semi
#help-33
echo pivot
sick needle
semi?
echo pivot
im not a math girlie, ima bio girlie but i am getting the hang of it
echo pivot
im majoring in bio
echo pivot
i want to graduate and then come back and get my astrophysics degree
sick needle
thats nice
echo pivot
yes
sick needle
,w tan (157.3)
echo pivot
so cool
elfin berryBOT
elfin berryBOT
echo pivot
-.418?
sick needle
wait what
echo pivot
thats the result
sick needle
oh oh
echo pivot
sin are you a computer science major
elfin berryBOT
sick needle
sin are you a computer science major
either that or doctor of medicine
still deciding
echo pivot
thats rounded of to -0.42
yeah that makes sense
sick needle
Now convert 157.22 degrees to radians
and you get ur answer
Hoping you know how to do that
:D
echo pivot
🫠
sick needle
Whatd you get?
echo pivot
i did
sick needle
What did u get?
echo pivot
i got 157.22pie/180
sick needle
that is?
sick needle
do that
echo pivot
2.74401
elfin berryBOT
sick needle
:D
sick needle
made me think about dropping trig tbh
i can explain it to you
in detail
because this concept you cant do
with that just sheets
its very easy, but you'd have to take baby steps
there were two unknown concepts for you that you had to do in this which i don;t think you've learned about before
so i have to explain you that
echo pivot
there were two unknown concepts for you that you had to do in this which i don;t...
yeah no i havent
i had it explained to me before but i didnt understand it and didnt want to bother my prof over it
sick needle
i had it explained to me before but i didnt understand it and didnt want to both...
well
if you can hop on vc
ill explain it to you in about
10 mins
maybe
well maybe not 10 but a few
echo pivot
okay
sick needle
js add me up
echo pivot
yeah my friend req are off so im gonna add you
marsh citrusBOT
@echo pivot Has your question been resolved?
white sun
Hi
true parcel
you find the points of intersection of those 2 equations
then find the area by integration(upper func - lower func)
and use points of intersection as the limits of the integration
lime citrus
How do I do this?
marsh citrusBOT
How do I do this?
jovial bear
dyk how to find out area of a sector
lime citrus
dyk how to find out area of a sector
nah
jovial bear
have you seen this formula
true parcel
(angle/360)pir^2
marsh citrusBOT
elfin berryBOT
Nalla Manithan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tribal frigate
,tex x -5 \equiv (mod 7)
elfin berryBOT
Nalla Manithan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
tribal frigate
,tex {\frac {x-2}{5}} = k
whole sleet
I think they meant to type:
x = 2 (mod 5)
x = 5 (mod 7)
@still temple
Chinese Remainder Theorem does apply. Did your class go over that?
Another alternative is that we can search for numbers that satisfy x = 2 (mod 5) until we also find numbers that satisfy x = 5 (mod 7)
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?
marsh citrusBOT
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wind agate
This topic is system of equations in 3 variables and i rlly did try my best to wrapped my head around it, but pls guide me to form the equations 😭
marsh citrusBOT
This topic is system of equations in 3 variables and i rlly did try my best to w...
glass silo
,rotate
elfin berryBOT
glass silo
(only does the last of the pictures it finds)
elfin berryBOT
wind agate
(only does the last of the pictures it finds)
thats the answer, our teacher give us the answers and let us try on our own
glass silo
thats the answer, our teacher give us the answers and let us try on our own
(I was saying that the rotate command rotates the last picture it spots)
wind agate
(I was saying that the rotate command rotates the last picture it spots)
oh okok
marsh citrusBOT
@wind agate Has your question been resolved?
marsh citrusBOT
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frozen pasture
marsh citrusBOT
frozen pasture
the last question pls!!
i understand solutions until the distance ^2 part
something to do with scalar resolute?
frozen pasture
sorry the symbols are not working?
wanton ferry
v.v = |v|^2
frozen pasture
yep
wanton ferry
That hw the got distance^2
frozen pasture
oh ok, but where did the n dot n come from?
wanton ferry
Is this chegg?
frozen pasture
i dont think so
wanton ferry
oh ok, but where did the n dot n come from?
