analog trellis
Awesome. π
#help-27
weak cove
thank you, I'll admit I spaced on the fact that I could've went and read a bit of my own textbook lol
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devout snowBOT
How to draw this
craggy prairie
Of g(x)
obsidian harbor
Nono
craggy prairie
How then
obsidian harbor
f(-2), f(2) is dirty
knotty bolt
they are both 4 right
obsidian harbor
because of f(2x)
knotty bolt
so you mean g(-2)?
craggy prairie
obsidian harbor
Yea
craggy prairie
Is thatβs true to do ?
obsidian harbor
Yes
craggy prairie
Okay and how I then subtract them
idle isle
help
devout snowBOT
@idle isle Has your question been resolved?
chilly escarp
unity
dark dawn
blazing edge
need help to do proof that sqrt(1+x) has a limit and i need to find delta for x greater than or equal to 1
devout snowBOT
need help to do proof that sqrt(1+x) has a limit and i need to find delta for x ...
blazing edge
this is what i did but i don't think its right
do i have to do it for both directions?
devout snowBOT
@blazing edge Has your question been resolved?
blazing edge
<@&286206848099549185>
jagged geyser
I want to ask whether you want to prove that sqrt(1+x) has limit AT ALL POINTS x>0, or just x = 0+ (i.e. what's the domain you want to prove?)
i.e.
Prove that there exists limit $\sqrt{x+1}$ at $x = c$, where $c>0$
or
Prove that there exists limit $\sqrt{x+1}$ at $x = 0^+$
woven radishBOT
kelvinchan9786
jagged geyser
@blazing edge (Tag me if you want me to reply. Otherwise I will miss your message even you send the message)
devout snowBOT
@blazing edge Has your question been resolved?
blazing edge
@jagged geyser ive got to show that f(x) has a limit for x -> 0
i need to identify the limit
and find the delta
blazing edge
and then i assume that x<0 and then D=2epsilon?
jagged geyser
Why x<0?
x is always larger than 0 (note that this is a one-sided limit, so 0<x<delta instead of 0<|x-0|<delta)
blazing edge
how come that x is always larger than 0? can i choose -1/2
jagged geyser
Definition of Limit:
Two-sided limit: $\forall \varepsilon >0: \exists \delta >0: 0<|x-c|<\delta \Rightarrow |f(x)-L|<\varepsilon$
One -sided limit: $\forall \varepsilon >0: \exists \delta >0: 0<x-c<\delta \Rightarrow |f(x)-L|<\varepsilon$
The part of $|f(x)-L|<\varepsilon$ must have $0<x-c<\delta$ as assumption.
woven radishBOT
kelvinchan9786
jagged geyser
Could you provide me the remaining steps, to see whether $\delta = 2\varepsilon$?
woven radishBOT
kelvinchan9786
jagged geyser
Yes, I think it is correct.
Actually $\sqrt{1+x} + 1 > 1$, so you can literally set $\delta = \varepsilon$ LOL
woven radishBOT
kelvinchan9786
blazing edge
oh well i think imma do it like this anyways
btw, how this is the first time i have multiplied with the conjugate in this type of assignment, how do you look and think thats what you need to do
jagged geyser
whenever you see sth like $\sqrt{x + a} + b$, you can think of conjugate, since $(a-b)(a+b)=a^2 - b^2$. You can eliminate the sq. root.
woven radishBOT
kelvinchan9786
jagged geyser
not only limit, but other subjects as well
vital shard
devout snowBOT
pastel pasture
Balance torque since the system is in rotational equilibrium
dense jay
you dont need it - the weight of the plank acts at the pivot so it doesnt cause any moments
dense jay
the key point is the pivot is central and the plank is 'uniform' - that means its weight acts at its center
moments = force x perpendicular distance, at the pivot the distance =0 so the moment of the weight of the plank is 0 here
dense jay
i would take them from the center
vital shard
alr ill try it
lofty monolith
how would i express x cubed-3x+2 as a product of three linear factors
red sierra
$x^3-3x+2$
woven radishBOT
jay.
red sierra
that right?
red sierra
@lofty monolith have you heard of the remainder theorem?
lofty monolith
no
red sierra
does this look familiar?
lofty monolith
does this look familiar?
no lol
havent been taught that uh
is that what this question is
red sierra
well, factoring can become easier when you know that
red sierra
havent been taught that uh
do you know the factor theorem?
if we call "a" a root of the equation, then f(a)=0
lofty monolith
ye
red sierra
do you also agree that (x-a) becomes a factor of f(x)?
lofty monolith
do you also agree that (x-a) becomes a factor of f(x)?
