#help-17
frank forum
ohhhhh
so you can figure out the length of C and B through pythagorean theorem now
(in terms of x)
frank forum
what do you mean
rain hollow
can you write the equations
frank forum
the formula for pythagorean theorem is $a^2 + b^2 = c^2$
twin meteorBOT
Xerunox
frank forum
therefore $C = \sqrt{8^2 + (5x)^2} = \sqrt{25x^2 + 64}$
twin meteorBOT
Xerunox
frank forum
work with that for now
rain hollow
what do i do with this??
rain hollow
ok what next
twin meteorBOT
Xerunox
rain hollow
yes now what
frank forum
which you can factor out a factor of 5 to get $5\sqrt{x^2 + 4}$
twin meteorBOT
Xerunox
rain hollow
now what?
rain hollow
yea ok thanck anyways
frank forum
np
rain hollow
can you help me with another problem that is not geometry
frank forum
sure
rain hollow
ok so in a club there are 320 seats and there are rows after they added 4 seats to each row and added 1 more row there was 420 seats in the club i need to find how many rows are in the club now
frank forum
$xn = 320\(x+1)(n+1) = 420$
twin meteorBOT
Xerunox
frank forum
$xn + x + n + 1 = 420$
twin meteorBOT
Xerunox
frank forum
$xn + x + n = 419$
twin meteorBOT
Xerunox
frank forum
$xn = 320 \therefore x + n = 419 - 320 = 99$
twin meteorBOT
Xerunox
rain hollow
That’s wrong
frank forum
is it?
frank forum
whats the
correct one then
whered i go wrong
ohhh wait yeah ok i see now hold on
$xn = 320 \ (x+4)(n+1) = 420 \ xn + 4n + x + 4 = 420 \ xn + 4n + x = 416 \ xn = 320, \therefore 4n + x = 416 - 320 = 96 \ 4n + x = 96 \ \text{let} m = 4n \ mn = 320\times4 = 1280 \ mx = 1280, m + x = 96$
thats as far as ive gotten
twin meteorBOT
Xerunox
frank forum
then you just solve for something that adds to 96 and multiplies to 1280
which uhhh
you can write as a quadratic
rain hollow
Right answer is 21 rows
frank forum
$y^2 + 96y + 1280 = 0 \ \text{quadratic formula:}\quad y = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$
nevermind you cant do that
oh yep
80 and 16
$4n = 80, x = 16$
twin meteorBOT
Xerunox
frank forum
$n = 20, x = 16$
twin meteorBOT
Xerunox
frank forum
$n + 1 = 21$
twin meteorBOT
Xerunox
frank forum
21 rows
rain hollow
how tho
frank forum
how tho
ill go through it again
$xn = 320 \ (x+4)(n+1) = 420 \ xn + 4n + x + 4 = 420 \ xn + 4n + x = 416 \ xn = 320, \therefore 4n + x = 416 - 320 = 96 \ 4n + x = 96 \ \text{let } m = 4n \ mn = 320\times4 = 1280 \ mx = 1280, m + x = 96 \ \text{turn into a quadratic (no real reason why im using y specifically)} \ y^2 - 96y + 1280 = 0 \ \text{solve using the quadratic formula: } y = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\ \text{returns } y = 80, y = 16 \ \therefore 4n = 80, x = 16 \ n = 20, x = 16 \ n + 1 = 21 \ \text{therefore there are now 21 rows, and 16 seats in each row}$
@rain hollow
rain hollow
and 16 seats in each row?
frank forum
and 16 seats in each row?
yes
twin meteorBOT
Xerunox
rain hollow
no there are 20 cuz of the +4
frank forum
oh yeah right
if you look at line 2 i did that correctly
i just expanded it out, thats why it looks like that
rain hollow
wich grade are you in?
frank forum
wich grade are you in?
11th
rain hollow
good job
vocal sleetBOT
Available help channel!
tepid osprey
vocal sleetBOT
scenic agate
What's going on with the logarithm? I'm not too well versed in logarithms so i'm probably wrong but wouldn't this problem just be basic math?
tepid osprey
anser key says 5.5yrs
yea I tried solving for T and failed so I watched ayoutube video using log but that also failed
hushed pewter
You want to solve, $200,000=150,000\cdot (1.053)^{12t}$, I believe.
tepid osprey
yes
scenic agate
Oh that's what's going on with the logarithm
twin meteorBOT
SWR
tepid osprey
yea
hushed pewter
How'd you get this?
hushed pewter
anser key says 5.5yrs
I got 5.5 months. 
tepid osprey
ok but where did i go wrong
hushed pewter
.053/12+1
Not sure why you are doing this.