In which part of the solution?
frozen pasture
nevermind i got that, now im just lost on their final step
would it not equal to this?
can you simply remove the square, and call it the magnitude?
frozen pasture
OHH
wanton ferry
Not distance
wanton ferry
What course are you taking
wanton ferry
University level?
frozen pasture
high school
marsh citrusBOT
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wind agate
Someone helpp 😭 the answer i got was math error so pls tell me what i did wrong
sour burrow
Someone helpp 😭 the answer i got was math error so pls tell me what i did wrong
i cant read anything its too low-quality, can you send it in a higher quality?
wind agate
i cant read anything its too low-quality, can you send it in a higher quality?
Dont mind the solution for the second picture cuz ik its wrong or maybe not i also dont know
sour burrow
Ok so you put the 4th eq you wrote into 1
sour burrow
yeah thats where it went down
sour burrow
in my opinion and experience
try to simplify the equation as much as possible before putting it in an equation
wind agate
What did i do wrong again 😭
wind agate
try to simplify the equation as much as possible before putting it in an equatio...
Ohh okok ill take note of it
sour burrow
mistakes happen
dont let it upset you tho
these mistakes are something that can be fixed with more practice
try to write the square or any kind of power smaller than normal and a bit higher
wind agate
I GOT ITT
wind agate
these mistakes are something that can be fixed with more practice
Hope so
wind agate
try to write the square or any kind of power smaller than normal and a bit highe...
Tqq for all the tips and tq sm for guiding me 🫶🏼
sour burrow
You are welcome and good luck on your exam ^^
marsh citrusBOT
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scenic adder
What is the average distance for a random point in a 1×1 square to the boundary in a random direction?
marsh citrusBOT
What is the average distance for a random point in a 1×1 square to the boundary ...
scenic adder
This is the correct answer from the Internet, but I don't understand how E(s) is obtained.
marsh citrusBOT
@scenic adder Has your question been resolved?
tight furnace
My guess would be start by fixing the arbitrary direction, say for example 37 degrees and try to calculate the answer in that case
Then use an integral to find the average over all the possible angles
marsh citrusBOT
@scenic adder Has your question been resolved?
scenic adder
My guess would be start by fixing the arbitrary direction, say for example 37 de...
Hmm... I guessed so too, but why does E(s) look like this?
marsh citrusBOT
@scenic adder Has your question been resolved?
marsh citrusBOT
@scenic adder Has your question been resolved?
marsh citrusBOT
@scenic adder Has your question been resolved?
scenic adder
<@&286206848099549185>
vestal elm
for this graph there is a question: what is the solution of f(x) < 0 and f(x) > 0 and i understand using the vertex (1,-3) which means x = -1,3 but i dont understand how to get to the answer (f(x) = -1<x<3 and f(x) = x<-1, x>3)
marsh citrusBOT
for this graph there is a question: what is the solution of f(x) < 0 and f(x) > ...
cyan parcel
Its pretty easy if u understand how a function works
f(x) returns a value for each input value of x, we then plug this value f(x) to the y axis
So we have a graph on OXY plane
Consider this blue point
Where x = -2
Then whats f(-2) = ?
vestal elm
how does that help me with inequalities?
the < and > confuse me
like i get x = -1,3 but i dont know why -1<x<3
vestal elm
The alligator bites the bigger fish
what about for f(x) > 0
the solution is x<-1, x>3
quasi patrol
Yes
If the alligator chooses to bite f(x)
Aka f(x) is bigger
Then x is less than -1 OR x is bigger than 3
vestal elm
but if f(x) is > 0 how could x be less than -1?
silk haven
can someone explain why the integral of 1/x dx = ln |x|
marsh citrusBOT
can someone explain why the integral of 1/x dx = ln **|**x**|**
silk haven
why absolute value?
proud ice
why absolute value?
Because you must consider integral of 1/x when x is negative
silk haven
Because you must consider integral of 1/x when x is negative
why isnt it undefined when x is negative
according to desmos the definite integral of the func of x -3 to 2 is undefined
proud ice
according to desmos the definite integral of the func of x -3 to 2 is undefined
This is undefined because you are crossing 0, where the integral is not defined
silk haven
This is undefined because you are crossing 0, where the integral is not defined
then why is it 0 when it's -2 to 2
proud ice
It shouldn't be
silk haven
oh
proud ice
That's an erroneous calculation if you're getting that
silk haven
visually it looks right though
why isnt it the def integral from -3 to 2 not equal to the def integral from -3 to -2?
because -2 to 0 and 0 to 2 cancel out
even though they cant be calculated
but why is the absolute value there in the first place
why isnt it just undefined
if integration is inverse derivative, then it should pass the horiziontal line test
proud ice
because -2 to 0 and 0 to 2 cancel out
They do not
silk haven
They do not
?