yh
red sierra
alright, so now you need to find a root of the equation
lofty monolith
calm
keen nacelle
you need to say how to find the first root?
keen nacelle
isn't that just trial and error?
red sierra
actually there is a rule
it should be a divisor of (constant)/(leading coefficient)
in this case that would be 2
lofty monolith
kk
red sierra
so your choices would be -2, -1, 1, 2
keen nacelle
it should be a divisor of (constant)/(leading coefficient)
so thats 2/1?
the coefficient of x^3 right?
red sierra
mhm
red sierra
did you find a root?
keen nacelle
if the constant was something like 64 would you have to go through all of the factors?
lofty monolith
did you find a root?
x=1?
red sierra
nice
red sierra
if the constant was something like 64 would you have to go through all of the fa...
yep, that's how the factor theorem works
keen nacelle
yep, that's how the factor theorem works
awesome
lofty monolith
tbf i can cheat it and just put in my calc
keen nacelle
then its just polynomial division right>?
lofty monolith
yeeee
lol idk why i asked on this i should know that
lmao
thanks anyway
learnt smth new
keen nacelle
i mean at least we learnt that rule
lofty monolith
ye
red sierra
do you know what to do next tho?
radiant willow
@red sierra plz cme to help 1
red sierra
ugh fine
lofty monolith
Other than expanding Left side what can I do
devout snowBOT
Other than expanding Left side what can I do
woven radishBOT
lofty monolith
Yes
red sierra
i think solving this graphically would be the easiest
lofty monolith
Ooooo
red sierra
sketch the graph cos4t in the domain of -30deg<= <=150deg
lofty monolith
Oh wait
They let 4x-120=200+/-360
Lemme just show
They went straight to it surprisingly
Seems long
red sierra
,w plot y=cos4x and y=cos200Β° from -pi/6 to 5pi/6
woven radishBOT
red sierra
god my brain's not functinoing
lofty monolith
dont worry haha
ill look at their working they do it this way usually so its fine
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gentle mantle
How do i solve this with wolfram
devout snowBOT
How do i solve this with wolfram
@gentle mantle Has your question been resolved?
gentle mantle
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devout snowBOT
β
devout snowBOT
@gentle mantle Has your question been resolved?
slender stone
what does the hint even mean
devout snowBOT
what does the hint even mean
pseudo basin
pick a point outside the circle and draw the two tangents to the circle from it
the segments you get will be the same length
slender stone
ah alright
there are four obvious congruent line segments
i see this is a parallelogram
also a rhombus, because all side lengths are equal
,w 11.1*4
woven radishBOT
feral agate
yes
slender stone
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torpid elbow
what characteristics can i use to sketch the graph of each function?
torpid elbow
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sage mountain
devout snowBOT
sage mountain
how he went from this to this
honest meadow
partical fraction decomp?
let me work it out and not be lazy for once
it looks like partial fraction decomp tho
first long division then with remainder do decomp
scarlet peak
When you have a square in the denominator, you have to have one of the terms be the square, and another be itβs square root
honest meadow
also if possible u factor the denominator like (x^2-1) becomes (x+1)(x-1)
scarlet peak
^^
sage mountain
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devout snowBOT
β
sage mountain
first long division then with remainder do decomp
true but why we do long division then remainder we do Perform partial fraction decomposition is it because Denominator degree < numerator degree ?
lean cape
We have a coin with parameter p β (0, 1), and we flip it n times. Let X denote
the number of heads. For which value of k is the probability P(X = k) maximized?
[Hint 1: Compare P(X = k) and P(X = k + 1).]
[Hint 2: Depending on p, there may be one or two solutions.]
devout snowBOT
We have a coin with parameter p β (0, 1), and we flip it n times. Let X denote
t...
lean cape
hello
just quick question before we start is k the number of heads?
and thanks in advance
first of all we know that P(X=K)=(n choose k) p^k (1-p)^k
and P(X=K)>P(X=k+1)
<@&286206848099549185>
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small raptor
devout snowBOT
https://gyazo.com/dcd8f1aa3b4ba2bdd242be94f90052ea
small raptor
My y axis is on a logarithmic scale
so how would i get the gradient of that line?
ofc the straight part so from x = 0.2 to 0.4
small raptor
or in linear scale
The ideality factor and
the saturation current are extracted from a plot of ln(I) as a function of V . From
the data, fit a linear trendline to the data at voltages between 0.3V < V < 0.4V .