Let me make sure I understand your definition of compound interest
tepid osprey
k
hushed pewter
after one month, I will get a 5.3% increase in my investment right? Or is it 5.3% annual interest?
scenic agate
after one month, I will get a 5.3% increase in my investment right? Or is it 5.3...
i'd assume it's 5.3 annual interest
tepid osprey
.053 compunded anually
raven owl
it says compounded monthly?
hushed pewter
,rotate
twin meteorBOT
hushed pewter
,w 1+(0.053/12)
twin meteorBOT
dire lake
hushed pewter
!occupied
vocal sleetBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
hushed pewter
,calc 200/150
twin meteorBOT
Result:
1.3333333333333
yep I got those
hushed pewter
just checking for my own sake
tepid osprey
very good sir
hushed pewter
This here makes no sense
to solve $1.3333...=1.00441666...^{12t}$, you take log of both sides
twin meteorBOT
SWR
hushed pewter
$\log(1.333...)=\log(1.00441666...^{12t})$
twin meteorBOT
SWR
tepid osprey
im lost what exactly is "log" and how does that get me 5.5 years
hushed pewter
an hs that me 5.5 years
hushed pewter
im lost what exactly is "log" and how does that get me 5.5 years
If you don't know what log is, it's gonna be really hard for you to solve these kinds of problems. How are you using log in your solution if you don't know what it is?
In short, log is defined to be a solution to an exponential equation.
tepid osprey
because I found it on a youtube video and on my calculator
so I thought Id give it a go
hushed pewter
Say you wanted to solve $a^x=b$. The solution is defined as a logarithm: $x=\log_{a}b$
twin meteorBOT
SWR
tepid osprey
i guess i need to look up a wuick youtuube video in logarithms because the whol X=LOGa b makes no sense
I get it is rewritten in log form
but im not sure what that is
ok
soooo one sec here I have a basic understanding of them now
its just raising each answer to a power
so I am at this stage here
so I would log12t?
or just log12 for both sides because what you do to one side you do to the other
@hushed pewter ?
hushed pewter
hushed pewter
In what universe are 1.33333... and 1.0044166... equal to each other?
tepid osprey
2000/150000 is 1.333333333 and 1+.053/23 is 1.004416667
because thats where the ended up on either side of the equal sign
i suppose its
hushed pewter
where did the 12t go?
tepid osprey
1.333333333=1.004416667^12t
thats where I am at I forgot to mark in the 12t
going back and fourth from PC to board
twin meteorBOT
SWR
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
hushed pewter
dammit
tepid osprey
lol ahh computers
hushed pewter
hushed pewter
what class are you in? What grade are you in?
hushed pewter
math..
hushed pewter
If you're learning interest rates, you should have absolutely learned log by now. It's taught in second year algebra courses, usually
tepid osprey
yea they clearly skipped it where I am going, its a distance learning thing
very annoying
im running into this lots and haing to back track each time
hushed pewter
yeah if you come back after a long time, there's a lot of review you need to suffer through
and classes may assume you already know certain things
tepid osprey
yea I am gonna have to pay a tutor to teach me logarithms now, thank you for getting me this far
tardy flint
vocal sleetBOT
hushed pewter
It looks right.
heavy yoke
maybe they want absolute value in the ln(x)?
hushed pewter
Try $\frac{1}{x^2}$ instead of $x^{-2}$ maybe?
twin meteorBOT
SWR
hushed pewter
maybe they want absolute value in the ln(x)?
oh. smart
vocal sleetBOT
hushed pewter
cloud = genius
tardy flint
fr
vocal sleetBOT
Available help channel!
soft wharf
how do i find the inverse of this? i've switched the x and y
vocal sleetBOT
how do i find the inverse of this? i've switched the x and y
heavy yoke
that's a good start. i would next try to get the log by itself
soft wharf
ok thanks ill try that
oh wait so that would just be dividing the y+2 onto both sides right
so then on the left its (x-1)/(y+2)
heavy yoke
no, the (y+2) is the input of the log function
heavy yoke
yes
soft wharf
okay now i have the log4(y+2) by itself
should i put it into exponential form? or is there an easier way to isolate y
heavy yoke
once you have the log by itself, we need to apply the inverse function of log, which is exponentiation
so $a^{\log_a (b)} = b$
twin meteorBOT
cloud
soft wharf
what are the variables in this situation
heavy yoke
a is the base of the log and b is the input of the log
soft wharf
is it not just 4^[(x-1)/-2)] = y+2?
heavy yoke
it is
soft wharf
oh ok! so then just bring -2 both sides then that should be the inverse?