proud ice
Whatever calculator you are using is probably assuming that you were doing an improper integral, in which case it would cancel out
But for a proper integral, it will always be undefined
proud ice
Yeah it's probably assuming improper integral then
proud ice
but why is the absolute value there in the first place
Now for this question
Because we still need to calculate integral of 1/x for when x is negative
And when $x<0$, you would find $\int \frac{1}{x}=\ln(-x)$
elfin berryBOT
SWR
silk haven
Because we still need to calculate integral of 1/x for when x is negative
why cant it just be undefined
why isnt it just undefined
ln isnt defined for neg numbers
proud ice
why cant it just be undefined
It's not undefined because it is definable
proud ice
ln isnt defined for neg numbers
You are correct. It is not.
silk haven
It's not undefined because it is definable
why is it definable though
proud ice
If x<0, then -x>0, so ln(-x) is defined
silk haven
but the derivative is ln(x) not ln (-x)
proud ice
but the derivative is ln(x) not ln (-x)
Inverse? Wdym?
silk haven
i meant the derivative of ln x = 1/x
we never heard or anything saying ln -x
oh wait i see how
proud ice
we never heard or anything saying ln -x
You can use chain rule
proud ice
Exactly right
silk haven
.close
marsh citrusBOT
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boreal heath
A car slows down from 28m/s to rest in a distance of 88m. What was its acceleration,assumed constant?
marsh citrusBOT
A car slows down from 28m/s to rest in a distance of 88m. What was its accelerat...
marsh citrusBOT
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ebon depot
Determine the point (x,y) on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1$ for which the area of the triangle with the corners $(0,-b), (x,y)$ and $(0,y)$ get the biggest area
marsh citrusBOT
Determine the point (x,y) on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1$ f...
elfin berryBOT
Merineth
ebon depot
I have an idea on what i'm supposed to do
It has something to do with derivatives to find the maxima
However i'm not entirely sure how to proceed
I know that the area of a triangle is $0.5bh$ where the base is the length from $(0,y)$ to $(0,-b)$ and the height is $(0,y)$ to $(x,y)$
elfin berryBOT
Merineth
cobalt sentinel
is the answer in terms of a and b
(the point (x,y))
i got (0.5a*(sqrt3), 0.5b) using lagrange mutlipliers, but i have no clue if i did it right lol
ebon depot
I'm not sure what you mean but afaik i'm supposed to find the point(x,y) which maximizes the area withing the ellipse
cobalt sentinel
yea it makes sense if the answer is in terms of a and b
otherwise it wouldn't vary with ellipse size
are u familiar with lagrange mutlipliers
ebon depot
No i'm not
cobalt sentinel
do you know gradient? $\nabla$
elfin berryBOT
Stephen
ebon depot
Yes
ebon depot
Calc 3
cobalt sentinel
Ok, I understand.
I'm not too sure on how to do the problem otherwise, I always just use L.M. for optimization
ebon depot
Well the Area is defined by the length between the points.
And since i'm given the equation for the ellipse. Couldn't i insert the area of the triangle into the ellipse equation?
Derive it for ciritcal points
cobalt sentinel
yea sure why not
ebon depot
I'm not sure but that'd be my guess
cobalt sentinel
try that and see what u get
ebon depot
<@&286206848099549185>
grizzled needle
<@&286206848099549185>
Everyone died
marsh citrusBOT
@ebon depot Has your question been resolved?
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sour pivot
marsh citrusBOT
sour pivot
why is the lim to 5^- undefined but 5^+ does not?
is this bcs in the LHL if we put 5 in the root it becomes root - 10?
turbid mica
is this bcs in the LHL if we put 5 in the root it becomes root - 10?
the root is negative
since thats not on the domain of real numbers for the root function it is undefined
turbid mica
the - and + sign means approaching from that side
turbid mica
5^- would be from the left, so you would go from -inf to 4.999999999 ... and 5 - 4.999999999 is negative
marsh citrusBOT
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prime junco
what does part b mean?
marsh citrusBOT
what does part b mean?
prime junco
i know the DE is exact but im not sure what its asking by the geometric or physical description of the solution
same here
for 4a I got y = 1/3 sin3x
and the graph is just a regular sin graph
so is the physical decription just that its wavy idk
marsh citrusBOT
@prime junco Has your question been resolved?
marsh citrusBOT
@prime junco Has your question been resolved?
severe pewter
I've seen a few memes about something with d and dx (in relation to integrals i think), but what do they mean? I kinda understand what integrals are, but not what they have to do with d and dx.
marsh citrusBOT
I've seen a few memes about something with d and dx (in relation to integrals i ...
whole sleet
tl;dr it's a notation for "variable we're integrating with respect to".