The intercept (V = 0) gives ln(I_S
). The ideality factor is extracted from the gradient
of the trendline, according to a rearranged form of Shockleyβs equation for a diode
under forward bias
SO i have volts across x and current accross y
but idk weather too ln the scale or ln the current
supple knot
yea i don't know what any of that means
figure out what scale you want
you currently plotted log-linear
small raptor
yea i don't know what any of that means
Ok forget that, if i were to get the gradient of that graph between 0.2 and 0.4
And than do something like (y-y1) = m(x-x1) to get an equation
would i ln that or e^x that
for it to fit the actual function
supple knot
you can just transform your y-values first so your data is in linear-linear form
then compute the slopes
small raptor
then compute the slopes
No i cannot the gradient of that line is what i need basically, but i cannot get a gradient of a the normal graph as it is constantly changing
supple knot
No i cannot the gradient of that line is what i need basically, but i cannot ge...
why can't you transform them?
as they change
small raptor
why can't you transform them?
I think im over complicating this
I think im literally just gonna look at that log graph and pick 2 points to find gradient
thanks
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devout snowBOT
devout snowBOT
Available help channel!
indigo zinc
devout snowBOT
lunar harbor
Note that four of the six faces of the rectangular prism aren't included in the surface area of the cylinder
indigo zinc
does that also go for rectangular prism?
lunar harbor
what?
indigo zinc
SA of whole cylinder: (2 x pi x 20^2) + (2 x pi x 20 x 65)
SA of whole rectangular prism: (2 x 14 x 15)
is that so far correct?
lunar harbor
You're only taking the two faces which are shared with the circular faces of the cylinder, as I said earlier.
indigo zinc
wdym
lunar harbor
The four faces whose sides are dashed aren't included in the surface area since they're inside the cylinder...
indigo zinc
are not included in the surface area of what?
lunar harbor
yes...
lunar harbor
looks good to me π
lunar harbor
,w 2 \cdot pi \cdot 20^2 - 2 \cdot \pi \cdot 20 \cdot 65 - 2\cdot 14 \cdot 15
woven radishBOT
lunar harbor
ok def put that in wrong lol
Edit: wrote - not +
,w 2 \cdot pi \cdot 20^2 + 2 \cdot \pi \cdot 20 \cdot 65 - 2\cdot 14 \cdot 15
woven radishBOT
lunar harbor
did you put it in the calculator correctly?
indigo zinc
yh and I ended up with what u got
lunar harbor
π
indigo zinc
14031.4, according to the textbook, that's the correct ans, srry u can't see properly with the thick highlight
indigo zinc
it's alright
I was thinking if we have to subtract the four sides of the rectangular prism, because the cylinder is hollow
lunar harbor
but that would decrease the surface area
indigo zinc
I tried this: 2( pi x 20^2-15x14) + 2(pi x 20 x 65) + 2(15 x 65) +2(14 x 65)
lunar harbor
actually omg
that's a good point
because if you hollow it out
then there's the stuff in the middle
π
,w (2pi)(20^2)+(2pi)(20)(65)-2(14)(15)+2(65)(14)+2(65)(15)
woven radishBOT
lunar harbor
ggs ^_^
lunar harbor
prolly hindered you but nice job lol
devout snowBOT
devout snowBOT
Available help channel!
brazen widget
devout snowBOT
proud nimbus
devout snowBOT
proud nimbus
how is this wrong ?
earnest stirrup
proud nimbus
can you please explain?
proud nimbus
yes which is 1\
proud nimbus
okay
earnest stirrup
devout snowBOT
woven radishBOT
TwisT
devout snowBOT
sinful mountain
$$u_{n+1} = \frac{n}{2(n+1)} u_{n} + \frac{3(n+2)}{2(n+1)}$$
I have to prove it converges.
So i know i have to prove that it has an upper bound and that it's increasing but i have no clue and have spent the past hour trying to figure it out.
woven radishBOT
TwisT
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Available help channel!
quaint citrus
How do I decide which value of phi is correct?
devout snowBOT
How do I decide which value of phi is correct?
quaint citrus
ive posted my work for the other parts as well
im not sure whether its pi/4 or 7pi/4
devout snowBOT
@quaint citrus Has your question been resolved?
lofty nacelle
arccos is a function defined from ]-1,1[ to ]-pi/2,pi/2[
you must have |arccos x|<pi/2 whatever your x is
so here the value 7pi/4 is impossible
devout snowBOT
lofty nacelle
np
devout snowBOT
Available help channel!
jagged coral
How do I explain why the solid volume of revolution formula can be used to find the volume of a vase? And why is the function for the domain of the vase, the radius (r) in the solid volume of revolution formula?
devout snowBOT
How do I explain why the solid volume of revolution formula can be used to find ...
