#help-28
1 messages · Page 11 of 1
Denascite
well now we can start
hmm lets say we plug those in
by saying that m > 0 , n>0 basicly always yields in positive right/
no matter what x1 or x2 are
plus we are taking absolute value of the elements
scalar multiplication
this one might be tricky , but same logic i guess
alright ill try to work something out, thanks for the help
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How do I tell which way the inequality sign goes
What’s the question
why square function is equal to linear
Question d
,rotate
Where are the points of intersection
You should also lay out what answers which question
For example, have i) for the graph
Then ii) shows the intersection points if any
Then iii) solves the inequality
How do I find points of intersection is it simultaneous equations
Yep
Points of intersection is where the x and y values of both equations are the same
Which is why simultaneous equations work
What
The 2 equations equal each other
Your 2 equations are:
y = 3 - x²
y = 2x - 12
@solemn ice Has your question been resolved?
How do I solve that simulatineously
@solemn ice Has your question been resolved?
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<@&268886789983436800>
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Hello, I would like to ask for help in mathematical analysis, I'm struggling with integration
alr
good to know
do you have a question?
which tequniques have you learnt
currently we are supposed to use substitution
which question do you need help in?
i would like to solve 15
integrate it?
yes
"integrate the following functions"
but i didnt send the text, because its in my first language
thats ok i speak all languages you can think of
all languages apart from that
:))
you sure its to inegrate and not differenciate it?
yes, 100% sure
is this calulator or non calc?
im not sure what that means
im confused because the previous problems were a lot easier to integrate, this one i cant think of a way to do it
What was the answer to question 11?
yes this one is a bit digusting
Cause this one is disgusting
idk how to type the syntax
Is it disgusting
$\sqrt[5]{x}$
mchw
you know what, im already tired as fck
im gonna ask the teacher tomorrow
if its a mistake in the book or something
maybe
i just thought i might be overlooking something
the answer i got was
thats why i came here
ohh lets see
whaaaaaaaaaa
well this is what an online calculator got...
its a bit ugly
however it would be fun to differenciate
True
alright, thank you
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how many anagrams we can compose from the word "TIZI OUZOU" such That two similar letters are not adjacent to each other?
@zenith kernel
Which two letters?
any two similar letters
Inclusion-exclusion principle
(4)(8C1)(7!/2^3)-(4)(3)(7C2)(5!/2^2)+(4)(3)(2)(6C3)(3!/2)-(4!)(5C4)
Oh not this directly
9!/2^4 minus what I typed
thank you
Np
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The questions is just about using limit laws. Should the final answer not be 8, not 7?
Want to make sure I'm not missing something here.
What is f(x) and g(x)?
^
Depends on what f(x) and g(x) approach
f(x) = 4
g(x) = 9
I see using these numbers how you would get the answer in the book. I thought that when you had lim as x-->a that you set the value of f(x) to a. This is evidently false.
4 + 1/3 * 9 = 7
lim x->a C = C
You plug in a into the function (only applies when the function is continuous at a, but ignore that)
They already tell you f(x) approaches 4, and g(x) approaches 9. In other words:
$\lim_{x \to 6} f(x) = 4$
RedstonePlayz09
$\lim_{x \to 6} g(x) = 9$
RedstonePlayz09
You might want to revise what limit means.
Having an intuitive understanding of it might help
So if I had something like $\lim_{x \to 6} x = ?$ then I would be able to set the ? value to 6?
Dirty
Yes
not always
But what about $\lim_{x \to 6} 2x$
RedstonePlayz09
Okay, need to remember to keep f(x) and x as separate ideas. (I understand how they are, just a slip of the brain)
2 lim(6)?
that limit is just equal to 2 * 6 which is 12
you could take the 2 out, but no reason to do that. just plug x = 6 in
Sounds good. I was just told we need to 'understand why we can just plug it in' which is why I was writing out one of the laws.
of course, you will soon encounter limits where you can't just plug in the value.
For example, limits as x approaches infinity, or where the function is undefined
f(x) means function of x with "x" as its parameter
x is just a variable though
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p has a point at 0.0 therefore p(0)=0
And p'(0) = 0 follows from the definition of a turning point
Let's say p(x) = a_nx^n + ... + a_1x + a_0, using this information you can deduce that a_0 = a_1 = 0
huh
So p(x) = a_nx^n + ... + a_2x^2, therefore p(x) = x^2(a_nx^(n-2) + ... + a_2) = x^2q(x)
Don't just give answers
interesting in germany we have different terms
a turning point would translate to wendepunkt which is where p' changes sign
ohh that's why
thanks a lot
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Got a quick one, why take negative here when integrating?