heavy yoke
is it not just 4^[(x-1)/-2)] = y+2?
you can think of that either as "putting into exponential form" or as "taking 4^(both sides)"
soft wharf
ohh i see ok
can i do anything about the fraction exponent or is that it
can i turn it into -sqrt4 with exponent of (x-1) or is that not the same thing
heavy yoke
you can turn it into a square root, but remember that a negative exponent is the same as 1/(something), not negative
soft wharf
hmm ok
i always get confused if its a negative exponent thats a fraction
where does the x-1 go if -2 becomes 1/2
or i mean
wait i think im confusing myself lol
heavy yoke
just apply exponent rules one at a time
soft wharf
ohhh so then it should be (x-1)/4^2
vast shale
You can't do it
T
The inverse function is x(y)
So you need to get x in terms of y
You have that $y=-2log_4(x+2)+1$
twin meteorBOT
Palahoo
vast shale
So, $-2log_4(x+2)=y-1$
twin meteorBOT
Palahoo
soft wharf
yes
vast shale
So, passing -2 to the other side, we get $log_4(x+2)=\frac{y-1}{-2}$
twin meteorBOT
Palahoo
vast shale
So, $x+1=4^{\frac{y-1}{-2}}$
twin meteorBOT
Palahoo
vast shale
$x=4^{\frac{y-1}{-2}}-1$
twin meteorBOT
Palahoo
vast shale
And so, you just need to simplify it
vast shale
$x=4^{\frac{y-1}{-2}}-1$
This is the inverse function. Just simplify it and that's it!
I'll need to get out now
vast shale
So, just call the helpers for any doubts, ok?
soft wharf
ok!
vast shale
Good Luck!
tacit sky
anyone know how to find imaginary roots with python code for root finding method ?
vocal sleetBOT
anyone know how to find imaginary roots with python code for root finding method...
flat whale
Newtons method is possible
tacit sky
so i need to make the output result complex?
vocal sleetBOT
@tacit sky Has your question been resolved?
vocal sleetBOT
@tacit sky Has your question been resolved?
Available help channel!
Available help channel!
cyan crest
good start, what did you get after subbing u = sqrt(x + 1)?
vocal sleetBOT
@supple patrol Has your question been resolved?
supple patrol
@cyan crest
supple patrol
yes
cyan crest
now
we need to deal with that x + 2 part
can you try rearranging u = sqrt(x + 1)
well it takes one step to arrive at u^2 = x + 1
but here comes the magic
if we want to arrive at x + 2
we just have to add 1 on both sides
now u^2 + 1 = x + 2
I think it should be really easy to evaluate the integral from here
supple patrol
then I have intgral of 2/(1+u^2) du
supple patrol
oh lol
cyan crest
you're also missing a factor of 2
so in the end you should end up with 2 * arctan(sqrt(x + 1)) + C
where C is a constant
supple patrol
arctan(u) +c
= 2* arctan (sqrt(x+1)) + C
cyan crest
then I have intgral of 2/(1+u^2) du
this is now good
supple patrol
yes oke but 1 question
supple patrol
why is this the wrong way
supple patrol
ohhh
cyan crest
you can't just go and pretend x is a constant
supple patrol
so when I use substitute method I always have to substitute everything
cyan crest
more specifically, you must either:
- Substitute every remaining old variable with the new variable, or
- Eliminate every remaining old variable via division cancellation, etc
vocal sleetBOT
cyan crest
seriously?
vocal sleetBOT
Available help channel!
frozen moss
hello
frozen moss
how is the limit for this 0]
0
wouldnt the number always be positive even if I enter a big negative number
like -99999999
that squared will be positive and it would just be 1/(whatever number)
edgy gulch
and there you go
frozen moss
so like how do I remember to think about this when I get question similar to this on my test
like I always jump to positive ifinity
because I see negative and then squared
proven garden
remember 1/infinity -> 0 and 1/0 -> infinity
proven garden
square root of negative number is not defined (for real numbers)
frozen moss
but its x --> 0
proven garden
so we can only calculate $\lim_{x\to0^+}\sqrt{x}$
frozen moss
so why is negative numbers accounted for
twin meteorBOT
WhereWolf(ping if needed)
proven garden
yes
hushed pewter
This is kind of a poor question, because in the analysis and topological definitions of limits, the answe should be 0
frozen moss
so why is it negative infinity
hushed pewter
,w plot ln(x)
twin meteorBOT
outer warren
why is this one DNE
should be 0
hushed pewter
I agree. Should be 0
outer warren
^+ isn't needed
if you can only approach 0 from the right, that's the limit that's implied
hushed pewter
@frozen moss how does your class define a limit?