@jagged coral Has your question been resolved?
jagged coral
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valid axle
I need help with this: $\int e^xsinx$
devout snowBOT
I need help with this: $\int e^xsinx$
woven radishBOT
afeAlway
valid axle
I tried doing integral by parts but after using the formula i realised it will keep being similar integrals over and over again
Meaning the integral I get by using the formula isn't any easier to integrate
valid axle
But like 2 times
wdym?
weary pebble
If you derivate sin(x), you'll get a cos(x)
valid axle
yeah
weary pebble
And then if you do it again on the integral of cos(x) exp(x), if you derivate cos you'll end up with a -sin(x)
valid axle
yep
weary pebble
Do it
valid axle
how does that help me
weary pebble
Like you have to integrate by parts 2 times
valid axle
$e^x sinx - e^x cosx - \int -e^x sinx$
weary pebble
In order to make appear the integral you want in the right hand side
woven radishBOT
afeAlway
valid axle
In order to make appear the integral you want in the right hand side
I don't get it
weary pebble
Exactly
And then
This is equal to integral of e(x) sin(x)
So you have 2 integral of e(x) sin(x) = e(x) sin(x)-e(x) cos(x)
So you have the answer
Search on youtube Integral of e^x sinx
valid axle
So you have 2 integral of e(x) sin(x) = e(x) sin(x)-e(x) cos(x)
but this what I get tho $\int e^x sinx = e^x sinx - e^x cosx + \int e^x sinx$
woven radishBOT
afeAlway
weary pebble
This is a video made by The Organic Chemistry Tutor
valid axle
This is a video made by The Organic Chemistry Tutor
link?
weary pebble
So you have a minus of the rhs
pulsar dock
Another way to do this is to notice that no matter how many times you differentiate or integrate e^x or sin(x), you will only have terms involving e^x, cos(x) or sin(x). So your answer must be in the form Ae^x cos(x) + Be^x sin(x). You then differentiate and gather like terms to conclude that the integral is the solution to the system of equations A + B = 0, B - A = 1.
valid axle
So you have a minus of the rhs
nvm i found it
weary pebble
Nice !
Search on internet this is a classic one
There is tons of infos on integration
valid axle
thank you so much tho
weary pebble
Sry if we didn't understood each other i'm not english
hollow edge
can anyone help on part b?
devout snowBOT
can anyone help on part b?
jaunty gazelle
what really is the 1st part of fundamental theorem of calculus? Is it literally just plugging in the values of the bound into the function given?
devout snowBOT
what really is the 1st part of fundamental theorem of calculus? Is it literally ...
jaunty gazelle
I ask this, because I'm sort of confused...how are the answers above correct?
steep brook
what really is the 1st part of fundamental theorem of calculus? Is it literally ...
A definite integral can be expressed into F(a) - F(b) , where a and b is upper bound respectively lower bound and F(x) is a primitive function
In this case f(x) = F(x) - F(5)
Differentiate both side.
You know through simple observation F(5) is a constant
So it results into fβ(x) = Fβ(x)
Not to be confused with that F(x) is the primitive function to f(x)
steep brook
So it results into fβ(x) = Fβ(x)
Fβ(x) is simply 1/(1+t^4) but instead of t, itβs x.
then fβ(11) = Fβ(11) which is just plugging in 11 into the fraction
devout snowBOT
@jaunty gazelle Has your question been resolved?
jaunty gazelle
Fβ(x) is simply 1/(1+t^4) but instead of t, itβs x.
Why?
jaunty gazelle
then fβ(11) = Fβ(11) which is just plugging in 11 into the fraction
Shouldn't that be 0 though?
Isn't the antiderivative of 11 0..
steep brook
Isn't the antiderivative of 11 0..
Iβm quite confused, are you perhaps new to the topic or?
jaunty gazelle
Iβm quite confused, are you perhaps new to the topic or?
Never mind, will just YouTube it.
devout snowBOT
@jaunty gazelle Has your question been resolved?
devout snowBOT
@jaunty gazelle Has your question been resolved?
elder terrace
devout snowBOT
elder terrace
Is this right? I donβt have the answer so Iβm not sure
devout snowBOT
@elder terrace Has your question been resolved?
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@elder terrace Has your question been resolved?