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How do you do the second part
on differentiating it would be
-sin(y)*dy/dx=1/2sqrtx, so you'll get dy/dx
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Hi, can someone explain to me this example?
which lines are you failing to understand ?
How the negative square root was used
Don't really see the connection even having the TB giving a brief explanation
when x approaches -oo, that means x is negative right ?
when we factor by x^2 in the sqrt, we have : sqrt(x^2 (4 + 3/x^2)) = sqrt(x^2)*sqrt(4+3/x^2)
and we all know that sqrt(x^2) = |x|
we know too that
|x| = x when x > 0 and -x when its negative
THANK YOU
Understand it much 🙏
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How to factor 81z^2+36z+4 and 4z^2-20z+25? They are squared but when I try to factor by grouping I get 9z(z+2)+2(9z+2) when the answer is (9z+2)(9z+2)
Which one are you trying to factor
For $4z^2-20z+25$ you can do what multiplies to 100 and adds to -20
Gama
for $4z^2-20z+25$ I got 2z(z-5)-5(2z-5)
EliteFriedRice
So factoring by grouping usually is reserved for polynomials with 4 terms from my understanding
Cause you’d group the first 2 and last 2
oh
i thought grouping was for when coeffiecient wasn't 1 and couldn't be factored
because then the equation would be
4z^2-10z-10z+25
because -10-10=-20 and -10*-10=100 100=25*4(coeffec)
NVM
i redid it and I was wrong, it was 2z(2z-5) and -5(2z-5)
sorry
Gotcha I was trying to see what was going Wrong but you found it haha
for 55 when grouping i got (9z)(z+2)+(2)(9z+2), how would i get (9z+2)^2
original equation was 81z^2+36z+4
nevermind
i just made a small mistake lol
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Probably a stupid question, but what is here meant by maximum?
I know what the maximum of a function is, but you're not given a function here 🤔
I was trying to help someone with this but was confused by this wording
you want to find the real numbers a,b such that a + 2b = 24 and ab is as big as possible
np
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i need help understanding piecewise functions
what about e,m
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what is the use of rational expression in daily life
calculus 🙂
passing a test
@red oracle Has your question been resolved?
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how do i do this
i know normal DA
@torn jolt sorry for the ping but you were able to help me a lot on the other question so could i get a little more help here
okay
and the numbers as A,B
so a x^3 = b y^3
You know 'a'
and you can calculate y/x
A x^3 * (y/x)^3 = b y^3
Does that make sense so far
i lost you at the last part
I'm not sure what DA is
dimensional analysis
This is what I had been doing so far for normal questions
Now I got to ones asking for cubed units
I don’t get that
That's a really long way of doing it but it makes sense
so in essence, a x^3 = b y^3
You get the conversion y/x, and basically do $a x^3 \frac yx \frac yx \frac yx = b y^3$
KurtDee
I'm not sure how to explain the intuition
Well I suppose you could either think of it two different ways
you're either 1. eliminating one part of the cubed unit at a time
or 2. you're calculating the conversion between cubes first
as to HOW it's done, you need to find "Xierons/Kygenes" first
And then you get the ratio of "cubic Xierons /cubic Kygenes" by raising to the third power
is it possible for you to like write down on paper the first few steps?
im better at visualizing stuff
or draw on an app
I can solve a different problem
yes thatll help too
KurtDee
so we need m/ft, which is $\frac1 {0.3} \approx 3.28$
KurtDee
$\frac {m^2}{ft ^2} = 10.76$
KurtDee
so actually we need to put this on the other side, $\frac{m^2}{ft^2} \frac 1 {10.76} = 1$
KurtDee
I should have done it like that to start with
finally, $20 ft^2 * \frac 1 {10.76} \frac{m^2}{ft^2} = 1.86 m^2$
KurtDee
You can also think of it like $m^2 = 10.76 ft^2$
KurtDee
in that case, you would still divide by 10.76 to get m^2
im trying to understand this but i just cant for some reason
looks right to me
thanks
now i have to do it with square
instead of cubed
is it similar?
or the same
but doing square instead of cube
oh it looks like it is
can you confirm
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this is stupid:
λd: 400÷410nm
the symbol between 400 and 410 (for some reasons discord can't display one futher one), is used as to denote a rage between 400 and 410 (nm)?
one futher one
?
@torn jolt Has your question been resolved?
why
so I suppose it's used to indicate a rage
what is a rage
it's from a led documentation
400 to 410 (nm)
and its about wavelength ?
yes
for rage I meant range
I'm sorry autocorrection
well I dont know what that notation means, but maybe try to understand the whole context
@torn jolt Has your question been resolved?
