>
please tell me if something is unclear and I would try to explain it better 
<@&286206848099549185>
final saddleBOT
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raw flint
.close
bleak hinge
Can somebody help me with this?
final saddleBOT
Can somebody help me with this?
bleak hinge
I’m really bad at binary
soft zealotBOT
odd rivet
do you know how binary works?
bleak hinge
Not really
dense coral
@bleak hinge how would you write the number 581 in base 10?
if you had to write it in powers of 10?
dense coral
<@760948612573298689> how would you write the number 581 in base 10?
*how would you write 581 in terms of powers of 10
i should have been clearer with my words
dense coral
no, trinity is giving an answer to my question i believe
trail crest
Oh
dense coral
in which case, she's right
bleak hinge
no, trinity is giving an answer to my question i believe
Yeah
Sorry I just prefer to write it
dense coral
now, you just want to do the same thing but in base 2 for your number
since 581 meant 5*10^2 + 8*10^1 + 1*10^0, we see that the digits are just the coefficients of the powers of 10
it works the exact same in base 2
but instead of powers of 10, you have powers of 2
the digits are still the coefficients
dense coral
unfortunately, no
here, let me give you another base 10 number
and i think you'll see where you went wrong
10305
try writing that in terms of powers of 10
dense coral
right, but it would be more accurate to write
1*10^4 + 0*10^3 + 3*10^2 + 0*10^1 + 5*10^0
that is also the key to writing your binary number in terms of powers of 2
each digit is a coefficient for a power of 2
including 0s
bleak hinge
Wouldn’t your more accurate one turn out to be 11,911?
dense coral
Wouldn’t your more accurate one turn out to be 11,911?
how so?
bleak hinge
Nevermind saw were I went wrong there sry
But I’m still super confused with the og question
dense coral
with what specifically?
base 2 isnt really that different from base 10
you just cant have the coefficients be anything other than 0 and 1
bleak hinge
Just the way it’s worded
dense coral
well, it's asking you to first write the number as powers of 2
bleak hinge
Like does it want me to convert the binary than put it into powers of 2?
dense coral
then find out what that is in base 10
dense coral
Like does it want me to convert the binary than put it into powers of 2?
theres nothing to convert
you've been given a binary number already
bleak hinge
I mean I thought 10110111 in binary was 183
dense coral
when i gave you a base 10 number, you didnt have to convert it to anything to write it in terms of powers of 10
when they give you a base 2 number, you dont have to convert it to anything to write it in terms of powers of 2
dense coral
I mean I thought 10110111 in binary was 183
10110111 is a number in base 2, that when converted to base 10, gives 183
they are two representations of the same thing
the question wants you to show how to convert between the two
bleak hinge
10110111 is a number in base 2, that when converted to base 10, gives 183
This doesn’t make sense to me
dense coral
why not?
bleak hinge
How do I write 10110111 as powers of 2?
dense coral
the same way i wrote 10305 as powers of 10
you need to keep the 0s as coefficients for some powers
dense coral
each digit is a coefficient for a power of 2
see here
i think you may have missed that?
bleak hinge
I don’t understand coefficients
dense coral
for the number 10305
i wrote 1*10^4 + 0*10^3 + 3*10^2 + 0*10^1 + 5*10^0
1 is the coefficient of 10^4, 0 is the coefficient of 10^3, 3 is the coefficient of 10^2, etc
notice how the coefficients are the same as the digits
1 is the "ten-thousands" digit, 0 is the "thousands" digit, 3 is the "hundreds" digit, etc
it is very much the same in binary
bleak hinge
Like this?
dense coral
but "ten-thousands" really means 10^4, which is a power of 10
bleak hinge
dense coral
in binary, the only difference is that you'll have powers of 2
bleak hinge
But in powers of 2?
dense coral
close, but you've miscounted
there's 8 digits in the number
you missed the 2nd one to the right
and that offset all the other ones
bleak hinge
Oh the 10
dense coral
no, the 2nd to the right
1*10^0 is good
but then you've written 1*10^2
you missed 1*10^1
bleak hinge
That’s what I meant
bleak hinge
Like the 10 in the number
bleak hinge
I mean the part I was missing was 1*10^1
dense coral
oh wait, i've missed that
you wrote it in powers of 10, when they want you to write it in powers of 2
bleak hinge
Yeah I realized that
dense coral
I mean the part I was missing was 1*10^1
you're missing 1*2^1, yes
bleak hinge
But can you help me make it with powers of 2?