There's a plethora of vague reasons we write this.
- It kinda looks like Riemann sums!
- It makes u-sub easier
- It cancels with a derivative in the integral
But none of that is like a "mathematical necessity"
main garnet
marsh citrusBOT
devout mauve
cause they want to use it in the next line?
to get whatever somewhere after that?
its not like using f(z_n) >= y is wrong
main garnet
its not like using f(z_n) >= y is wrong
it is when u look at the entire proof tho
cz the proof involves
saying
soemthing >= y and something <= y and therefore it is = to y
however in this case we know f(c) > y but since earlier in the proof we also showed f(c) <= y wouldnt that be wrong
main garnet
cause they want to use it in the next line?
the whole proof if u wanna see
devout mauve
even if f(z_n) > y, that wouldnt translate to the limit
main garnet
why not
devout mauve
for example if z_n = 1/n > 0, then still lim z_n = 0
devout mauve
in general if a_n > b, then still lim a_n >=b only
marsh citrusBOT
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true basin
Need help with b part
marsh citrusBOT
Need help with b part
true basin
The question states: find the moment of area about y-axis for the part of surface generated by the line x=4 (red line)
I'm so confused,
Btw the whole shape is rotating around the x-axis
marsh citrusBOT
@true basin Has your question been resolved?
marsh citrusBOT
@true basin Has your question been resolved?
edgy elk
On this I have to set e^y = y^2-7
and then solve for y
but I have no idea how to do that
marsh citrusBOT
edgy elk
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scenic birch
marsh citrusBOT
scenic birch
The answer is E but I can’t figure out how to get it
upper timber
I see you have the region sketched out already
Imagine rotating it around the y axis
How would you cut it up into circles? What would the radii of the circles be?
upper timber
I think the bound is right but I don’t know
No, precisely because they’re horizontal
So you should integrate with respect to y
scenic birch
And it is disk method right?
still temple
Why did you square y^3?
scenic birch
Cus I was just throwing stuff in my calculator and it would be the value of X
upper timber
Don’t worry about that yet we have bigger problems to fix
If you’re integrating with y your bounds should be from 0 to 2
Then you find the radii in terms of y
scenic birch
Ok
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still temple
marsh citrusBOT
still temple
How do i do this? Is there a trig identity for this?
stoic slate
Use subtitution
To get in the denominator something u must recall
From the derivative of arctan
stoic slate
I said derivative
still temple
o
stoic slate
U know derivative of arctan
still temple
Not off the top of my head
stoic slate
It is 1/(x^2+1)
stoic slate
Ok so use subtitution to get that denominator or something similar
still temple
im stuck
void trail
.
stoic slate
What sub u did
stoic slate
That doesnt make too much sense
still temple
this looks closer to the question
stoic slate
1/4 integral 1/(sqrtu(u+4)) du
still temple
wait so what was u
stoic slate
Ok so if u do that sub
stoic slate
1/4 integral 1/(sqrtu(u+4)) du
U get this
still temple
still temple
stoic slate
U are suppose to know how to do this steps btw
If u cant, you should try easier exercises with subtitutions
Now u need another sub
I tell u the sub and u do it
still temple
ok
marsh citrusBOT
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open dune
A math class consists of 24 engineering majors, 12 science majors, and 6 business majors. 8 of the engineering students, 6 of the science majors, and 3 of the business majors are female.
What is the probability that a student selected at random is a business major given the student is a male?
marsh citrusBOT
A math class consists of 24 engineering majors, 12 science majors, and 6 busines...
knotty frost
Do you know bayes rule?
open dune
was wondering if this is just 6-3/42
open dune
Do you know bayes rule?
no
knotty frost
Can you show your work
Are you just doing # of business majors who are male / number of men
open dune
yes trying to find what the probability that a student selected at random is a business major given the student is a male
knotty frost
Then no ur answer is incorrect sadly
You are doing # of male business majors / total number of students
knotty frost
Do you know how to count the number of total men?
You were able to find the number of male business majors, so try doing that with all the majors
open dune
25 total men
knotty frost
So what should your answer be?
open dune
is it 6/25?
knotty frost
No
Now you’re doing # of man + woman business majors / number of male business majors
open dune
is it because they are asking to find the chance that out of the total men what would be the chance that they would be in business?