frozen moss
idk man
frozen moss
square root of negative number is not defined (for real numbers)
what bout this
he said it should be DNe
DNE
vocal sleetBOT
@frozen moss Has your question been resolved?
inland hound
vocal sleetBOT
inland hound
Can I do this the same way I do limit definition or is this different
<@&286206848099549185>
paper depot
!15m
vocal sleetBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
paper depot
Can I do this the same way I do limit definition or is this different
yes except you do not take the limit
lapis meteor
3x
inland hound
What happens to the H then
paper depot
What happens to the H then
it just stays as h
inland hound
it just stays as h
Can you wait I wanna do it two
Rama
Rq*
@paper depot check pls?
paper depot
one thing i see immediately is all your sevens are missing their middle stroke
also missing closing parenthesis off the very end
however the final answer $-\frac{3}{(x+h-7)(x-7)}$ seems correct
twin meteorBOT
Ann
inland hound
one thing i see immediately is all your sevens are missing their middle stroke
Wdym middle stroke sorry
paper depot
^
patent nymph
they write 1 as |
paper depot
it also helps people not misread your sevens as ones
vocal sleetBOT
viscid pumice
hollow scaffold
help
hollow scaffold
i need help starting and solive the problem
?
<@&286206848099549185>
<@&286206848099549185> if it helps this is the answer provided by the key
.close
livid horizon
Still need help? Ig I just got it
vocal sleetBOT
Still need help? Ig I just got it
hollow scaffold
Still need help? Ig I just got it
ya
hollow scaffold
mhm
livid horizon
Lets first sketch the graph of the parabola
livid horizon
The depth is said to be 1ft
So this distance would be from origin
hollow scaffold
yeah
livid horizon
Let the vertex be at (-1,0)
Equation of parabola is
y² = 4a(x+1)
Now the distance between the rims is 20
ie the y intercepts
hollow scaffold
yeah
livid horizon
So what point on the y axis does it pass through?
livid horizon
Yes exactly
livid horizon
Equation of parabola is
y² = 4a(x+1)
So just substitute it over here
hollow scaffold
oh yeah
livid horizon
Coz it's y intercept
livid horizon
Ye
hollow scaffold
ohhhh
livid horizon
Ye
hollow scaffold
yo ty bro
livid horizon
Np
livid horizon
Np
cyan shadow
chilly garden
Hello, can someone help get to the next step to the answer of -7 from
chilly garden
6a-6+5
paper depot
!original
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
chilly garden
Prompt: Compositions. Perform the indicated operation. 1) h(a) = 2a + 5 | g(a) = 3a -3 | Find (h of g)(-1)
paper depot
right...
ok
so you have found h(g(a)) as 6a - 6 + 5 (unsimplified)
you want h(g(-1))
according to what you just sent here
paper depot
you have found h(g(a)) as 6a - 6 + 5 (unsimplified)
you want h(g(-1))
do you understand this y/n
chilly garden
yes
paper depot
right
chilly garden
but not a lot
paper depot
first off do you understand that 6a - 6 + 5 can simplify as 6a - 1
just to get that out of the way
chilly garden
yes
paper depot
so then you are facing this problem:
$h(g(a)) = 6a - 1 \ h(g(-1)) = ; ?$
twin meteorBOT
Ann
paper depot
which is simply a "plug and chug" problem
chilly garden
and how from this step does it go to -7?
paper depot
well... to find h(g(-1)) you replace a with -1 in h(g(a)) don't you
chilly garden
oh so
6(-1)-1=-7
I tried it with another problem and it worked thank you @paper depot
.close
bitter copper
Integrate e^(-t^2)-3t
vocal sleetBOT
Integrate e^(-t^2)-3t
paper depot
$\int (e^{-t^2} - 3t) \dd{t}$?
twin meteorBOT
Ann
paper depot
is this your problem?
twin meteorBOT
Joanna Angel
tribal moss
i say
bitter copper
$\int (e^{-t^2} - 3t) \dd{t}$?