bleak hinge
How can I make 10110111 as powers of 2?
dense coral
it is a **base 2** number
do you understand what this means?
bleak hinge
Not really
dense coral
let me give you a non-binary number, but not base 10
here's a base 16 number
51
since it's in base 16, each digit represents a coefficients of powers of 16
so this number is 5*16^1 + 1*16^0
NOT "51"
as in the base 10 number
bleak hinge
Isn’t 5*16 80?
dense coral
yes
dense coral
huh?
bleak hinge
Oh wait I kinda get it know
Since it’s base 16 it’s 516^1 because of the 5 and 116^0 cause of the 1?
Sorry don’t know why the stars disappeared
dense coral
yes, the digits of a number in any base represent the coefficients of the expansion of the number in terms of powers of the base
in base 31, the number "10" is given by
1*31^1 + 0*31^0
which you can see is equal to the base 10 number 31
dense coral
again, as i've said before, each digit is a coefficient of a particular power of 2
i've given you examples in bases 16, 10, and 31
it is no different in base 2
bleak hinge
I just don’t get it with a longer number
dense coral
why? theres nothing different about a longer number
you just have a larger expansion to do
here's a "long" number in base 3:
2010102
thats equal to 2*3^6 + 0*3^5 + 1*3^4 + 0*3^3 + 1*3^2 + 0*3^1 + 2*3^0
each digit is a coefficient for a power of 3
starting from 3^0 on the right, and ending with 3^6 on the left
bleak hinge
But what’s the base I have since it’s also asking me to convert to base 10 in standard form
dense coral
you can convert to base 10 standard form after having written out the number as powers of 2
dense coral
here's a "long" number in base 3:
2010102
for instance this base 3 number i can convert into base 10
dense coral
thats equal to 2*3^6 + 0\*3^5 + 1\*3^4 + 0\*3^3 + 1\*3^2 + 0\*3^1 + 2\*3^0
using this expansion
bleak hinge
That’s not what I’m asking
dense coral
i see, then what are you asking?
bleak hinge
How do I know what the base of the number is
bleak hinge
So the base is 2?
bleak hinge
Like I said before I’m really bad at binary
dense coral
fun fact, base 16 is called "hexadecimal"
so theres not really a "standard" naming convention as far as i know
people just say base x
2,3, 10 and 16 are major exceptions afaik
they are "binary", "trinary", "decimal", and "hexadecimal" respectively
so if you see those words, you automatically know the base
actually i lied
base 12 also has a name, and is somewhat common to see
"duodecimal"
all the other bases have names too, but i never see them used so yeah
soft zealotBOT
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dense coral
yeah that's it
now to convert it to base 10, just compute that sum as you normally would
soft zealotBOT
bleak hinge
This is the entire question?
dense coral
iirc, standard form just means to write the number normally
dense coral
Thanks so much for keeping up with me
no worries
bleak hinge
,close
dense coral
its .close
bleak hinge
.close
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tranquil ledge
I just need help understanding stuff
final saddleBOT
I just need help understanding stuff
tranquil ledge
in algebra 1
loud sundial
loud sundial
Just post the question and someone will help
Beating around the bush just makes it take longer for you to get said help
final saddleBOT
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clear crown
i don't get the logic here
final saddleBOT
i don't get the logic here
trail crest
I guess II. is like sides
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@clear crown Has your question been resolved?
buoyant mesa
Hi everyone. Im having a little trouble with the first step in differentiating the following function using the "product rule".
final saddleBOT
Hi everyone. Im having a little trouble with the first step in differentiating t...
buoyant mesa
In the first step, I want to isolate v and u where, (see formula above)
Is anyone able to help me in baby steps
<@&286206848099549185>
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@buoyant mesa Has your question been resolved?
twin wing
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twin wing
so 4 hours to unload a moving truck for nathan
6 hours for iris to unload a tuck
would it not take them 10 hours together?
wait thats not an option lol
maybe if they work together, we can average out?
vital crag
No because Nathan could do it faster by himself
twin wing
true
final tangle
consider first finding how fast they each are in Trucks/hour
trail crest
maybe if they work together, we can average out?