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This is the first time polynomials have been explained to me like this… is this true what I have written near the bottom?
If so, what would a polynomial be called if it contains complex numbers or asymptotes?
This is from Professor Leonard btw
Well, i wrote that but I could be wrong.. he was saying negative exponents
well if you mean that having a term a/x could lead to asymptotes then you're right
everything else is correct
The a/x was mine. I will adjust that
everything else is good
Wow
This is the first time I have learned this..
I imagined polynomials as including all of the above
Imaginary numbers, asymptotes, you name it
I guess I was over complicating things
the domain is not all real numbers only if there's a radical or fraction
which then introduces dividing by 0 and i
What do we call functions that do have complex numbers or asymptotes, if not polynomials functions? And are structured like a polynomial with highest degree first with constant at the end
just functions
pretty sure
Ah OK…
yeap
Complex function maybe?
function is good enough
they dont really have a particular name
yeah
Polynomial can refer to binomial, trinomial, and anything above right? but not monomial? Or is it one of those all encompassing terms
yeah
Like square and rectangle lol
everything but monomial
not vice versa
open up a ticket if you have more doubts
yea
Sorry one more question to keep it on polynomials.. is it true anything above 4th power polynomial with a constant you will have a hard time using the quadratic formula?
Maybe even impossible to solve if 5th power with constant? Iirc it’s the constant that is the issue here, more than the power itself. Without constant it can be done?
yeah
well
there's a quadratic, cubic, and quartic formula
I'd suggest you use factoring or differentiation to solve anything above 3rd degree
tip: don't search up the quartic formula
Lol
it gives me nightmares
I hope I won’t need to use it for Calc 1 or 2
probably not
OK good
if you do get a polynomial with a degree of 4 or higher you'll be taught a diff method of solving it
not the formula
Got it, thanks!
np
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Trying to figure out why plugging in the x value here gives me the wrong y value
,w 5x-2y+3z=20, 2x-4y-3z=-9, x+6y-8z=21
So those are the correct x,y, and x values
$\begin{tabular}{r} 5x-2y+3z=20\ +2x-4y-3z=-9\ \hline 7x-6y=11\end{tabular}$
dopediscorduser
[\begin{tabular}{r} 129x+6y=669\ + 7x-6y=11\ \hline x=5\end{tabular}]
dopediscorduser
dopediscorduser
??
where did the 129x + 6y =669 come from?
One sec
It came from 5x-2y+3z=20, multiplied to a lcm to cancel out the z terms
I’ll write it out in latex
[7(5)-6y=11]
[y=\frac{24}{6}]
Alpha Kappa
Common lcm 3 and 8 of 24
[8(5x-2y+3z=20)]
[3(x+6y-8z=21)]
[\begin{tabular}{r} 40x-16y+24z=160\ + 3x+18y-24z=63\ \hline 43x+2y=223\end{tabular}/]
To eliminate the y term, LCM between 2 and 6 is 6
[3(43x+2y=223)= 129x+6y=669]
[\begin{tabular}{r} 129x+6y=669\ + 7x-6y=11\ \hline x=5\end{tabular}/]
dopediscorduser
Compile Error! Click the
reaction for more information.
(You may edit your message to recompile.)
Alright
I guess I’m just bad at arithmetic
happens
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Given the following equation system:
- y = x^2 - 5x
- y = 2x - 10
Find the intersection point of the line with the parable and represent it on paper
Just solve x^2 - 5x = 2x - 10
x1 = 2 and x2 = 5
Now find the y values
Now just draw them on a plane
That's it
I'm italian so i translated that way; the teacher wants us to draw the parable too
Actually I dont
I have to find them
ah right for some reason I thought it was factored already
If u mean the interception points with the X axis
Do i keep y = x^2 -5x that way and solve it?
you find where y=0
but yeah vertex first probably
well you can do it either way really
I dont think it comes out right
by setting y = 0 in the parable's equation
The intersection point with the X axis are 5,0 and 0,0
yeah
Ok
then you can just draw the rest by feeling
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Np
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is there any way to solve it without using L-Hopital's rule?
How is L defined?
It's In
So L(x) = lnx?
Yes
factor out -1/2, and you'll have a definition of the derivative
Well $\lim_{x\to{3}}\frac{L(x) - L(3)}{-2x + 6} = -\frac{1}{2}\lim_{x\to{3}}\frac{L(x) - L(3)}{x - 3} = -\frac{1}{2}L'(3)$
half not third
mb
A Lonely Bean
I'm trying to figure out how it get there, especially since I don't know logarithm principles
but tysm
is that I dont know derivatives yet
You don't know what the derivative of ln is?
nope
Eh you can look up a proof that it's 1/x
The thing is that i dont know if I can give a task with tools that I have not yet given in the course
I mean, is there no other way to do it? (no derivatives)
Well you can use that proof to justify why L'(x) = 1/x
@midnight prawn Has your question been resolved?
