thank you for all the help
#help-33
unborn echo
wind wadi
np
unborn echo
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bright hedge
Hello! I have a problem with a math exercise.
The problem says: "find the existance field of this function"
y = arccos[e^(2sinx-1)] with 0 ≤ x ≤ 2π
bright hedge
the solution is:
[0 ≤ x ≤ π/6 V 5/6π ≤ x ≤ 2π]
I begin putting the existance condition of arccos.
I put:
-1 ≤ e^(2sinx-1) ≤ 1
but I dunno how to proceed
<@&286206848099549185>
marsh citrusBOT
@bright hedge Has your question been resolved?
marsh citrusBOT
@bright hedge Has your question been resolved?
distant peak
I begin putting the existance condition of arccos.
I put:
-1 ≤ e^(2sinx-1) ≤ ...
exp cant be negative and equal to 0, so just say :
exp(2sin(x) -1)<=1
you know how to solve this
bright hedge
okk
so with "exp" you only refer to the exponential.
So I have to write:
2sin(x) - 1 ≤ 1
And then solve it
I try
bright hedge
exp cant be negative and equal to 0, so just say :
exp(2sin(x) -1)<=1
but
there's something else again
it's greater or equal to 1
(2sin(x) -1) ≥ 1
distant peak
so with "exp" you only refer to the exponential.
So I have to write:
2sin(x) ...
whatt ??
what you just wrote is wrong af
exp is not a number, you cant say exp < 1
exp is a function
and what I mean is exp(2sin(x)-1) cant be negative nor equal to 0
you didnt study exponential function ?
bright hedge
exp is not a number, you cant say exp < 1
exp is a function
aaaaaah yes now I understand
in my country we don't write "exp"
so I misunderstood
The "e" is called "natural base", but
f(x) = a^x is "exponential function"
f(x) = e^x is "exponential function with Nepero's e base"
marsh citrusBOT
@bright hedge Has your question been resolved?
noble crescent
Can someone tell me where I went I wrong. I’m supposed to figure out the whether system is inconsistent or dependent if it doesn’t have a single ordered pair.
marsh citrusBOT
Can someone tell me where I went I wrong. I’m supposed to figure out the whether...
noble crescent
I hope it’s neat enough for you to read, I did a lot of erasing 🙃
embarrassing
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pearl zealot
Ayo
pearl zealot
I need help with an eqaution
Because im tired af and braindead rn
2-1/4x²=1/4x² how do i solve for x
Pls help
wind wadi
do you mean (1/4)x^2 or 1/(4x^2)
pearl zealot
What you mena
wind wadi
$\frac{1}{4} x^2$
pearl zealot
Just normal 1/4x²
elfin berryBOT
nvx
wind wadi
or $\frac{1}{4x^2}$
pearl zealot
Yea
elfin berryBOT
nvx
pearl zealot
The first
wind wadi
$2 - \frac{1}{4} x^2 = \frac{1}{4} x^2$
elfin berryBOT
nvx
wind wadi
try bringing the x terms to one side
pearl zealot
How do i do that is the question
wind wadi
by adding
pearl zealot
11th Class maths is exhausting man
wind wadi
add (1/4)x^2 to both sides
pearl zealot
yea then i get?
The left one disappears
and on the right side what do i get?
x²/2?
wind wadi
yes
wind wadi
1/4 + 1/4 = 2/4 = 1/2
wind wadi
same thing with (1/4) x^2 + (1/4) x^2
pearl zealot
and x² +x² is
2x² isnt it
I dont understand where i get the x²/2 from
Why the 2 is under the x² now
Its not like i divide them yk
wind wadi
okay so just by factoring you get
$$\frac{1}{4}x^2 + \frac{1}{4} x^2 = x^2 \qty(\frac{1}{4} + \frac{1}{4}) = x^2 \cdot \frac{1}{2} = \frac{x^2}{2}$$
elfin berryBOT
nvx
pearl zealot
But why does the 1/4 goes behind the x now
wind wadi
wdym
ripe helm
Ohh
pearl zealot
Nvm i see
ripe helm
ik what u mean
pearl zealot
1/2*x² is the same thing as what you have written
wind wadi
yes
ripe helm
Yup
elfin berryBOT
nvx
pearl zealot
Because?
wind wadi
The left one disappears
^
ripe helm
Ur not done
ripe helm
Well you haven’t solved for x yet
It’s still squared
And it’s still being divided by 2
ripe helm
Yes
pearl zealot
Ye
ripe helm
Oh right
pearl zealot
But idk how to call the x with the 2 sticks
bright jay
The x with two sticks?
wind wadi
lmao
ripe helm
Absolute value?
pearl zealot
Idk bro im not from america or britain
lmao
So i had to set them equal
2 eqautions
And now i need to get the point where they cross each other yk
And now i have x
and i just set it in in one of them right=
?
Doenst really matter wich one no?