||More like having resistors in parallel||
twin wing
lol you must like physics
if a resistor is in parallel, wont you add the resistors
and then divide by amount of resistors added
im pretty sure
trail crest
No you add in series. But in parallel its $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}$
soft zealotBOT
casework
trail crest
Im pretty sure if you just plug in 4 and 6 you would actually get a correct answer
Not sure though
final tangle
how are you getting 1/10
twin wing
1/r+1/r2
trail crest
**casework**
Yea this would work
final tangle
that's not how adding fractions work
final tangle
$\frac 1a + \frac 1b \redneq \frac{1}{a+b}$
soft zealotBOT
ℝαμΩℕωⅤ
trail crest
Yes
twin wing
lowkey i dont understand the relationship between a parallel resistor with my question
can we do a different approach tbh
im not going to look at my gre question and instantly think RESISTORS
tbh
final tangle
consider first finding how fast they each are in Trucks/hour
vital crag
lowkey i dont understand the relationship between a parallel resistor with my qu...
You don't need to
vital crag
im not going to look at my gre question and instantly think RESISTORS
Yea you shouldn't
final tangle
and then what about iris
trail crest
can we do a different approach tbh
The computation will stay the same
twin wing
1/6=.16
twin wing
The computation will stay the same
understandable
twin wing
ok 1/4+1/6
trail crest
||You can always look at it like a capacitor but in series||
final tangle
now with consistent units, of trucks/hour
you can add them to see how fast they unload together
final tangle
now read carefully what the question is asking for
final tangle
48, not 38
trail crest
Looks right
final saddleBOT
trail crest
Interesting thing btw : https://en.m.wikipedia.org/wiki/Parallel_(operator)
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mellow crystal
im not sure how to go about this
final saddleBOT
im not sure how to go about this
trail crest
Does it tell you the thickness of a box?
mellow crystal
no
trail crest
Or is this just show how you would do it
mellow crystal
they only told me what’s on the photo
trail crest
Any ideas?
mellow crystal
no 😭
trail crest
Well you can at least tell me how many pieces of paper does one box have
mellow crystal
2500
mellow crystal
i’m not sure
trail crest
Well if 1 sheet of paper is thick y mm how thich are 2 sheets of paper?
final tangle
no
mellow crystal
please help
final tangle
how are you getting 2mm
final tangle
if there are 3 apples in a box, how many apples are in two boxes?
mellow crystal
6
final tangle
and how did you reach that value?
final tangle
yes
same idea applies here
the thickness isn't known,
so we're using a variable to represent that
mellow crystal
so?
final tangle
1 sheet of paper is thick y mm how thick are 2 sheets of paper?
same idea applies here
mellow crystal
what’s thick y mm ??
final tangle
mm is the unit
y is a variable representing some unkown quantitiy
because you aren't given the numerical value
final tangle
yes
now lets go back to the first part
how many pieces of paper does one box have
2500
Lets say box is thick x cm
How thick is 1 sheet of paper
mellow crystal
1cm?
mellow crystal
so a box has 2500 sheets of paper and the box is thick x cm, we don’t know the thickness of the paper because we don’t know the thickness of the box right?
final tangle
we don't know the numerical values
hence why we're intrducing the variable x to represent that
we'll get an expression with x
so that if/once we get the numerical value, we could plug that in the get the individual thickness
apply the same ideas as you would if you had a numerical value
if i gave you a numerical value for the thickness of the box,
e.g. 5000cm (don't worry about the unrealistic size)
and there are 2500 sheets
how would you determine the thickness of a sheet?
mellow crystal
2500/5000?
final tangle
yeh
mellow crystal
x/2500?
final tangle
yes, that'll be for one sheet
mellow crystal
2x/2500
mellow crystal
x/1250
final tangle
yes
we'll get an expression with x
so that if/once we get the numerical value, we could plug that in the get the individual thickness
and that describes how you'd be able to get an estimate
measure the box, then divide by 1250
final tangle
!done
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If you are done with this channel, please mark your problem as solved by typing .close
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primal relic
when you're trying to integrate a composition function with the substitution rule, does du cancel out with dx?
final saddleBOT
when you're trying to integrate a composition function with the substitution rul...
primal relic
like isn't du just du/dx and then you multiply that with dx per the chain rule, so it's just du?