-3t is also raised to the power of e
bitter copper
$\int (e^{-t^2-3t}) \ d{t}$
tribal moss
you cant compute it, unless it is an improper integral
twin meteorBOT
Napoleon Brandy
tribal moss
that is related to Gauss- Poisson integral
bitter copper
Yeah I was rly confused when trying to solve it
Okay I’ve probably gone wrong somewhere else
tribal moss
$\int_{-\infty }^{\infty }e^{-t^{2}}dt=\sqrt{\pi}$
twin meteorBOT
Joanna Angel
tribal moss
this , integral is famous
one of the easiests way
is to compute special double integral on all plane
are you suppsoed to prove it too ?
ok, yoru integral, you want to get, you need to transform, suueing vertex form to my integral i wrote
beacsue
later
you need to use the formula i wrote above too
that is allprocess you need to do
eventlayy you re supspoed to prove it as wlel depends on fauclty you study at
look:
$\int_{-\infty }^{\infty }e^{-t^{2}-3t}dt=\int_{-\infty }^{\infty }e^{-\left( t+\frac{3}{2} \right)^{2}+\frac{9}{4}}dt=$
twin meteorBOT
Joanna Angel
tribal moss
i used vertex form of the trinomial
is i tclear?
next you take the constant out, and you use susbtituion fo rthe rest
bitter copper
Hmm okay I see how you’ve transitioned but I’m not sure how that helps, oh right yep okay nvm I’m going to try that now
bitter copper
Thank you
tribal moss
yvw 🙂
bitter copper
I’m not too sure what substitution to make?
Oh wait
Hmm okay
I think I’ve done it wrong or just forgotten some basic maths ngl
Actually it seems good
I’ve ended up with (e^9/4)*root pi
tribal moss
cool )
bitter copper
Okay I check it, it works
tribal moss
your instructor might ask you if you know
bitter copper
I’ve never looked at it like that so that’s a rly nice learning experience
bitter copper
how to prove this value of Gauss-Poisson integral
I’ll look into this but It seems like a very famous integral so I know it exists but not how to exactly prove it
Can you look at all undefined integrals in the region infinity to -infinity?
Like if you have no bounds is it accepted to always do it like that?
tribal moss
yes we can
bitter copper
Ah perfect
tribal moss
only
if integral is convergent
but in such a case is satisfied
the literature is the very rich of proofs of this value
i perosally know 11 ways to prove it
there are ppl who collect them lol
bitter copper
Pfffff that’s amazing
I remember it being mentioned before as the Euler-poison integral
*poisson
But yh thank you so much!
.close
vocal sleetBOT
tribal moss
yvw 🙂
vocal sleetBOT
Available help channel!
vale ermine
If the determinant of 3 points in 3d is zero doesn't that mean they are collinear?
vocal sleetBOT
If the determinant of 3 points in 3d is zero doesn't that mean they are collinea...
vale ermine
If so why (1,0,-1) , (0,-1,1) , (-1,1,0) is a equilateral triangle but the determinant is zero ,
tribal moss
you may verify it manually, if they belong to one line
find euqation of th elien which goes thorugh first two points
and next verify
wheher third point
vale ermine
so the determinant way is wrong?
vale ermine
So all this time i had some wrong concept
The determinant works for only points like (x,y) (y,z) and not for the (x,y,z) can i say it like that?
tribal moss
i write such a formula here:
vale ermine
wheher third point
Yea i was taught that method just got confused why the determinant wasnt working
tribal moss
$\overrightarrow{a}=\left[ x_{1},y_{1},z_{1} \right]\\overrightarrow{b}=\left[ x_{2},y_{2},z_{2} \right]\\overrightarrow{a}=\left[ x_{3},y_{3},z_{3} \right]\\\text{ then: }\\\left( \overrightarrow{a}\times \overrightarrow{b} \right)\circ \overrightarrow{c}=det\begin{bmatrix}
x_{1} & y_{1} &z_{1} \
x_{2}& y_{2} &z_{2} \
x_{3}& y_{3} &z_{3}
\end{bmatrix}=0\Leftrightarrow \text{ }\text{ }\text{ vectors are complanar}$
twin meteorBOT
Joanna Angel
vocal sleetBOT
@vale ermine Has your question been resolved?
wide shale
Equilateral triangle T1 is similar to equilateral triangle T2 on a scale of k = 1/2. The area of triangle T2 is 300 cm² larger than the area of triangle T1. The area of the larger of these triangles is:
vocal sleetBOT
Equilateral triangle T1 is similar to equilateral triangle T2 on a scale of k = ...
wide shale
Can someone fast help please
paper depot
why fast?
astral needle
paper depot
are you in a test rn?
vocal sleetBOT
@wide shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
sharp atlas
vocal sleetBOT
sharp atlas
Need help with this question
wary mantle
Need help with this question
What about it?
wary mantle
Also is this a test
sharp atlas
Yuh
wary mantle
We shouldn't help with cheating on a test...
vocal sleetBOT
@sharp atlas Has your question been resolved?
vocal sleetBOT
@sharp atlas Has your question been resolved?
lean tulip
the problem is 3^x = 18 | 3 to the power of x = 18
im pretty sure you would root each side by x but after that im not sure where to go
lean forge
ln
strange crater
logarithm, not root
lean forge
and if you don't know what a logarithm is you could also study the function
3^x is strictly increasing and positive, and continuous on R, 3^0 is 1 and 3^3 is 27, meaning 3^x=18 has exactly one solution, then you could use different method to approximate it
vast shale
how do i solve this nonlinear diophantine equation:
(x² + 1)(y² + 1) + 2(x - y)(1 - xy) = 4(1 + xy)
vocal sleetBOT
how do i solve this nonlinear diophantine equation:
(x² + 1)(y² + 1) + 2(x - y)(...