Yea
marsh citrusBOT
@pearl zealot Has your question been resolved?
lilac siren
Why is the derivative of 1/A, which I'll write as [1/A]' = -[A]' / A² ?
lilac siren
where A is any function
mystic minnow
1/A = (A)^-1
apply power rule and chain rule
lilac siren
1/A = (A)^-1
apply power rule and chain rule
So far I've only seen product rule of two function A*B and I tried to thereby deduct the rule for division of two functions A/B, but it seems I'm failing at this point without looking at further rules
lilac siren
1/A = (A)^-1
apply power rule and chain rule
what would be the power rule in this case?
when seeking [A^-1]'
mystic minnow
[x^n]' = nx^(n-1)
lilac siren
[x^n]' = nx^(n-1)
ah right thought too intricately
although it's any function, does this still apply?
mystic minnow
yes, if you also use chain rule
reef edge
i need help
marsh citrusBOT
i need help
reef edge
(x^k)^-3(x^5)=1/x^13
marsh citrusBOT
@reef edge Has your question been resolved?
marsh citrusBOT
@reef edge Has your question been resolved?
marsh citrusBOT
@reef edge Has your question been resolved?
marsh citrusBOT
@reef edge Has your question been resolved?
remote breach
why does b not include the x
marsh citrusBOT
why does b not include the x
remote breach
like why isnt b (p-2)x
echo bough
usually the form is
ax²+bx+c
if you replace a by 1
b by (p-2) and c by 1
what do you get?
marsh citrusBOT
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rancid lodge
Hi, can the rational number $\frac{1}{4}$ be constructed as a finite sum of $\pm \frac{1}{p_i}$ where every $p_i$ is prime? (The same prime numbers can be used multiple times)
marsh citrusBOT
Hi, can the rational number $\frac{1}{4}$ be constructed as a finite sum of $\pm...
elfin berryBOT
Yuese
rancid lodge
I suspect the answer to be no, but I can't prove this
stoic saddle
the denominator of any sum of such prime unit fractions will be squarefree i think
you are looking at fractions of the form $\sum_{i=1}^{n} \frac{c_i}{p_i}$ where $p_1 < p_2 < \dots < p_n$ are primes and $c_i \in \bZ$
elfin berryBOT
Ann
stoic saddle
the denominator of this fraction will be $p_1p_2 \dots p_n$, not divisible by 4 no matter what
elfin berryBOT
Ann
rancid lodge
the denominator of this fraction will be $p_1p_2 \dots p_n$, not divisible by 4 ...
Ohhhh I see
Thank you!
.close
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paper copper
An experiment that was carried out 100 times resulted in some measured values of a certain quantity. How would you go about presenting the experimental mean value (both result and accuracy, preferably in terms of confidence interval)
marsh citrusBOT
An experiment that was carried out 100 times resulted in some measured values of...
paper copper
Studying scientific writing and came upon a situation like this and I cant wrap my head around what to do
marsh citrusBOT
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marsh citrusBOT
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marsh citrusBOT
@paper copper Has your question been resolved?
marsh citrusBOT
@paper copper Has your question been resolved?
round sparrow
marsh citrusBOT
round sparrow
How does cos^2theta turn to 1 + cos2theta?
high pine
How does cos^2theta turn to 1 + cos2theta?
it's an identity of double cosine
use 2nd form to get yours
and notice that they've divided constant by 2, since 1 + cos2theta = 2cos^2theta
aka 50 becomes 25
ivory laurel
Why is | x |^2 = x•x
marsh citrusBOT
Why is | x |^2 = x•x
marsh citrusBOT
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main idol
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pure vector
What is the difference between a biconditional and an equivalence? I'm not sure of getting the nuance.
marsh citrusBOT
What is the difference between a biconditional and an equivalence? I'm not sure...
hazy lion
theres a cool answer on MSO
pure vector
idk if thats super helpful
To be honest, I do get the equivlaence, it's the biconditional which I'm not 100% sure of gettng. Like does the biconditional say that statemetns have the same truth values?
and if they do,t hen then are equivalent?
hazy lion
idk i dont wanna say now since im wondering if theres some larger thing im missing lol
theres a lot of discussion here https://math.stackexchange.com/questions/2649394/difference-between-biconditional-and-logical-equivalence
which may get more to your question than i could
pure vector
so youre not sure mmmh
hazy lion
im not sure i know enough to get to the root of your question
but i think your question could lead you to something meaningful
so i dont want to give you some nonsense answer
you should seek out people smarter than me 
pure vector
Thanks for the help still though
short wadi
I understand there is an easier way to find determinants, but I have to use this one. My answer is wrong however. Right answer is -28. Where is my mistake?
marsh citrusBOT
I understand there is an easier way to find determinants, but I have to use this...
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lone heart
marsh citrusBOT
lone heart
the answer is supposed to be this
I’m not sure where you get the -2 leading coefficient, and bracket of (x+4) from
—I think I went wrong with factoring the -2x^2 -12x -16 and that messed it all up?