I can't do that 
Alright without mentioning L'(x)
Just go from limit of (L(x) - L(3))/(x - 3) to 1/3
According to the proof
I don't know how to do it
(L(x) - L(3))/(x - 3) = L(x/3) * 1/(x - 3) = L((x/3)^(1/(x-3)))
From here you can do a substitution, t = 3/(x - 3)
So the limit now is L((1/t + 1)^(t/3))
Which is the same as 1/3 * L((1 + 1/t)^t) as t approaches infinity
Does the limit inside the L look familiar?
I don't understand how you go from multiplying the (1/(x-3)) to passing it as an exponent
Yes, is the limit e, right?
Yes, so the limit is basically 1/3 * L(e)
And L(e) = 1 by definition
So it's just 1/3
Can u explain me that, please?
I see, now i understand, thank u so much!
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If the magnitudes of two vectors are 3 and 4, and the angle between them is 40, determine the magnitude
of their cross product.
use cross product formula 💀
why the skull?
vvell it vvas straightforvvard
magnitude of cross product uses sin
Vector A * Vector B * sin theta
this is the magnitude of cross product of 2 vectors a and b
thanks!!
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Hello
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in this example, why do the solution steps consist of first consolidating the terms in the numerator and then subtracting the denominator from the top two terms, rather than first subtracting the denominator from the top two terms, and then consolidating them?
There's a power rule that if a power is a negative number, it becomes a fraction
For example, 2^-2 = 1/(2^2)
When you multiply numbers with the same base number (in this case, p), you add the powers
So in reality you can't subtract from both of them individually
I hope that answers your question
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Just to be sure, this solution should have the $\mathscr{A}$ and $\mathscr{B}$ interchanged right?
(Apart from in the parentheses).
CoffeeMan
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@subtle leaf Has your question been resolved?
The measurable functions on B and A, i.e.
$f \in M(\mathscr{B}) \iff \left( \forall X \in \mathscr{B} (\mathbb{R}) \colon f^{-1} (X) \in \mathscr{B} \right)$
where the $\mathscr{B}(\mathbb{R})$ is the borel-sigma algebra.
CoffeeMan
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Wilhelm has $84 of coins in his wallet. There is 4x as many $5 dollar coins as $1 coins. How many of each does Wilhelm have?
JazzBo
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he has only coins and 5 dollar bills right?
we can extract some equations from this info
bills equal 5
coins equal 1
therefore 5b+1c=84
Well, it’s directly translated from Swedish. SEK (Swedish Crowns) whereas he has them in coins
where b and c are the numbers of bills/coins
next we know we have 4 times as many bills as coins
this means
b=4c
we can substitude this into the first equation
So its not 4b = 1c?
we can test this
lets assume we have 1 bill
4 times 1 equals 4
so we would have 4 coins
which is the opposite of what we want
The amount of bills is four times the amount of coins
so we have
5b+1c=84
b=4c
setting b to 4c in the first equation we get
20c+1c=84
the rest should be easy
Ok thanks
Wait
What is the answer I’m getting?
4 can’t be the bill nor the $1 coin
20c+1c=84
21c=84
c=4
remember that c is the amount of coins
so we have 4 coins
b=4c=16
Sorry, I’m really bad at math. But how do I get this to the answer
Can you solve it so I can watch an example
Please
what exactly are you stuck on?
Getting b=4c=16 in to the total amount of each coin
we know c=4 right?
Yeah
ok
Oh wait
we know we have 4 times as many bills as coins
So I multiply both sides
so b=4c
Till it’s 84
^^
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Can someone help me?
How would I simplify this?
Ok so you’d want to distribute the exponent
Oh ok...How do I do that?
So you’d apply it to each term to get
$2^3x^3y^{2^3}$
Oh
Bot troubles 
;o
Gama
What would the outcome be?
So what’s 2^3
Yep and now
y 8?
So we know we have
8x^3y^2*3
When we have an exponent to an exponent you multiple then
Umbraleviathan
My bad 
My last question I need help on is this:
Sorry I was taking my dog out how do I multiply the problem?
Do I multiply the exponents to the number?