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dusk sand
am i dumb? where did i mess up, trying to solve for c in this piecewise function
dusk sand
,rotate
woven radishBOT
patent salmon
id like to help but whats
is a bit unclear...
patent salmon
heh
woven radishBOT
acoustic vault
you said -4+6=-2
brave vapor
Can someone help with the part b
devout snowBOT
Can someone help with the part b
brave vapor
Here is what I tried
devout snowBOT
@brave vapor Has your question been resolved?
devout snowBOT
@brave vapor Has your question been resolved?
brave vapor
then use what you did in from 2-3 reverse
(Q wedge R) implies S?
acoustic vault
yes
brave vapor
What to do after that?
acoustic vault
i think you just do the same with the left one aswell
devout snowBOT
@brave vapor Has your question been resolved?
brave vapor
<@&286206848099549185>
acoustic vault
What to do after that?
did you do it with the left one aswell
then do (P wedge Q) implies (R wedge Q)
use this
where p=(P wedge Q) and q=(R wedge Q) and r=S
brave vapor
Yes
devout snowBOT
Available help channel!
burnt apex
Find the values of a and b so that the polynomial if x^3+ax^2+bx+6 has (x-2) as a factor and leaves a remainder 3 when divided by (x-3).
devout snowBOT
Find the values of a and b so that the polynomial if x^3+ax^2+bx+6 has (x-2) as ...
burnt apex
See, i got problems like this before
but then there was no remainders
so i could jsut equate them both
whereas here i dont seem to get a definite answer
winter patrol
apply remainder theorem
and factor theorem
then solve a system of equations
burnt apex
apply remainder theorem
and factor theorem
then solve a system of equations
hey hey, hey, im in 9th this is my revision for exams our portion doesnt even have factor theorem in it, remained theorem understood
this is what i got till now
like in other one u just subsitute value of x
and then u equate them both
winter patrol
factor theorem is a special case of remainder theorem where the remainder is 0 ( because there is no remainder when dividing by something that is a factor)
burnt apex
and then u keep taking of the numbers untill only variable is left
burnt apex
factor theorem is a special case of remainder theorem where the remainder is 0 (...
so what u are asking me to do is the same thing?
substiute x
wait a minute
14+4a+2b=33+9a+3b-3
14+3-33+4a+2b=9a+3b
17-33=9a+3b-4a-2b
-16=5a-1b
-16-5a=1b
what should i do after this?
@winter patrol
winter patrol
where's all that coming from
you are given two pieces of information, you should get an equation for each one
going to use p(x) to represent your polynomial for convenience
what info/equation can you get from
p(x) has (x-2) as a factor
(apply only this and nothing else)
burnt apex
where's all that coming from
i substiued both x-2 and x-3 in both the cases
and equated them
winter patrol
you shouldn't be doing that
burnt apex
alright wait
winter patrol
read my last message
burnt apex
x^3 + ax^2 + bx + 6
2^3 + a(2^2) + b(2) + 6
8+4a+2b+6
14+4a+2b
4a+2b=0-14
2b=-14-4a
like this?
@winter patrol
winter patrol
yes, but you should've had = 0
starting from the second line
x^3 + ax^2 + bx + 6
2^3 + a(2^2) + b(2) + 6 = 0
8+4a+2b+6 = 0
14+4a+2b ** = 0**
4a+2b=0-14
burnt apex
x^3 + ax^2 + bx + 6
2^3 + a(2^2) + b(2) + 6
8+4a+2b+6
14+4a+2b
4a+2b=0-14
x^3 + ax^2 + bx + 6
3^3+a(3^2)+b(3) +6 = 3
27+9a+3b+6=3
9a+3b=3-33
9a+3b=-30
3b = -30-9a
burnt apex
yes, but you should've had = 0
starting from the second line
yes, ik that, i just did it so that i culd make it simpler
winter patrol
always make the effort to notate things clearly/properly
burnt apex
x^3 + ax^2 + bx + 6
3^3+a(3^2)+b(3) +6 = 3
27+9a+3b+6=3
9a+3b=3-33
9a+3b=-30
3b ...
so now my two equations are
- 3b = -30-9a
- 2b=-14-4a
winter patrol
otherwise it will come across as misunderstanding
burnt apex
otherwise it will come across as misunderstanding
yep, alright
burnt apex
so now my two equations are
1. 3b = -30-9a
2. 2b=-14-4a
now what?
winter patrol
you have a system of equations,
solve via substitution or elimination to determine the values of a,b
burnt apex
you have a system of equations,
solve via substitution or elimination to determi...
what?
so like this?