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
silk musk
how do i solve this nonlinear diophantine equation:
(x² + 1)(y² + 1) + 2(x - y)(...
Solution in integer?
@vast shale
vocal sleetBOT
desert epoch
hazy trout
is minimum value of a directional derivative still the magnitude of the gradient or -gradient?
vocal sleetBOT
is minimum value of a directional derivative still the magnitude of the gradient...
hazy trout
if this is a confusing question, I'm asking if the directional derivative has a max value of 5 in same direction of gradient vector, then the min value is 5 or -5 in opposite direction?
vast shale
is minimum value of a directional derivative still the magnitude of the gradient...
max is +, min is -
misty belfry
if this is a confusing question, I'm asking if the directional derivative has a ...
yeah they have same magnitude
vast shale
of the magnitude of gradient if that’s what you mean
hazy trout
I'm confuse on whether to put a negative sign in my final answer
This is the question: "Find the maximum and minimum values of the directional
derivative Duf at the origin in the u direction, as u varies and state the directions
along which the max and min occur"
so is it correct to say direction derivative has a min of 5 or -5 in direction opposite of gradient?
I'm thinking since I already accounted for the negative when I specified the direction, but some sources online put negatives on both direction and magnitude
vocal sleetBOT
@hazy trout Has your question been resolved?
molten mesa
Good afternoon!
vocal sleetBOT
Good afternoon!
molten mesa
Implicit derivative
Just want to confirm that is right
No test I'm at home lol
strange crater
at a glance, I don't think so. you need the product rule for a couple of the terms
vocal sleetBOT
@molten mesa Has your question been resolved?
strange crater
yes looks ok
molten mesa
I have one doubt
When I'm applying the product rule
Can you check if the signs are ok at the right side of the =
I was a lil bit confused there
Product rule being applied to (x^3)-5x(y^2) = 3x^2-(5x)(2yy')-(5)(y^2)
The rule says uv'+u'v
But I did u'v-uv'
Cuz the initial thing is a-b
or u-v
a-uv
I dunno if I explained myself correctly lol
vocal sleetBOT
molten mesa
.reopen
vocal sleetBOT
✅
stark epoch
https://i.imgur.com/6O7AmIY.png
I've got no idea where to even start... lmao
vast shale
look at where the function starts and ends
stark epoch
(0, 0) and (12, -3) ?
stark epoch
oh yeah
vast shale
oh nvm, you just have to find the area of the triangle
i thought this was an integration subtractive problem
vast shale
if i say a set A is uncountably infinite then can i say |A| > |N| ? (N is the natural numbers)
vocal sleetBOT
if i say a set A is uncountably infinite then can i say |A| > |N| ? (N is the na...
valid turtle
if i say a set A is uncountably infinite then can i say |A| > |N| ? (N is the na...
Haa bhai ig
vocal sleetBOT
@vast shale Has your question been resolved?
tame brook
if i say a set A is uncountably infinite then can i say |A| > |N| ? (N is the na...
yes
vocal sleetBOT
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Available help channel!
round eagle
vocal sleetBOT
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@round eagle Has your question been resolved?
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@round eagle Has your question been resolved?
halcyon wing
draw a diagram, plz
vocal sleetBOT
@round eagle Has your question been resolved?
hollow zephyr
I'm stuck on a second-order partial derivatives problem. I'm checking my answer with a student from previous semesters with confirmation from their professor, but its seems like there is a difference between my answer and theirs, and I am unsure who is correct.
vocal sleetBOT
I'm stuck on a second-order partial derivatives problem. I'm checking my answer ...
hollow zephyr
This is the question
This is my answer
This is their answer
The difference between both is that I do not have 2dz/dx
Is my answer correct, or theirs, and why?
north sky
vocal sleetBOT
north sky
so i did get C=48i-42j
and to get the direction its tan-1(y/x)
and when i do that
i get 41.1
which is none
so how's the answer is 320
okay forget about the first question
any idea how to solve this?
vocal sleetBOT
@north sky Has your question been resolved?
sonic zinc
any idea how to solve this?