.close
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still temple
marsh citrusBOT
still temple
is it correct!
leaden monolith
No idea what I’m looking at
leaden monolith
Yeah you should post the question first lol
still temple
Yeah you should post the question first lol
i summarized it on top of the problem i was solving
lmao
😅 lmao
marsh citrusBOT
@still temple Has your question been resolved?
light sentinel
marsh citrusBOT
leaden monolith
What have you tried
light sentinel
well idrk where to start
i did a similar question earlier but this one is harder
this is the other one i did:
leaden monolith
Well here’s what I’m thinking, if a line intersects a parabola only at 1 point, it’s either a vertical line, or it’s tangent to the parabola
Does that make sense?
light sentinel
yeah the question says tangent
leaden monolith
Right, and if I write my line like y = mx + b
Do you agree that this is a line but not a vertical one?
light sentinel
yeah
leaden monolith
Now if I tell you my line mx + b intersects the parabola x²
How would you find where they intersect?
light sentinel
using discriminant formula?
leaden monolith
(Your answer will be in terms of m and b as they are constants I haven’t given you)
leaden monolith
using discriminant formula?
Not quite, I want to find when are 2 lines intersecting
If a point (r, s) lies on the line y = x²
That means s = r²
If a point (r, s) lies on the line y = mx + b
That means s = mr + b
If this (r, s) point lies on both the curves then surely r² = s = mr + b
light sentinel
ohh i see
leaden monolith
The idea here is that the points of intersection between x² and mx + b will be when x² - mx - b = 0
Ah but this means in general we will have 2 intersections
leaden monolith
Well here’s what I’m thinking, if a line intersects a parabola only at 1 point, ...
Ok but we note from here that we dont want 2 intersections
Rather we want only 1 intersection
Here’s where the discriminant comes in
marsh citrusBOT
@light sentinel Has your question been resolved?
light sentinel
hey ive been trying to figure out how do it even after all he help u gave me i ant figure it out
could u help a bit more pls
leaden monolith
could u help a bit more pls
Alright, so when this equation x² - mx - b = 0 has 1 solution only, our line touches the parabola only at 1 point, aka is tangent to the parabola
We can “force” it to have 1 solution by making the discriminant of x² - mx - b to be = 0
We lastly also need to use the fact that our line y = mx + b has to go through the point (1, -2)
This means whatever m and b we have, it needs to satisfy -2 = m(1) + b
This is what it means for (1, -2) to lie on the line y = mx + b
We have 2 unknowns m and b, and here
leaden monolith
We can “force” it to have 1 solution by making the discriminant of x² - mx - b t...
1
leaden monolith
This means whatever m and b we have, it needs to satisfy -2 = m(1) + b
2
2 equations, so we just need to solve for the solutions here
light sentinel
k ty
marsh citrusBOT
@light sentinel Has your question been resolved?
calm stump
Doing basic calc, my answer to this question is 3x^2 * ex + x^3 * ex. The answer is different according to my lecturers mark scheme, just want to confirm if I am right or wrong and how their answer is right (if it is).
marsh citrusBOT
Doing basic calc, my answer to this question is 3x^2 * ex + x^3 * ex. The answer...
calm stump
heady lark
do you have to darivate it ?
fervent rampart
that's the same thing but factoring out x^2 e^x afterward
calm stump
ah ok
heady lark
an easy way to remeber this formula is left d right d
mark uv as u is left and v is right
heady lark
k
calm stump
.close
marsh citrusBOT
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novel juniper
$\lim_{x\rightarrow0}\frac{\left(\tan\left(x\right)-\sin\left(x\right)\right)}{\sin^3\left(x\right)}$
marsh citrusBOT
$\lim_{x\rightarrow0}\frac{\left(\tan\left(x\right)-\sin\left(x\right)\right)}{\...