5b = -30-14-9a-4a
5b = -44-13a
winter patrol
also you didn't manipulate your equation properly
burnt apex
also you didn't manipulate your equation properly
ok. big words confuse me
what should i do?
winter patrol
27+6 isn't 36
3^3+a(3^2)+b(3) +6 = 3
27+9a+3b+6=3
9a+3b=3-36```
what's with the -36 on the rightchanged it
so these are the correct two equations
- 3b = -30-9a
- 2b=-14-4a
should i add them both to do this
5b = -30-14-9a-4a
5b = -44-13a
winter patrol
not much point in adding like that if you aren't eliminating a variable
burnt apex
not much point in adding like that if you aren't eliminating a variable
exacctly, so what should i do?
winter patrol
have you ever solved via elimination before?
winter patrol
look upsolving systems of equations by elimination
here the simplest approach would be to first simplify each equation individually
note that all terms in each equation have a common factor
burnt apex
1b = -30+14-9a+4a
1b = -16-5a
like this?
can u give me the solution for it and then explain me in brief? i cannot really understand what you're saying me to do here
- 3b = -30-9a
- 2b=-14-4a
2b= -30 -9a -1b
2b = -14-4a
-30 -9a -1b = -14-4a
-16 = -4a+1b+9A
-16=5a+1b
-16-b = 5a
something like this ? @winter patrol
winter patrol
no
burnt apex
ok can u give me the solutiona nd explain whaty u did?
i just want to learn quickly, im wasting too much time on a sinlge question
winter patrol
can you simplify only this equation
3b = -30-9a
winter patrol
note that all terms in each equation have a common factor
this does not require you to know anything about the values of a,b
winter patrol
can you simplify -9a/3?
winter patrol
apply the same idea to the other equation
burnt apex
2b = = -14-4a
b = (-14-4a)/2
b = -7-2a
winter patrol
yes
you can now do substitution and/or apply the transitive property of equality
or if you wanted to do elimination, you can subtract the equations
restive river
hey
hybrid snow
You could think of it as the direction of greatest initial increase
So it could have 3, etc
hybrid snow
Oh yeah
It's pretty important
The derivative of a function is defined as the gradient dotted with the tangent vector
Gradients are also used to determine function behavior
restive river
it's just the partial derivatives of the function ?
restive river
a big deal of nothing basicallly ?
hybrid snow
Once you learn path integrals they'll become a life saver lol
restive river
.close
half sundial
In the coordinate system, a triangle is drawn. A new triangle that is congruent with the first one must be drawn into the coordinate system. It has its longest side between the points (-1,-4) and
(-1.8). What coordinates can the third corner have? Enter all possible solutions. The already drawn triangel have the points (2,-1), (8,-1) and (7,2)
devout snowBOT
In the coordinate system, a triangle is drawn. A new triangle that is congruent ...
half sundial
<@&286206848099549185>
restive river
hello : )
i think this problem has something to do with the distance formula?
since the already drawn triangle's sides are given, you can have the sss criterion of congruency and have one solution fulfilled : D
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quasi storm
yo
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@half sundial Has your question been resolved?
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@half sundial Has your question been resolved?
tame sage
If 5 persons can do 5 jobs in 5 days then 50 persons can do 50 jobs in how many days?
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If 5 persons can do 5 jobs in 5 days then 50 persons can do 50 jobs in how many ...
tame sage
I don't really have questions on this problem but what topic does these kinds of problems fall under?
hushed wraith
Direct and inverse proportions ig?
frank cape
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frank cape
<@&286206848099549185>
magic walrus
Okay, so the median is the one directly in the middle. And the two quartiles are the ones in the middle of each half
So you're right, the median is Ghost (1990) with 217.6 million
there are 12 entries higher than it, so the first quartile would be the one in the middle of that. Right between 6th and 7th
frank cape
there are 12 entries higher than it, so the first quartile would be the one in t...
that makes sense, but i'm still confused about how to answer the question
magic walrus
if you take the two quartiles, and you find the number halfway between them, the average
then do you get the median
frank cape
if you take the two quartiles, and you find the number halfway between them, the...
nope
but idk how to explain that/the principle behind it
magic walrus
i would just write like, what the quartiles are, and their average, and note that it isn't equal to the median
wait it gives the quartiles. i can read i promise
visual urchin
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visual urchin
I have found that 1. Is C
Off of calculations
And 2 is (3024,1612,5681)
How would I find 3.
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visual urchin
<@&286206848099549185>
umbral crag
I'm stuck on the question 'Determine the matrix of the reflection in the plane with normal vector n = (1, -2, 1)'. Further context is that there are three vectors (1,0,0) (0,1,0) and (0,0,1). I haven't tried anything because I can't comprehend the question. Is there someone that could please help me out with this?
devout snowBOT
I'm stuck on the question 'Determine the matrix of the reflection in the plane w...
pseudo basin
are you familiar at all with the concept of matrix of a linear transformation?
umbral crag
are you familiar at all with the concept of *matrix of a linear transformation*?
only barely
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lavish plank
hey guys I have a bit of an issue with this question. I can't quite begin. I am greek so the I don't know how you guys would say Ξ³Ξ½Ξ·ΟΞΉΟΟ Ξ±ΟΞΎΞΏΟ ΟΞ± so I am using google translate. I have prove that f(x) will always be (constantly going up for any x?)