<@&286206848099549185>
grave ginkgo
—I think I went wrong with factoring the -2x^2 -12x -16 and that messed it all u...
maybe you could try to factor out the -2 from this first, and then try factoring the resulting polynomial to make it easier
lone heart
OH
i looked it over sm and never noticed that that helps sm thank youuuuuuuuuuuu
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austere plover
Consider points A(2, −3, 4), B(0, 1, 2), and C(−1, 2, 0). a. Find the area of parallelogram ABCD with adjacent sides AB→ and AC→ . b. Find the area of triangle ABC. c. Find the distance from point B to line AC.
marsh citrusBOT
Consider points A(2, −3, 4), B(0, 1, 2), and C(−1, 2, 0). a. Find the area of pa...
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pure vector
Can somebody help me understand how is a bicondtional different from an equivalece?
marsh citrusBOT
Can somebody help me understand how is a bicondtional different from an equivale...
@pure vector Has your question been resolved?
marsh citrusBOT
@pure vector Has your question been resolved?
marsh citrusBOT
@pure vector Has your question been resolved?
astral pumice
Close your ticket 😠
marsh citrusBOT
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spring briar
hey quick question
marsh citrusBOT
hey quick question
spring briar
strong stag
pq-formula?
spring briar
so on the 5th line he replaced -5x with -8x + 3x. i see how he got the the -8 and 3 through the 2x^2 and -12 but why did he replace the -5x
like what does the -5x have to do with it since it was the only variable not used in getting that answer
still temple
so on the 5th line he replaced -5x with -8x + 3x. i see how he got the the -8 an...
-8x + 3x = -5x
raw ember
marsh citrusBOT
raw ember
Need help with this one
marsh citrusBOT
@raw ember Has your question been resolved?
marsh citrusBOT
@raw ember Has your question been resolved?
still temple
stuck here , thanks
marsh citrusBOT
stuck here , thanks
quaint hill
please don't ping moderators for mathematics help.
after 15 minutes, you can ping helpers as the rules say
dry nest
yes
and it is said the graph continues the same way
so like a line
and for 10 donations, you expect 60
what would you expect for 60 donations by linearity
dry nest
linearity is the property of being linear, so like a line
a line has constant rate of change
still temple
going up by 30 every time? @dry nest
dry nest
so, when number of donations goes from 0 to 10, expected value goes from 0 to 60
so if we increase donations by 10 again, to 20, what would expected value be
still temple
so if we increase donations by 10 again, to 20, what would expected value be
60-120?
dry nest
yea so it goes from 60 to 120
easiest way to think about this is, when donations increase by 1, expected value increases by 6
so, to calculate expected value for 60 donations, what do you think you should do
still temple
so, to calculate expected value for 60 donations, what do you think you should d...
360?
still temple
thanks for the help by asking me questions helps me learn it instead of u doing it for me appriciate it @dry nest
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clear plume
are these two expressions given in absolute value equivalent to eachother? i) I t - 1 I = -10 ii) I t + 10 I = 1. I'm supposed to write an expression where t is exactly 1 unit away from -10
marsh citrusBOT
are these two expressions given in absolute value equivalent to eachother? i) I ...
clear plume
sorry wrote ii) wrong, fixed
lean flame
Let's solve:
|t-1|=-10
t-1=-10 <=> t=-9
Or t-1=10 <=> t=11
|t+10|=1
t+10=1 <=> t=-9
t+10=-1 <=> -11
So no they are not equivalent?
Also for your question (ii) is correct
clear plume
so only the second one shows that t is 1 unit away from -10?
lean flame
Yes
clear plume
oooh because in the first one t is 11, and that's not 1 unit directly from -10?
but when solvin the second one we find that t is -9 and -11, but the first one is wrong cause solvin it makes t -9 and 11
right?
marsh citrusBOT
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ivory finch
can anyone confirm that the formula to know the number of digits of a given number n is
floor(n/(10^k))=0 with k the number of integers ?
marsh citrusBOT
can anyone confirm that the formula to know the number of digits of a given numb...
main idol
how did you come up with that formula
ivory finch
the questions is to basically make a small formula with the floor function to determine the amount of digits of an integer n
if you take a positive integer abcdef
abcdef/10^6 = 0,abcdef
so floor (n) = 0
and i guess -1 for negative integers
but like i see many flaws with it
since every number q greater than k also verifies floor(n/10^q)=0 despite not beeing the number of digits
so i guess we have to specify k is the smallest integer to verifie it
elfin berryBOT
riemann
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somber ridge
Is this true or false? I think it's true as it definitely is without transposing, but I'm not sure if it is after the transpose.
marsh citrusBOT
Is this true or false? I think it's true as it definitely is without transposing...
somber ridge
Same worry for this question, I know its true if not transposed, but I can't wrap my head around what happens in the case of a non-square matrix
Just in case its not clear, N() is the null space and R() is the rank
<@&286206848099549185>
Sorry, R() is the range, not the rank
gilded cape
<@&286206848099549185>
you'd probably get an answer in #linear-algebra
somber ridge
ok thx
marsh citrusBOT
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marsh citrusBOT
small raft
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carmine rover
marsh citrusBOT
carmine rover
why does the ln(3) not turn into 0 in the y'
and why do we skip product rule
is he just skipping product rule bc he knows ln(3) is a constant?