elfin berryBOT
ƒ(Why am. I here)=I don't know
calm vortex
you can factor out 1 - cos x
novel juniper
yeah
calm vortex
then you can convert the bottom sin^2 to 1 - cos^2
calm vortex
np
novel juniper
$\lim_{x\rightarrow0}\left(\frac{\left(1^x+2^x+3^x...n^x\right)}{n}\right)^{\frac{a}{x}}$
elfin berryBOT
ƒ(Why am. I here)=I don't know
novel juniper
so here
what series am I looking at
I suspect something factorial
hmm
Let me ignore the 1/x for now
that's just 1 in the bracket
so let the limit be L
$\lim_{x\rightarrow0}\left(\frac{\left(1^x+2^x+3^x...n^x\right)}{n}\right)^{\frac{a}{x}}=L$
elfin berryBOT
ƒ(Why am. I here)=I don't know
novel juniper
$\frac{a}{x}\ln\left(\lim_{x\rightarrow0}\left(\frac{\left(1^x+2^x+3^x...n^x\right)}{n}\right)\left(\right)=\ln\left(L\right)\right)$
elfin berryBOT
ƒ(Why am. I here)=I don't know
novel juniper
hmm
now I l'hopital i I guess
I feel that would turn messy real fast though
$\frac{a\left(\ln\left(2\right)2^x+\ln\left(3\right)3^x........\right)}{\lim_{a\rightarrow\infty}\sum_{a=1}^na^x}$
elfin berryBOT
ƒ(Why am. I here)=I don't know
novel juniper
hmm
still temple
the hell
novel juniper
I know lol
It's a a fun problem though ngl
I think I almost got it
nah, I'm getting an e 
calm vortex
do you have any guess if what it is?
still temple
**ƒ(Why am. I here)=I don't know**
what if you take n common from num?
novel juniper
what if you take n common from num?
why won't this work though
still temple
my brain hurts to go your way
novel juniper
is it $(n!)^\frac{a}{n}$
elfin berryBOT
ƒ(Why am. I here)=I don't know
calm vortex
yea
calm vortex
**ƒ(Why am. I here)=I don't know**
did you take x out of the limit
calm vortex
idk what you did but your expressions are kinda fishy
novel juniper
Let me re-write them
calm vortex
**ƒ(Why am. I here)=I don't know**
in this, the x is outside of the limit
calm vortex
**ƒ(Why am. I here)=I don't know**
and suddenly its a -> infinity not x -> 0
using l'hopital's rule is correct but something weird's going on with your limits
novel juniper
$\left(\lim_{x\rightarrow0}\left(\frac{a}{x}\right)\ln\left(\frac{\left(1^x+2^x+3^x...n^x\right)}{n}\right)\right)$
elfin berryBOT
ƒ(Why am. I here)=misery
novel juniper
Now I apply L'hopital's rule
calm vortex
take the a out, it doesnt matter, and to make it look a bit simpler, write ln(fraction stuff) as ln(1^x + ...) - ln n
novel juniper
$\left(\lim_{x\rightarrow0}\left(a\right)\left(\frac{\left(\ln\left(1\right)1^x+\ln\left(2\right)2^x....\ln\left(n\right)n^x\right)}{\frac{\left(1^x+2^x+3^x....n^x\right)}{n}}\right)\right)$
elfin berryBOT
ƒ(Why am. I here)=misery
novel juniper
this is ln(L)
calm vortex
1/n on the numerator went missing
calm vortex
it should be $\lim_{x\rightarrow0}\left(a\right)\left(\frac{\frac{1}{n}\left(\ln\left(1\right)1^x+\ln\left(2\right)2^x....\ln\left(n\right)n^x\right)}{\frac{\left(1^x+2^x+3^x....n^x\right)}{n}}\right)$
elfin berryBOT
Ham
novel juniper
where did the 1/n in the num come from
calm vortex
it's 1^x+2^x...n^x/n
so when you differentiate that there will still be 1/n multiplying the whole thing
novel juniper
don't get it
the differential of ln(1^x+2^x+3^x...)
is
$\frac{1^x\ln\left(1\right)+2^x\ln\left(2\right)+3^x\ln\left(3\right).....}{1^x+2^x+3^x...n^x}$
right?
elfin berryBOT
ƒ(Why am. I here)=misery
calm vortex
yea
novel juniper
so where did the 1/n come from
$\frac{n\left(1^x\ln\left(1\right)+2^x\ln\left(2\right)+3^x\ln\left(3\right).....\right)}{1^x+2^x+3^x...n^x}$
wait
elfin berryBOT
ƒ(Why am. I here)=misery
novel juniper
it shoudl be this
calm vortex
that sill looks wong
calm vortex
so where did the 1/n come from
you were differentiating ln((1^x+2^x+3^x...)/n) not ln(1^x+2^2+...)