E = 2A-B
Simply put the values
U get E
And then find its magnitude
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pallid ruin
7.3.2 I don't know what to do for this one what does jointly proportional mean
pallid ruin
ok ty
flat whale
a = (constant) * b * c
pallid ruin
a = (constant) * b * c
Foes that mean a is equal to 2?
flat whale
Foes that mean a is equal to 2?
How'd you get this
Get in the habit of always explaining your answer
pallid ruin
Get in the habit of always explaining your answer
Oh srry
does that make any sense?
flat whale
Yea looks right
wet shuttle
Help with these 2 questions please
turbid root
i need help with this question. i know i have to use some sort of double angle identity but im stuck as to where to start
vocal sleetBOT
i need help with this question. i know i have to use some sort of double angle i...
reef hare
vast shale
struggling to wrap my head around this one, why does 7^-36*9^24 = 7^36/9^24?
outer warren
negative exponent law
$$a^{-n} = \frac{1}{a^n}$$
twin meteorBOT
ℝαμΩℕωⅤ
vast shale
I understand negative exponents to some degree, its just this one in particular messing me up
outer warren
apply the law ^ above
vast shale
I can simplify it to 9^-24*7^36 or 9^-24/7^-36 but im just confused by this in particular
outer warren
${\red{a}}^{-\blue{n}} = \frac{1}{{\red{a}}^{\blue{n}}} \ \
{\red{9}}^{-\blue{24}} = \what$
twin meteorBOT
ℝαμΩℕωⅤ
outer warren
you're doing
$$p^n = \frac{1}{p^{-n}}$$
pretty much the same law
vast shale
ohhh okay i think i get it
twin meteorBOT
ℝαμΩℕωⅤ
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
hi
vast shale
this equation represents a parabola only for a = 4
how would i calculate that value aljebrically
livid horizon
For a general 2 degree equation to be a parabola,
h²-ab=0
e=1
livid horizon
There would be
I'm not sure about it
But you could take the equation of a line(say, lx+my+n=0) and a focus (p,q), and for a conic, the ratio of distances from the line to the point(e) is fixed
(It's 1 in case for a parabola)
vast shale
yes i know that
vocal sleetBOT
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oblique gazelle
Does the sum of convergent sequences give a convergent sequence?
paper depot
what do you think
oblique gazelle
what do you think
I think not always
paper depot
do you have a counterexample in mind
oblique gazelle
for example a sequence that converges to 0 and another sequence that converges to 1?
both convergent but the sum will be divergent, yeah?
oblique gazelle
because there are two sub sequences that converge to two different numbers
paper depot
you're talking about sum, not interleave
oblique gazelle
oh I have no idea what interleave is. So what do we mean by sum?
vast shale
if $\p{a_n}{n \in \N}$ and $\p{b_n}{n \in \N}$ are convergent real sequences then [
\lim_{n \to \infty} \p{a_n + b_n} = \p{\lim_{n \to \infty} a_n}+ \p{\lim_{n \to \infty} b_n}
]
paper depot
from two sequences a_n and b_n, you construct their sum by just...
oblique gazelle
I think of it like putting the terms of given sequences next to each other
paper depot
adding each corresponding term together
like
a_1+b_1, a_2+b_2, a_3+b_3, a_4+b_4, ...
oblique gazelle
adding each corresponding term together
ohh that makes more sense
paper depot
thats what addition means
were you thinking of like
a_1, b_1, a_2, b_2, a_3, b_3, ...?
twin meteorBOT
vast shale
you can prove the above theorem
oblique gazelle
a_1, b_1, a_2, b_2, a_3, b_3, ...?
yep
paper depot
yeah, that's interleave.
paper depot
and THEN you need them both converging to the same point for the interleaved seq to converge obviously.
oblique gazelle
is the sum of divergent series always divergent?
paper depot
no
oblique gazelle
yeah makes sense
paper depot
also are you once again sure that you are not confusing sequences vs. series
oblique gazelle
yeah
so we could make up two divergent sequences such that their sum gave a convergent sequence
that is if we added n1, n2, n3 terms to each other :>
paper depot
you could just take a divergent sequence and then itself times -1.
their sum would be 0
vocal sleetBOT
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lyric pewter
Find the limit of the function as (x, y) approaches (0, 0).
the answer is D but i dont understand at all
lyric pewter
so i plug in r^2cos^2(theta)/r^2
and then it cancels out to be cos(cos^2(theta))
which eventually becomes cos(1)
but i dont understand why from that it becomes no limit
white whale
No, you can't just plug a random function for x and y.