obsidian bone
Yes
Since ln(3) is a constant there is only one term with a variable which means you dont need to use the product rule
And as such the ln(3) won't disappear as it is a constant to the variable
carmine rover
got it
carmine rover
And as such the ln(3) won't disappear as it is a constant to the variable
but
if it was 3x-4
the -4 would disappear by the time we reach y'
why did the ln(3) not at least disappear and go on to be cancelled?
obsidian bone
The ln(3) did get cancelled out though?
carmine rover
no yeah i know that but
why did it reach the point of being cancelled
and not turn into a 0 when he reached y'
because from what i recall in derivative rules
constants go to 0?
ln(3) would be a constant here
obsidian bone
Ah okay I just misread your question. Constants dont go to zero if they are attached to a variable. When you derive 5x^2, the 5 doesnt go to 0
carmine rover
ohhhhh
i see it now
now if it was ln(3) + log blah blah
then ln(3) would go to 0
but since here we're multiplying its binded
that makes sense tysm
obsidian bone
Yes exactly and np
marsh citrusBOT
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marsh citrusBOT
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lofty gorge
"a triangular sail is 9m taller than it is wide. The area is 56 square meters. Find the height and base of the sail"
marsh citrusBOT
"a triangular sail is 9m taller than it is wide. The area is 56 square meters. F...
grave ginkgo
"a triangular sail is 9m taller than it is wide. The area is 56 square meters. F...
this is just a system of two equations. you probably know the formula for the area of a triangle is A=1/2(bh). and the problem gives you h=9+b ("[it] is 9m taller than it is wide"). all you have to do is solve that system of equations
lofty gorge
this is just a system of two equations. you probably know the formula for the ar...
like 12x+9y=10
3x-4y=3 ?
grave ginkgo
like 12x+9y=10
3x-4y=3 ?
yeah, you would go about solving this problem the same way you would go about solving that
grave ginkgo
what does t represent?
grave ginkgo
you're probably overthinking it, just plug h=9+b into A=1/2(bh) and solve for b
like so: A=1/2(b)(9+b). and since A=56 you can solve for the only unknown, b
lofty gorge
so solve using quadratic formula? distribute 1/2, multiply both sides... no that can't be right. that's way too much for a triangle
solve for b
thank you for the help
grave ginkgo
yeah no problem :) let me know if you need anything else
long pollen
marsh citrusBOT
long pollen
Is there an easy way to do this?
brisk lagoon
If only it was 512 instead
sour relic
xdd
late geode
have you tried anything?
grave ginkgo
this doesn't work because getting rid of the exponentials means applying log_8 to both sides of the equation, and log(a+b+c) is not the same as log(a)+log(b)+log(c)
grave ginkgo
yup
long pollen
Fuck
grave ginkgo
i mean, if it did work, you would just be left with -4=-4 which doesn't really help you lol
grave ginkgo
let me try my hand at this, give me a moment
late geode
group terms with x and y
do some factorisation
grave ginkgo
yeah, try to make one of the exponentials look the same as another exponential
grave ginkgo
np :3
long pollen
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marsh citrusBOT
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slender comet
Question says to calculate tan v, this is a right triangle. Ill show my math.
slender comet
to use tan I need the adjatent so I used 3^2 + x^2 = sqrt=73^2
which ended up being x^2 = 64 thus x=8
and to get tan v I need to use the inverted since I want the angle, so I divide opposit with adjatent
hidden plaza
Yeah
hidden plaza
What’s the opposite?
slender comet
3 accoring to the image above
hidden plaza
And the adjacent?
slender comet
I got 8
hidden plaza
So 3/8
hidden plaza
You use inverse tan when you want to know the angle
slender comet
well the question does say calculate the tan v, doesnt say angle, I just assumed v= angle in this case
hidden plaza
$\tan v = 3/8 \implies v = \arctan{\frac{3}{8}}$
elfin berryBOT
Pure
slender comet
aaah
hidden plaza
Yes
slender comet
that makes sense, thank you very much sir 😄
hidden plaza
slender comet
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gray shale
$\operatorname {sinh}(x)={\frac {{{\rm {e}}}^{{x}}-{{\rm {e}}}^{{-x}}}2}$
gray shale
$\operatorname {cosh}(x)={\frac {{{\rm {e}}}^{x}+{{\rm {e}}}^{{-x}}}2}$
hushed egret
odd and even parts of the exponential?
solutions to y'' = y?