novel juniper
hmm
calm vortex
no
novel juniper
why not
calm vortex
which n
novel juniper
the one in the denominator here
novel juniper
ah, that's $x$ ok
elfin berryBOT
ƒ(Why am. I here)=misery
calm vortex
it's still there in the denominator
calm vortex
then plugging in x = 0 wouldn't cause any issues
calm vortex
np
novel juniper
.close
marsh citrusBOT
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remote drift
can someone help me on this
marsh citrusBOT
can someone help me on this
violet badger
do you have the
eqn
in 1st one
ax^3+bx^2+cx+d=0
-d/a = product of roots
c/a = sum of product of roots taken 2 at a time
c/a divided by -d/a
or c/-d
thats your answer
(of the eqn in 1st answer)
remote drift
do u want the equation?
violet badger
nah
remote drift
it is 2u^3 + 12u^2 + 27u +25
remote drift
-27/25
remote drift
how do u do it in simpler terms
remote drift
more pls 
remote drift
like can u show me on whtieboard or paper
remote drift
maybe on paint
violet badger
im on a laptop
you gotta wait for a while
go read this
and also realise if u subbed x=u+2
a (alpha) = some value of u + 2
if for a the eqn in x = 0
then for a-2 eqn in u =0
remote drift
i thought it would be -1/6 as its a sum
violet badger
no wtf
remote drift
like adding all the terms and i had a new equation
violet badger
nawww
remote drift
could you help me on this other one while we wait
violet badger
i guess
violet badger
hmm wait
you must be getting u*root(u) + 5u + 7
now sqaure that
fully
i think*
gtg
remote drift
ok
marsh citrusBOT
@remote drift Has your question been resolved?
cinder mason
what is the domain of this function
marsh citrusBOT
what is the domain of this function
cinder mason
the answer says (-infinity, -1) U (1, infinity)
but i got (-infinity, -(1/3)) U (1/3, infinity)
late geode
show work/reasoning
cinder mason
late geode
you didn't copy down the expression correctly
fallen spade
x can’t be 0
late geode
you sqrt changed
fallen spade
1 or -1
cinder mason
you sqrt changed
oh thanks!
fallen spade
Yeah you can’t take stuff out of root
marsh citrusBOT
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frail lodge
In general, for proving existence questions of the type "prove that there exists ... with properties/restrictions ...", can I first assume the properties/restrictions, then work backwards to construct the object?
Take for example question b) here. Can I first assume that $U=im \pi$ and $\pi^2-\pi$ to find such a linear transformation $\pi$?
marsh citrusBOT
In general, for proving existence questions of the type "prove that there exists...
elfin berryBOT
Kakaka
frail lodge
marsh citrusBOT
@frail lodge Has your question been resolved?
main mica
There are A and B cities. And we have Two buses when the first one entered B.the second one was 1/5 of the full road away from B. Need to find the first bus speed if he is 20km/h faster then the second
marsh citrusBOT
There are A and B cities. And we have Two buses when the first one entered B.the...
cyan parcel
Pretty easy if u just assign unknown value as a variable
Then try to make the variable cancle themselve out
main mica
what part?
lucid bridge
illustrate point A and B on a line
main mica
ohh
severe dawn
the question itself
lucid bridge
i think your explanation is sufficient, im only asking you to draw so you can understand better
main mica
ok
lucid bridge
after you have drawn, point out how much distance first and second bus have travelled from the starting point
main mica
Something like this?
main mica
ok i need a equation now right?
lucid bridge
if you call the entire path 5x then you wont need to deal with fractions btw
lucid bridge
ok i need a equation now right?
since first bus travelled 1/5 of the path more than the second bus, you can compare their speed actually
you can call first bus' speed whatever you want
i would prefer letting speed of first bus be 5v
in this case, try to find out speed of second bus
lucid bridge
nah
first bus went 5x units while second one went 4x units
first one has speed 5v so what should other have
using the equation x= v.t
they travelled these distances at the same time so they have the same time value
main mica
ok so t is the same
lucid bridge
first one has speed 5v so what should other have
if you know this, you are two steps away from the answer
main mica
4v is the seconds speed?
main mica
firs busses speed
lucid bridge
you know the v value, you also called speed of first bus 5v
lucid bridge
100 what tho
main mica
x=4/5x-20
main mica
100 what tho
km/h
lucid bridge
x=4/5x-20
did you mean to type plus 20 instead of minus?