<@&286206848099549185>
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help
<@&286206848099549185>
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is sine or cosine better?
imo sine is a bit more curvy
but sin(x) = x close to 0
Engineer moment
🙂
Cosine obv cause it’s just sine + more 
its like asking whos better, pilot or copilot
clearly the pilot
hence the copilot is a co-pilot
Copilots don’t receive enough recognition
They have all the skills of the pilot but don’t get the fame
Therefore cosine is ultimately underestimated
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I’m did something wrong can someone put me on the right direction
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is that right?
here's how it looks in a graph
looks good
so y=1/2x+1.5, is right?
both of the equations are the same so yes they both work
thanks 👍
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i need help on Estimating Integers it's really hard and i have a quiz tomorrow think you can help me out.
Please don't occupy multiple help channels.
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Joe completed a trip of 503 miles in 8 hours. His speed during the day was 4 mph faster than her speed at night. She traveled 368 mi during the day and 135 mi at night. Find her speeds during the day and the night.
I'm not sure how to use the s=d/t equation to make an equation to solve for variable x.
sorry. youre looking at the unfilled in variable box. ignore the equations to the right
Your unknown is the speed at night, call it x, you know the speed at day is x+4
thank you
im gonna solve this out quick and post my result if i could get your input
Let's see what you have
trip of 503 miles in 8 hours : so you can deduce the average speed
368 mi during the day: d for day
135 mi at night: d for night
s= d / t
d= ?
okay so my day speed came out to be 6.3176 and my night speed came out to 2.3176 mph..
that doesnt seem right
Well you can check it
If you do 368 mi with a speed of 6.3176 and 135 with a speed of 2.3176
Does it takes 8 hours to make the trip?
Here's my updated work. And I used the time equations to find the speed
So that wouldn't work cuz it would obviously be equal to 8
WAIT I'm dumb
Again
Why would time be equal to eachother
yeah i meant a plus my b
It's 368 too
not 308
fk
just in case you wrote it 308
What do you find?
Yeah, you can check it it's wrong
how would i check?
hmm
yeah
Not sure what you wrote
the number inside the root was wrong. I used symbolab to assist and started the problem with 308 instead of 368
Ho wait yeah
First, distributing
so 8x^2 - 471x - 540 = 0
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when you factor out 1/2 you would only have 1/x inside I think
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hello I don't know how to solve for most of these problems
the power to 1/3 is odd
so first part first?
Are you familiar with the exponent rules/laws
yes up til fractions and I get lost
like 1/3
the 2nd problem on that list
well pretty much everything except the first one, even if I had some examples of how you would solve those particular problems it would help me figure these out
So you know this law $(a^m)^n = a^{mn}$
Pure
You can apply this for the second q
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hey
i got this but no minus sign
how come the answer has a minus?
du = -sinx dx, from here
ohh
wait how
Derivative of cos is -sin
oh my god
its late
i forgot its deriavtive n not integral
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Looking at a practice exam. What is the curly looking P?
yes
Thank you. Forgot those existed. Going to do a couple practice problems to refresh myself.
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I'm having some issues just understanding a bit of negation exercises.
Like why is b >=?
I understand where the > comes from as you're saying the opposite of a statement.
idk im being silly
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Say you collect all the cards that show a “5” [there should be 10 of them]. Imagine drawing 7 times,
with replacement, from this group of cards; what is the probability that you would will observe:
one set of three matching suits
two sets of two matching suits (that aren’t the same as eachother and not the same as the set of three)
“deck has 10 suits with normal 13 denominations” 130 cards total.
Why are there 10 "5" in a card deck?
I only see 4 "5"
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what is a set?
where are you stuck?
Result:
57.4
How does the second task work? I know how to calculate that you draw a card twice, but how when you want to draw two cards twice?
You have to make a computer programm again for this?
nvm this is also like a programm for this
so is a good coinflip that i get 2 times the same number twice lets see
,w 7 random numbers between 1 and 10
,w 7 random numbers between 1 and 10
like 10 times but no number three times
Result:
22.96
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@scarlet galleon Has your question been resolved?
@scarlet galleon Has your question been resolved?
@scarlet galleon
Can you find a vector lying in the plane?
@proven jay
@scarlet galleon Has your question been resolved?
Express RHS as a matrix-vector multiplication, then u and v are just s-column and t-column in the matrix.
The reason that direction vectors can be found in this way is due to the “geometric meaning” or context of the matrix 🙂
O
thanks!
@humble steppe sorry one thing
so I can always find direction vector like this given 3 parametric equations right
It depends. If what you encountered is linear, “well-behaved” equations, then you can do that.
i see
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Could someone help me make sense of this rational partitioning problem? Might be mistranslating that, but the problem is to rewrite this rational polynomial as the sum of two rational polynomials
On this form, except I don't have enough constants in the rightmost rational
oh