-isin(ix) and cos(ix)?
still temple
$\sin(x) = \frac{e^{ix} - e^{-ix}}{2i}$
hushed egret
many reasons i guess
elfin berryBOT
rbit ✨
still temple
then you have
gray shale
odd and even parts of the exponential?
odd and even part?
i don't really see
hushed egret
you can write decompose any function into its odd and even parts
still temple
-i*sinh(ix) = sin(x)
elfin berryBOT
gray shale
hum is there a condition that need to satisfy f or it's really any kind of function?
hushed egret
i mean
do you see any condition in that equation
okay i guess f(-x) needs to be defined when f(x) is
but
otherwise no
still temple
i guess some conditions on the domain
hushed egret
still temple
but its an easy task to prove this decomposition
gray shale
ok so ch(x) + sh(x) = e^x?
still temple
yeah
hushed egret
ch and sh 
gray shale
it means cosh and sinh when you're lazy
x)
if i remember a unity hyperbolic or something like that verify the equation x^2 - y^2 = 1
hushed egret
,w isin(ix)
elfin berryBOT
elfin berryBOT
gray shale
if i remember a unity hyperbolic or something like that verify the equation x^2 ...
x is cosh and y sinh right?
elfin berryBOT
gray shale
ok i see easily that it verify this equation but with just the equation x^2 - y^2 = 1
how do you solve that and find x = e^x +.... and the same for y
hushed egret
cosh and sinh arent the only parametrisation which satisfy that
notably you can also choose sec and tan
,w sec^2(x) - tan^2(x)
elfin berryBOT
hushed egret
and also 1/2 (t + t^-1) and 1/2 (t - t^-1)
,w (1/2 (t + t^-1))^2 - (1/2 (t - t^-1))^2
elfin berryBOT
hushed egret
actually you can put any function in place of t
and itll work
sec and tan are just another example of this where you put e^ix instead
limpid matrix
Hello! I'm struggling a bit with solving a simple substitution task. The equation I have to solve is as follows: -4x^2 = -32.84x^2 + 49. What I'm struggling with is factorising the polynomial. I'm able to do it with easy terms but I don't understand how I'm supposed to find the factors of the one I'm left with. I'd appreciate some tips 🙂
marsh citrusBOT
Hello! I'm struggling a bit with solving a simple substitution task. The equatio...
wind wadi
Do you know how to solve quadratics?
you can just use the quadratic formula if you don't want to factor manually
limpid matrix
Could you give me an example? I'm not a native english speaking person so I'm not sure if I'm thinking about the same thing
hidden plaza
Could you give me an example? I'm not a native english speaking person so I'm no...
$x=\frac{-b \pm \sqrt{ b^2 -4ac}}{2a}$
elfin berryBOT
Pure
limpid matrix
$x=\frac{-b \pm \sqrt{ b^2 -4ac}}{2a}$
oh yea I do know that formula, I'm just a bit confused because photomath rewrites the formula to 100s^2 - 196s - 625s + 1225 = 0 and then factorising is easy but I had no idea how to get those numbers
hidden plaza
It’s not easy. I mean most people would be able to see this and immediately think of the factors. Photo maths method is probably harder than the normal one.
With big numbers like this it’s probably better to just plug things into the formula imo
limpid matrix
I see. I didn't really think of using the formula honestly, i'll try it thank you
hidden plaza
limpid matrix
Okay so I tried it with the formula but honstely it still seems unsolvable without a calculator
I'd have to find the square root of a huge number
fleet sierra
marsh citrusBOT
fleet sierra
Is this right? And how should I continue solving this?
The answer should be - 14
high pine
you haven't calculated an angle
I'd say in this case it's easier to just expand brackets
instead of De Moivre's
fleet sierra
I'd say in this case it's easier to just expand brackets
How should i expand the brakets? I know how to raise to a power only when the complex number is in polar form
high pine
How should i expand the brakets? I know how to raise to a power only when the co...
like we usually do it in algebra
look
$$(2-i)^4=((2-i)^2)^2=(4-4i-1)^2=$$
$$=(3-4i)^2=9-24i-16=-7-24i$$
elfin berryBOT
Modus
high pine
Why it's better to expand? I'd say the angle doesn't look good, because it's arctan(-1/2)
in some cases (especially when exponents are higher) we use De Moivre's
fleet sierra
Generally, how can i find the angle in radians when it is in the form of cos(8/sqrt(5)) for example?
high pine
Generally, how can i find the angle in radians when it is in the form of cos(8/s...
angle of z = a + bi is arctan(b/a)
what you did is formula for cos(φ) and sin(φ)
basically cos(φ) = a/|z| and sin(φ) = b/|z|
but it's easier to convert them to the tangent (just use tan = sin/cos)
you should rewrite it as cos(φ) = 2/sqrt(5) and sin(φ) = 1/sqrt(5), what you did is incorrect btw
fleet sierra
I hope im not bothering too much, but how would we do the expression when the nubers are in polar form?
high pine
you mean how do we convert polar form into algebraic?
fleet sierra
Nope. How do we add two numbers in polar form. Or in other words how should I continue my answer
high pine
thing is you should try once again because your solution is wrong so far (angle)
we usually don't add complex numbers in polar form since it's inconvenient (especially if angles aren't same)
De Moivre's formula lets us remove exponents, then we can just calculate trig expression in order to get value of a whole expression
fleet sierra
Thank you 
high pine
here angle is arctan(-1/2)
$$(\sqrt{5})^4 \cdot \Big(\cos \Big(4 \arctan \Big(-\frac{1}{2}\Big)\Big) +i \sin \Big(4 \arctan \Big(-\frac{1}{2}\Big)\Big)\Big)$$
elfin berryBOT
Modus
high pine
it isn't that easy as you can see
marsh citrusBOT
@fleet sierra Has your question been resolved?