it seems like you called speed of first bus v here
lucid bridge
it seems like you called speed of first bus v here
then you found speed of second bus as 4v/5
then you get a different value for v
and still solve the equation
lucid bridge
soo 100km/h is the answer
yeah
you can do the question as many times as you want, by setting up your own custom unknown for first bus speed
main mica
Ok got it thank
Btw are you good at pyramid problems i solved one but just need to confirm that my answer is right
severe dawn
send it
main mica
got a pyramid with a equalavent triangle as a base the the cercumscribed circles radius at the base is 20 the side hight is 26 need the volume
Got 2400sqrt3 need to confirm if its right
So first we need the base triangles side
severe dawn
So first we need the base triangles side
can you draw it
main mica
Then we find the inscribed circles radius to set up pyth to find the hight
And then 1/3 *areabase * h
lucid bridge
Got 2400sqrt3 need to confirm if its right
how did you get this?
lucid bridge
2600sqrt3
main mica
Ok take me thro what you did
Step by step
@lucid bridge
What did you get as the base triangles side length ?
marsh citrusBOT
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Available help channel!
real token
Hello
crude mango
break up the log
brittle coral
Hello, do you know all the log rules
real token
Hello, do you know all the log rules
No😭 please tell me by steps
crude mango
$\log x^y=y\log x$
elfin berryBOT
mXd
brittle coral
Then that yeah
marsh citrusBOT
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Available help channel!
severe wing
Needs explanation. I have tried this question by equating the Transpose of the Matrix to it's Inverse, also tried using the fact that the product of the Transpose of the matrix with itself is the Identity Matrix. Can this be done in a concise manner?
marsh citrusBOT
Needs explanation. I have tried this question by equating the Transpose of the M...
copper raven
there's another characterization of orthogonal matrices which will help you reduce the number of equations you're dealing with
what conditions should the columns of an orthogonal matrix satisfy ? @severe wing
marsh citrusBOT
@severe wing Has your question been resolved?
severe wing
there's another characterization of orthogonal matrices which will help you redu...
If we consider the matrix as a rectangular arrangement of column vectors then the dot product between columns have to be zero, and every column must have a norm of 1?
copper raven
If we consider the matrix as a rectangular arrangement of column vectors then th...
if not, then look at what this says about a b c specifically
severe wing
yes, I have solved it now. I got two equations by taking the product of column 3 with other two products and taking the norm of column 3. Then I solved for the quations.
copper raven
alright
severe wing
I'll check whether the solutions yield the orthogonal matrix by. I just checked if the solutions for a, b, and c atisfy the equality A*transpose(A) = I. Surely they satisfy.
marsh citrusBOT
severe wing
if not, then look at what this says about a b c specifically
.reopen
marsh citrusBOT
✅
severe wing
if not, then look at what this says about a b c specifically
Thank You for the help. This is my first time ever using a forum to clarify my doubts.
.close
marsh citrusBOT
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placid gate
hi just now learning how to solve this stuff and im not sure if its correct i was wondering if someone could double check my work,
marsh citrusBOT
hi just now learning how to solve this stuff and im not sure if its correct i wa...
@placid gate Has your question been resolved?
marsh citrusBOT
@placid gate Has your question been resolved?
marsh citrusBOT
@placid gate Has your question been resolved?
half karma
The first three make sense but can someone pls explain why no.4 converges and 5 depends on G(u)? I cant think of an example
marsh citrusBOT
The first three make sense but can someone pls explain why no.4 converges and 5 ...
calm vortex
The first three make sense but can someone pls explain why no.4 converges and 5 ...
number 4 try conjugating
marsh citrusBOT
@half karma Has your question been resolved?
still temple
how many odd whole numbers less than 3000 can be formed using the digits 0 through 5 with repetition?
marsh citrusBOT
how many odd whole numbers less than 3000 can be formed using the digits 0 throu...
still temple
This problem confuses me so much, like what is it even asking
stray fern
it's asking how many odd numbers are there from 1 to 2999 that can be formed with just {0,1,2,3,4,5}
for example 25, or 2543
novel juniper
you are given the numbers 0,1,2,3,4,5
you have to form odd numbers less that 3000 using these digits
stray fern
even digits can be used but it has to be an odd number
true parcel
no, its asking to form odd numbers
not that u have to use odd digits from 0 to 5
for ex 1235 is odd
lilac siren
how many odd whole numbers less than 3000 can be formed using the digits 0 throu...
How many options do you have for the first digit
still temple
2?
lilac siren
0,1,2 => 3
still temple
oh
lilac siren
Consider "00001"