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hey guys I have a bit of an issue with this question. I can't quite begin. I am ...
lavish plank
<@&286206848099549185>
supple knot
hey guys I have a bit of an issue with this question. I can't quite begin. I am ...
Do you know derivatives?
The part "constantly going up for any x" is equivalent to derivative being positive
proud abyss
Prove that f'(x)>0
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lavish plank
Prove that f'(x)>0
ok and what method do I use? ΞΞΞ€
Average value theorem says google translate that is ΞΞΞ€
mean value theorem
that is what ΞΞΞ€ is
lavish plank
Prove that f'(x)>0
ok that is is easy this is always true. I proved that
supple knot
mean value theorem
Start by reading the mean value theorem and understanding it
lavish plank
Start by reading the mean value theorem and understanding it
did that. I understand what is the necessary information I need for me to use it
and I believe everything here is true for this to happen
supple knot
and I believe everything here is true for this to happen
State all the parts of the theorem and the interval
lavish plank
State all the parts of the theorem and the interval
I am so sorry but what is interval?
I have to go to school. I may open the ticket lat
*later
!close
.close
devout snowBOT
supple knot
I am so sorry but what is interval?
[a, b]
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Available help channel!
dusk sand
used quadratic equation to try to find (x,y) for f(x) of tangent line =6.
my end answer was incorrect, but would like to know where did i messed up
dusk sand
you can ignore everything at the top. my x values are corrent
but not my y-values (middle of page downward)
just focus on this part:
,rotate
woven radishBOT
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.close
north mirage
can someone help me with this
devout snowBOT
can someone help me with this
velvet rapids
stark sinew
!claim
pseudo basin
you claim a channel by posting your question in it, for future reference
though this works too ig. but don't delete that !claim now
stark sinew
pseudo basin
what an angle.
stark sinew
...
pseudo basin
okay, so to write out your problem in a more readable manner
woven radishBOT
Ann
pseudo basin
@stark sinew is this your problem?
stark sinew
yep
pseudo basin
okay, and what is troubling you?
stark sinew
the calculation has been a week since the teacher explains this, he forgets everything
pseudo basin
do you know how to multiply numbers in scientific notation?
stark sinew
no...
pseudo basin
failing that, do you know your exponent laws? or index laws, or whatever you call it where you're from
stark sinew
failing that, do you know your exponent laws? or index laws, or whatever you cal...
I understand it now I'm from Brazil my English is crap
pseudo basin
$10^{24} \cdot 10^8 = ; ?$
woven radishBOT
Ann
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@stark sinew Has your question been resolved?
restive river
hello : )
in the law of exponents, when two numbers with the same base are multiplied, their powers can be added : D
stark sinew
k wait
stark sinew
3.7
stark sinew
3.3? or 3.1
restive river
what do you think?
stark sinew
3.3
restive river
correct β
burnt apex
or if you wanted to do elimination, you can subtract the equations
is the final answer a = -3 and b = -22
stark sinew
.close
green depot
is the final answer a = -3 and b = -22
No
green depot
.open
green depot
is the final answer a = -3 and b = -22
@burnt apex
This right?
Sorry For bad quality .. I am currently at school
burnt apex
Find the values of a and b so that the polynomial if x^3+ax^2+bx+6 has (x-2) as ...
.
this was the question
green depot
Checks this
green depot
so uh a is -3
Yes and b = -1
gritty snow
Help q no 2
burnt apex
x^3+ax^2+bx+6
2^3+-3(2)^2+b(2)+6
8-12+2b+6
2+2b=0
2b=0-2
b=-2/2
?
yep -1
i must have done some calculation mistakes
no wait i wrot3e -2 but then i copied it as -22
my bad
sand portal
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long pasture
!status
devout snowBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
show your work, thanks!
sand portal
show your work, thanks!