I just want to clarify, I suppose
final tangle
du/dx = stuff
du = stuff dx
primal relic
is du not the same thing as du/dx
final tangle
it is not
primal relic
what is stuff referring to?
oh like the derivative of u
but I thought du just meant the derivative of u
and that derivatives are rates of change
final saddleBOT
@primal relic Has your question been resolved?
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@primal relic Has your question been resolved?
final saddleBOT
@primal relic Has your question been resolved?
naive tapir
but I thought du just meant the derivative of u
du is a slight change in u. dx is a slight change in x. du/dx is the ratio, which represents the derivative of u with respect to x (how fast u changes when x is changed)
ancient hatch
When do I isolate the radical while solving radical equations, and when do i not?
final saddleBOT
When do I isolate the radical while solving radical equations, and when do i not...
ancient hatch
here, i had to completely isolate the radical (including the coefficient)
but it wasn't the case with this one?
i get a diff answer when if i don't do it the right way
warm python
here a substitution would probably make it easier
ancient hatch
how does that work..?
ancient hatch
I'm sorry my slow self does not understand
warm python
if $n=x^2$
soft zealotBOT
Why am. I here
warm python
then you simply have to solve $25+10x=\sqrt{3}x$
soft zealotBOT
Why am. I here
warm python
why did you square both sides?
ancient hatch
to get rid of the radical. do i not have to do that?
warm python
you simplt have $5=x(\sqrt3-1)$
soft zealotBOT
Why am. I here
ancient hatch
where is the 1 coming from?
I'm so sorry, this is new to me, so it's taking time
warm python
I subtracted one from both sides and then factorised
rancid hound
I subtracted one from both sides and then factorised
Do u mean subtracted x from both sides ?!
ancient hatch
ohhhhhh i get it now
warm python
Do u mean subtracted *x* from both sides ?!
Yes,my bad
rancid hound
This one is absolutely correct
warm python
Divide both sides by $\sqrt3-1$
soft zealotBOT
Why am. I here
ancient hatch
ahhh got it
warm python
Now you have found x, you can find n from it too
rough wyvern
why does it calculate the 2nd derivative too? to find candidates for extreme value, do we derive until we cant anymore?
final saddleBOT
why does it calculate the 2nd derivative too? to find candidates for extreme val...
formal trail
the sign of the second derivative at critical point tells us whether it's a maximum or minimum
rough wyvern
so the first derivative is to find candidates of extreme value and the 2nd derivative is used to determine whether its a max or min. ?
formal trail
yes
rough wyvern
the sign of the second derivative at critical point tells us whether it's a maxi...
what do u mean by critical point ? is it the max/min point ?
formal trail
a critical point is a point where the first derivative is equal to 0. A critical point can be a maximum, a minimum, or neither. the only points that can be maxima or minima are critical points
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wanton pine
A force of 7.5x10^-4 N north acts on a charge at point P in an electric field of strength 6.0x10^-5 NC^-1 north. Calculate the magnitude and sign of the charge.
final saddleBOT
A force of 7.5x10^-4 N north acts on a charge at point P in an electric field of...
final saddleBOT
@wanton pine Has your question been resolved?
formal trail
what is the relationship between the electric field and the electric force?
open shore
F=qE
If a charge moves upwards due to a. Electric field going up, just means positive charge
The definition of a north electric field line is that a positive charge moves north if placed in that field
final saddleBOT
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errant steeple
1/r ∂u/∂θ=-∂v/∂r proof Cauchy–Riemann ?
final saddleBOT
1/r ∂u/∂θ=-∂v/∂r proof Cauchy–Riemann ?
errant steeple
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@errant steeple Has your question been resolved?
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@errant steeple Has your question been resolved?
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potent turret
Is it true that P(A = True | B = True) = 1 - P(A = True | B = False)? Assume the events A and B can only have two outcomes.
final saddleBOT
Is it true that `P(A = True | B = True) = 1 - P(A = True | B = False)`? Assume t...
unique aspen
Is it true that `P(A = True | B = True) = 1 - P(A = True | B = False)`? Assume t...
no
for example, suppose i rolled two dice completely independently
P(first one is a 6 | second one is a 6) =/= 1 - P(first one is a 6 | second one is not a 6)
potent turret
I should rephrase to avoid the XY problem.