upper briar
test
marsh citrusBOT
sage heath
marsh citrusBOT
Available help channel!
still temple
I don’t understand surds or algebra can someone help me
marsh citrusBOT
I don’t understand surds or algebra can someone help me
grave sparrow
what don't you understand
still temple
well I’ve tried to learn surds but it just doesn’t make much sense to me. And algebra I don’t get the -0 numbers and the division there’s more but I don’t know how to explain it
and I’m the uk and I’m starting college next week and I think ill be behind everyone have I haven’t had any form of education in the past 4 year I haven’t even done my exams so I’m behind on most things
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
wind wadi
ur question is?
still temple
can someone help me understand surds and algebra more bc I’m stumped
marsh citrusBOT
@still temple Has your question been resolved?
solid echo
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
brisk lagoon
can someone help me understand surds and algebra more bc I’m stumped
Start learning from Khan Academy
still heart
what is a surds
brisk lagoon
And read your textbooks and practice them
brisk lagoon
what is a surds
roots, etc. iirc
brisk lagoon
can someone help me understand surds and algebra more bc I’m stumped
If you have a specific question about what exactly you are having trouble understanding, then you can ask that here. Otherwise it is better that you learn on your own from the right study materials
brisk lagoon
bro why did they make a new word of that
It doesn't make much sense to me either
But sometimes words catch on
wary bluff
How would one go on about solving this without L'hopital rule?
marsh citrusBOT
How would one go on about solving this without L'hopital rule?
upper briar
hm u can try e^ln everything
sweet pawn
This is the logarithm
marsh citrusBOT
@wary bluff Has your question been resolved?
wary bluff
hm u can try e^ln everything
wym
upper briar
like
upper briar
ye
but
with that ln u can do some splitting etc
just like magic-
kinda like how sometimes u multiply the whole eq by 3
its the same eq but helps u solve it easier
marsh citrusBOT
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Available help channel!
fathom solstice
how can i evaluate the sum $\sum_{k=1}^{n}\left\lfloor \log _{b}k\right\rfloor$
elfin berryBOT
임도현
fathom solstice
i was thinking of using double summation in this case, such as $\sum_{k=1}^{n}\sum_{j=1}^{\log_{b}k}1$
elfin berryBOT
임도현
fathom solstice
but not sure whether its right or not and even if its correct how to evaluate
marsh citrusBOT
@fathom solstice Has your question been resolved?
fathom solstice
<@&286206848099549185>
marsh citrusBOT
@fathom solstice Has your question been resolved?
marsh citrusBOT
@fathom solstice Has your question been resolved?
bitter dawn
I would suggest to decompose your sum using the powers of $b$
elfin berryBOT
black_couscous
bitter dawn
Try to compute the sum for $n = b^{m}$
elfin berryBOT
black_couscous
bitter dawn
The rest will follow
bitter dawn
Okay
$\sum{k=1}^{b^{m}}\left\lfloor \log {b}k\right\rfloor = \sum{k=1}^{m}k(b^{k}-b^{k-1}) $
bitter dawn
Consider $x \longmapsto \underset{k=1}{\overset{b^{m}}{\sum}}x^{k}$, derivate it and evaluate in $b$
elfin berryBOT
black_couscous
bitter dawn
It's a function that you can derivate
fathom solstice
what is derivate?
bitter dawn
Like f'
fathom solstice
oh wait so i have to use calculus for this
bitter dawn
Yes
fathom solstice
but isnt that just $\sum_{k=1}^{b^m} kx^{k-1}$
elfin berryBOT
임도현
fathom solstice
.close
marsh citrusBOT
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Available help channel!
river quartz
marsh citrusBOT
@river quartz Has your question been resolved?
marsh citrusBOT
@river quartz Has your question been resolved?
unborn glade
e^3
Ur welcome
I honestly don't know how you're supposed to realize this but it's easy to solve if you set x = e^y
Aka x = e^lnx but that looks ugly
marsh citrusBOT
@river quartz Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
timber rampart
hello! i have another question to an exercise i got, which is:
Find a counterexample that shows that the following statement does not apply in general:
Let M, M1, M2 be nonempty sets so that.
M1 ⊂ M, M2 ⊂ M, M1 ∩ M2 = ∅
Then also applies
M1 ∪ M2 = M.
Also give an example for which the statement holds. Connect M1, M2 as well as their complements with the help of set operations in such a way that thereby
M is obtained.
It is confusing 'cause the numbers of M1 are also in M or would it have to be M ⊂ M1 so that the statement applies :0
marsh citrusBOT
hello! i have another question to an exercise i got, which is:
Find a counterex...