((4-1) / 2x4)x(log(4)+log(1)+2(3log(1))
long pasture
you can just take a pic if you don't wanna type it out
hmmm
i think "3 trapezia" means you'll have to split it into 3 such trapezia
and yours just splitting into two?
lemme draw real quick
that is you'll have to calculate all 3 areas, which are red, green and blue
long pasture
so, each height of the trapezia is of
(4-1)/3 = 1 unit
long pasture
i used a different method but its still wrong
oh okay, mind showing? (on a photo perhaps)
sand portal
i put it in a calculator
long pasture
i see
long pasture
well, as you can see, the method i introduced is about adding all the areas of the shapes
is that what you've learnt?
sand portal
yea
long pasture
or did you just learn something like
(b-a)/(2n) ( f(a) + 2f(a+...)....+...f(b))
long pasture
so, each height of the trapezia is of
(4-1)/3 = 1 unit
recall
then
red: (1Γ(log(1)+log(2))/2
all good till here?
sand portal
no...
long pasture
hmmm
sand portal
whats the 1x at the start for
long pasture
1 is the height, 1Γ is one times
sand portal
oh ok
sand portal
all good till here?
then yea
sand portal
yea i get it
long pasture
and finally blue: (1Γ(log(3)+log(4)))/2
then add them all up, it would be
(log(1)+2log(2)+2log(3)+log(4))/2
got it?
sand portal
yea
long pasture
is it correct?
sand portal
it is
long pasture
π
sand portal
so (4-1)/2x3 will be put in the beggining?
and times the (log(start)+log(end)+2(log(between 1 and 4))?
fair zodiac
I couldn't apply the boundary conditions on the equation below
devout snowBOT
I couldn't apply the boundary conditions on the equation below
fair zodiac
I have found the solution u(x,y,z) however when i plugged in the solution this is what i got any ideas on how i should proceed?
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fair zodiac
any ideas?
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fair zodiac
help
fair zodiac
.close
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stone stump
try adding or subtracting something so you can factor the LHS
mellow panther
multiply both sides by (x+y+z)
coral tulip
Use identity
$xΒ²+yΒ²+zΒ²-xy-yz-xz=\frac{1}{2}((x-y)Β²+(y-z)Β²+(z-x)Β²)$
@restive river
woven radishBOT
Anagh
mellow panther
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mellow panther
Anagh already gave you the hint
proof? your question doesn't require a proof
there are not, there's only 2 solutions
assuming my calculations are correct
why do you think there would be infinitely many solutions
ah, a little oversight on my part
I thought we can get unique solution from the 3 equations
more complicated?
The solution you have was exactly what I did, the first page is what I thought
No
why should I? This is already pretty good
I'll be honest with you, I have an exam tomorrow so I have to study for it
and even if I didn't, I don't get payed for this so no reason to exert myself
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dreamy cedar
how do i manipulate the bottom equation
devout snowBOT
how do i manipulate the bottom equation
polar chasm
how do i manipulate the bottom equation
Would you like to use substitution or add/subtract the equations?
dreamy cedar
i would pike to use substitution
polar chasm
Then you need to get a certain variable (Y or X) to one side, and everything else on other side
dreamy cedar
i just want to know how i could manipulate the bottom equation to make x the subject
then i can figure out the rest
polar chasm
First add 5x to both sides
and then subtract 23 from the both sides
and then divide by 5
dreamy cedar
ok thanks
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dense sleet
how do i know what quadrant each answer will be in?
devout snowBOT
how do i know what quadrant each answer will be in?
lunar harbor
how do i know what quadrant each answer will be in?
jade sundial
Hi is there somebody who can help me with a complete induction task?
jade sundial
The task is:
for all n > 2
For n = 2 everything was easy.
But now for n = n + 1 im struggeling
lunar harbor
Note how you need to work with $(5 \cdot 2+8\cdot 3+\cdots +(3n-1) \cdot n)+(3n+2) \cdot (n+1)$
woven radishBOT
Civil Service Pigeon
lunar harbor
Think of how your inductive hypothesis relates to this
jade sundial
Yeah the (3n + 2) * (n + 1) is pretty similar to the main (3n - 1) * n
I think I dont have to factor out the (3n + 2) * (n + 1) or?
lunar harbor
Hint: consider substitution
jade sundial
Ah I have an Idea, give me a mom
How do I get the induction requirement here right?
Im confused
Would the requirement be
(n + 1)Β³ + (n + 1)Β² -2 or / (n + 1)^5 - 2
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@jade sundial Has your question been resolved?
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Available help channel!
limber wraith
How do i factor
devout snowBOT
How do i factor
small raptor
How do i factor
which one are u stuck on
limber wraith
2= (a+b)(a-b)
5 = (a +- b)^2
small raptor
Mhm
limber wraith
which one are u stuck on
1 3 4 6
limber wraith
oh ok
limber wraith
2= (a+b)(a-b)
5 = (a +- b)^2
Is this right?
limber wraith
a^2-2ab+b^2 (a+b) ?