So far, I have P(H), P(not H), P(C|H). I am trying to find P(H|C). I thought Bayes' Theorem would be useful here, namely the extended form:
P(A|B) = P(B|A)*P(A) / (P(B|A)*P(A) + P(B|not A)*P(not A))
I wanted to use the extended form because I don't know P(B) for the regular form.
The reason I asked my initial question is because I'm having trouble finding P(B|not A).
unique aspen
I should rephrase to avoid the XY problem.
So far, I have `P(H)`, `P(not H)`, `...
i'm not sure it's possible.
for example, suppose i rolled two dice completely independently. let H be the event the first one is a 6, C be the event the second one is a 6.
then P(H) = 1/6, P(H') = 5/6, P(C | H) = 1/6.
and P(H | C) = 1/6.
but now suppose i rolled two dice, but: the second one magically has a 1/6 chance of rolling a 6 if the first one rolls a 6, but 0 chance of being 6 if the first one isn't 6.
and again let H be the event the first one is a 6, C be the event the second one is a 6. then:
then P(H) = 1/6, P(H') = 5/6, P(C | H) = 1/6
but P(H | C) = 1.
so precisely because we don't know P(C | not H) from the information given; in the first case it's 1/6, in the second case it's 0, which makes all the difference
final saddleBOT
@potent turret Has your question been resolved?
potent turret
Here's a screenshot of the full problem I'm trying to solve.
And here's some assumptions I've made.
unique aspen
yeah that'd be helpful to have since the start
ah
ok
it's because it must either be a hurricane or a tropical storm
there's no third possibility
so you know P(H) = 0.69, P(C | H) = 0.08, P(C | T) = 0.2
then P(H | C) = P(C | H)P(H)/(P(C | H)P(H) + P(C | T)P(T))
just use that
@potent turret
potent turret
Are you implying that in this case, P(C|T)*P(T) is equivalent to P(C|not H)*P(not H)?
unique aspen
yes
it's implicit in the question
otherwise, as we see, it's impossible to get an answer
the question implies 'either T or H will happen'
potent turret
That makes sense. I failed to recognize that H and T had that relationship.
potent turret
.close
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burnt fjord
Solve the matrix equation: A(B+X)^-1*A^-1 = A^2*C, when A={{2,-3},{1,2}}, B=1/7*{{2,-4},{-1,-12}} and C=1/7*{{2,3},{-1,2}}
final saddleBOT
Solve the matrix equation: `A(B+X)^-1*A^-1 = A^2*C, when A={{2,-3},{1,2}}, B=1/7...
burnt fjord
I know I should simplify the left side as much as possible but not sure how to go about it
barren hound
$A(B+X)\inv A\inv = A^C$ ?
soft zealotBOT
hayley!
barren hound
or do you mean $A\inv C$ on the right
soft zealotBOT
hayley!
final saddleBOT
@burnt fjord Has your question been resolved?
burnt fjord
or do you mean $A\inv C$ on the right
oh sorry, I lost a 2, it's A^2*C on the right
austere spire
im reading a discrete math book and got to this part:
final saddleBOT
im reading a discrete math book and got to this part:
austere spire
can someone help me understand how, in the part where it says "sometimes people use a method that they believe....... they perfrom the following steps: [shows steps]", it's seen as invalid argument?
dense coral
can someone help me understand how, in the part where it says "sometimes people ...
it’s as they say: doing that means you have first assumed that the statement is true, then deduced a tautology from it
you have not shown that the original statement is true however
austere spire
from the first example they gave, how can the original statement be proved, this statement:
dense coral
start with one side, and show it must be equal to the other
I’d recommend starting from the right
austere spire
yea but that is what they did in the first example, this:
but the book said that's invalid
dense coral
no, this is assuming the statement is true in the first place and deducing a true statement at the end
doing this doesn’t mean the initial statement is true
you need to start on one side, and keep making steps until you get the other
austere spire
yea but in the first sentence, it said this:
dense coral
yes, that’s fine too
austere spire
like u transform the left hand side first
dense coral
key word is independent
austere spire
then the right hand side
austere spire
yea but that is what they did in the first example, this:
are the transformations not done independently here?
dense coral
Nowhere did they say you can assume the statement true and then perform manipulations
dense coral
are the transformations not done independently here?
No they are not
there’s an equality sign throughout
which does not make it independent
austere spire
sorry can you show me how it would look like if they were transformed independently
dense coral
okay, let me get some paper
austere spire
btw this is how the book proved the same statement previously