@timber rampart Has your question been resolved?
marsh citrusBOT
@timber rampart Has your question been resolved?
timber rampart
.close
marble kiln
how many 6 digits numbers are there which contains three 2s and two 5s?
still temple
leading zeros allowed?
marble kiln
nope
still temple
have you tried calculating all the ways you can distribute the 2s on the 6 spots and then multiply that by the ways you can distribute the 5s on the remaining 3 spots?
marble kiln
yeah but i dont get the right answer
still temple
have you got 60 ways? and then times 8 for the remaining digits and then minus the ways having a leading digit
still temple
also is it exactly that many digits or at least?
marble kiln
in the question is says contains three 2s and two 5s
so i guess it is exactly
did u get the same answer?
still temple
yes i got 470
quick quiver
The final answer supposed to be R but I don’t know why and this is what i got
still temple
marsh citrusBOT
still temple
ohh
still temple
You start from the inside.
so 5^(5^1/2) is the second log?
crystal wraith
uh what?
still temple
im a bit idiotic
crystal wraith
$\log_2{(\log_5{5^{\frac{1}{2}}})}$
elfin berryBOT
What the hell am I doing here?
raven olive
Is texit fixed?
crystal wraith
Did you not see how I just used it?
still temple
$\log_5{5^{\frac{1}{2}}} = 5^{5^{\frac{1}{5}}}$
elfin berryBOT
InfiniteAxis
crystal wraith
What no, that's wrong.
still temple
What no, that's wrong.
no the latex
i did the syntax correctly
im surprised about that
crystal wraith
But does that matter if you're doing the math wrong?
crystal wraith
About that, well done.
still temple
But does that matter if you're doing the math wrong?
where am i going wrong?
elfin berryBOT
What the hell am I doing here?
still temple
3125
still temple
crap
crystal wraith
Does that make sense?
elfin berryBOT
What the hell am I doing here?
crystal wraith
yeah that.
still temple
ohhh okay
crystal wraith
Now about your problem, can you simplify it?
still temple
so that second log is 5^x = 5^1/2
or fifth
i forget
wait no its half
so x = 1/2
?
and then 2^x = 1/2
still temple
so its $\log_2{\frac{1}{2}}$
elfin berryBOT
InfiniteAxis
still temple
which equals -1
fallen galleon
still temple
yeeeee
still temple
i got another question
a^2 + b^2 - c^2 + 2ab
how do i simplify this
im thinking is (a + b)^2 + c^2
and thats the most i can do
but idk
nvm
i got it
marsh citrusBOT
Available help channel!
cinder dust
I need some help with a physics problem regarding forces on ramps, sorry if it's a shitty diagram but I am trying to get the acceleration of the force parallel to the ramp, if the mass is being pushed by a horizontal force. I think i have the x component of the horizontal force relative to the ramp, but in trying to get the backwards force from gravity i have to get a different angle than theta, and in the problem i'm doing, I can only define the acceleration in terms of F, m, theta, and g, nothing else
marsh citrusBOT
I need some help with a physics problem regarding forces on ramps, sorry if it's...
cinder dust
I don't know how else I would get the acceleration, if i even got the right equation to this.
marsh citrusBOT
@cinder dust Has your question been resolved?
still temple
I'm self learning Gradients and Directional Derivatives
marsh citrusBOT
I'm self learning Gradients and Directional Derivatives
still temple
Did I choose the right answer here?
I firstly calculated the gradient of f(x,y,z), which is:
So I choose answer A, but I'm not sure which criteria to use to choose the point
lost apex
You want f_y, the rate of change with respect to y. That's the jhat component of the gradient
marsh citrusBOT
@still temple Has your question been resolved?
still temple
but how do I choose a point so that the j^ component decreases
lost apex
You want a point where f_y<0
still temple
oh
lost apex
Yeah, because f_y is a derivative. You're looking for a point where f is decreasing as you move in the +y direction
loud eagle
Hey can someone help me with this problem? I am 100% lost LOL
I found the circumference of 785 and I know that 150 feet around is .191 of the circle but I don't know where to go from there.
marsh citrusBOT
Hey can someone help me with this problem? I am 100% lost LOL
I found the circu...
elfin ivy
Could I see the diagram you drew of the situation?
elfin ivy
Mark on the circle for me the point where Drew boarded the Ferris wheel and the approximate point where she has traveled 150 feet around
loud eagle
elfin ivy
Alright, are you able to figure out the angle those two points make with the center of the circle?
Said another way, can you figure out the angle that Drew has traveled around the circle?
loud eagle
19.1%
elfin ivy
She's traveled 19.1% of the way around the circle, yes, but what angle does that correspond to?
loud eagle
68.76 degrees
elfin ivy
Draw that angle on your diagram
loud eagle
elfin ivy
Alright nice, how well do you know your trig?
loud eagle
not well at all im just starting
i think i use sin somehow because what im looking for is on the y axis but that's all i know
idk what to input
elfin ivy
Okay, first I'm going to need you to draw the horizontal line segment connecting the point where Drew stopped to the radius on the left.
loud eagle
is that not the line where the angle is
elfin ivy
Yes
the sides of that angle are radii because they go from the center of the circle to its circumference
elfin ivy
We're going to draw a right triangle
loud eagle
ok so where do i draw the line
elfin ivy
Like this
elfin ivy
The stop is where Drew is located
We want to find her height off the ground
Can you find a segment on the diagram whose length is her height off the ground?