To show how this function has no limit, try lim y-> 0 f(0, y) and lim x->0 f(x,0)
They will disagree in value.
lyric pewter
ooooooooooooooooooooh
i mean i dont think the function is random no? for other questions similar i pugged r etc but i think i understand when you separate the limit like that it makes more sense whyd itd be no limit
cyan talon
you're getting cos(cos^2(theta)), that's already suspect, depending from which angle you approach (0,0), you'd get different answers
but yeah it's more obvious if you look explicitly at 2 paths which give you different limits
lyric pewter
ahhh yeah i think i see it way better
when you separate the limits it becomes way more obvious
white whale
You can't just substitute x and y with a function over a new variable r because the multivariable limit requires the value to be same over all such functions, and you can get two different values for different functions, which then results in no limit
vocal sleetBOT
twin meteorBOT
Cabbage
empty frigate
i think doing u = e^x - 1 should work fairly nicely
yep
then for u^5/(u+1) that becomes u^4 - u^3 + u^2 - u + 1 - 1/(u+1) (i think)
it's a little annoying but you only get 5 terms instead of 2^5 terms
vocal sleetBOT
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Available help channel!
swift meteor
x is the month number . y is number of views per month ( on a channel level ) (note y is in terms of 1000000 , i.e y=5478 for
example means 5478000000)
Fit the second degree polynomial/parabola for the collected data i.e. y = ax^2+bx+c using
matrix inversion method set x = {1,2,3,4,5,6,7,8,9,10} set y= {47,39,15,67,47,24,42,32,28,33}
vocal sleetBOT
x is the month number . y is number of views per month ( on a channel level ) (n...
@swift meteor Has your question been resolved?
vocal sleetBOT
@swift meteor Has your question been resolved?
vocal sleetBOT
@swift meteor Has your question been resolved?
teal saffron
vocal sleetBOT
turbid forum
vocal sleetBOT
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Available help channel!
proud crypt
vocal sleetBOT
proud crypt
im not sure what to do now after drawing out the function
vocal sleetBOT
@proud crypt Has your question been resolved?
proud crypt
<@&286206848099549185>
jagged scroll
look at the three intervals. 0 to -1, -1 to -3 and -3 to -infinity.
at these points which function is greater than the other.
proud crypt
ay i didnt ask for this helper
vast remnant
How would I evaluate this limit?
vocal sleetBOT
How would I evaluate this limit?
lucid bane
How would I evaluate this limit?
start by assuming the limit exists, and taking logs of both sides.
vapid wedge
$lim x->0+ \frac{sin(ax)}{x^3+x}$
vocal sleetBOT
$lim x->0+ \frac{sin(ax)}{x^3+x}$
twin meteorBOT
Merineth
twin meteorBOT
Merineth
vapid wedge
How do i determine what a should be
livid horizon
**Merineth**
Is that the right hand limit at x=0?
vapid wedge
no
livid horizon
Oh ok
vapid wedge
$lim x->0^+ \frac{sin(ax)}{x^3+x}$
livid horizon
Anyway so
twin meteorBOT
Merineth
livid horizon
You can rewrite the denominator as x(x²+1) right?
vapid wedge
Yes
vapid wedge
I tried that however
$\frac{sin(ax)}{x(x^2+x)} = \frac{sin(ax)}{x} * \frac{1}{x^2+1}$
twin meteorBOT
Merineth
livid horizon
Lim of sinx/x is 1 as x tends to 0
livid horizon
**Merineth**
Yes but
livid horizon
Lim of sinx/x is 1 as x tends to 0
Note that here the term inside sin and the denominator x have to be the same
So if the term inside sin is ax, the denominator has to be ax too for the limit to be 1
vapid wedge
ooooooh
so the variable in sin(ax) and the denominator has to have the same variable
livid horizon
Yeah
vapid wedge
$\frac{sin(ax)}{x(x^2+x)} = \frac{sin(ax)}{ax} * \frac{1}{x^2+1}$
twin meteorBOT
Merineth
livid horizon
**Merineth**
Multiply a in the numerator too
vapid wedge
why?
livid horizon
Coz to make the denominator same, you should multiply with a no both in numerator and denominator
Or else the fraction will change
For ex
vapid wedge
This is what we are trying to accomplish, right?
livid horizon
$\frac{2}{3}$ is the same as $\frac{22}{32}$ and not $\frac{2}{3*2}$
twin meteorBOT
Lorentz
vapid wedge
Yes, but if we multiply both nominator and denominator with a we'll not get the formula
livid horizon
**Merineth**
Same with here
vapid wedge
This is what we are trying to accomplish, right?
this formula