If not, draw one in
elfin ivy
Cool. Are there any other segments in the diagram with the same length as the one you just drew?
loud eagle
yes the connecting line that we made the triangle with
elfin ivy
Why is that?
loud eagle
im not entirely sure but something to do with symmetry im guessing
ohh wait no it's because of the radii they both are radii of a different circle
elfin ivy
Here's the problem with that: You don't actually know if the endpoints of those segments belong to a single circle
So that reasoning isn't actually valid
Let me draw a diagram for you
loud eagle
ok
elfin ivy
For the moment, let's ignore the segment you just drew. (We will draw it back in in a moment.)
Instead, let's first draw the line that represents the ground.
loud eagle
ok
elfin ivy
Notice that the ground is perpendicular to the radius in the middle of the diagram.
That's the line from the ON point to the center of the circle
loud eagle
yes
elfin ivy
To find the segment you just drew, we drop a perpendicular from the STOP point to the ground
loud eagle
alrihgt
elfin ivy
okay it's not letting me post the image for some reason
loud eagle
yes you posted it 4 times now LMAO
loud eagle
hahaha
elfin ivy
okay let me go delete those
gotta love buggy internet connection
Anyway
You see that red right angle?
loud eagle
yes
elfin ivy
That means the angle right next to it is also a right angle:
And thus the figure with the blue angles is...
loud eagle
a rectangle
loud eagle
yes
elfin ivy
So that connecting line you drew to make the right triangle might not actually be the height of Drew. But the segment on the left is.
elfin ivy
Alright, now using your trig knowledge, your task is to find the length of that segment
You can't find it directly: You're going to need to do it in a few steps.
loud eagle
alright
elfin ivy
To figure out how, first tell me: Which segments can you find the lengths of?
loud eagle
all of the lines touching the radius and the border all equal 125
but that's all i know right now
elfin ivy
Is this what you have?
loud eagle
yes
elfin ivy
Okay cool. There are two important things to note here:
(1) The hypotenuse of the right triangle is 125 ft since it is also a radius of the circle.
(2) The height of Drew plus some uknown segment on the left is equal to 125 ft.
Real quick -- You're not colorblind, are you?
loud eagle
nope
elfin ivy
Okay cool I'm going to mark that segment in green
loud eagle
okay
elfin ivy
Here's the million dollar question: Can you figure out how to find the length of the green segment?
loud eagle
if i knew the length with the blue segment connected to the triangle i think i could
but i don't know how without it
elfin ivy
Well then, can you find the length of the blue segment connected to the triangle? :P
loud eagle
no i dont know how
elfin ivy
Okay let me focus on just the right triangle for now
Do you know how to find the length of the hypotenuse?
loud eagle
yes it is 125 because of the radius length
rose heart
one of ur angle values is wrong
elfin ivy
Just noticed, sorry about that
rose heart
a 61 21 90 triangle isnt posisble
loud eagle
oh wait i know how
125cos69
elfin ivy
Yup! If you remember SOH CAH TOA, then cos(69 deg) = Adjacent / Hypotenuse = Green segment / 125
So Green segment = 125 cos 69deg
loud eagle
ok that is 44.79
which means that now we just do 125-44.79?
and then that should be the answer yes
elfin ivy
Bingo
You should get something like 79.71 feet if you use all of the digits for the angle
loud eagle
ah i see
alright so for the second part of them problem im just going to be using negative sin/cos to find the reverse yeah?
elfin ivy
There will probably be some form of inverse sine/cosine involved, yes
Show me your diagram first
loud eagle
loud eagle
yes
so am i trying to find the angle of the triangle
because i think from there i can find how far around he is easily but i dont know how to find it
elfin ivy
Do you know what the hypotenuse of the right triangle is?
loud eagle
yes 125
elfin ivy
Then apply SOH CAH TOA
oh wait hold on
Okay now I see the problem
Good news: You are give the height, so you can figure out the length of one of the segments of the triangle
elfin ivy
Which angle is 0?
loud eagle
theta my bad
elfin ivy
Like this?
loud eagle
yes
elfin ivy
No i mean theta or 0 or whatever symbol, I just want to make sure we're talking about the same angle ;)
loud eagle
LOL yeha
elfin ivy
Okay so remember how sin(theta) is actually Opposite / Hypotenuse?
You've got Adjacent / Hypotenuse in the diagram
loud eagle
oh ye so it's actually cos
elfin ivy
Yeah, ya gotta be careful about that
Okay, so cos(theta) = 93.1/125
Then theta is arccos(93.1/125), right
elfin ivy
So the angle that Matteo traveled through is...?
loud eagle
138.142?
loud eagle
301.22 i think