i get it
#help-38
dry copper
you dont š
wraith hinge
you dont š
if that assumption is right then i get it
if not
then i dont get it š
wraith hinge
this would be dz right ?
so this is right
dry copper
wraith hinge
you didnt represent dz
dry copper
i did
wraith hinge
oh yeah
dry copper
from z0 to z1
dry copper
so this is right
no, it is not right
not anywhere
from z0 to z1 only
like, the end of the segments
you drew it in the middle
little glen
you dont š
this is some gaslighting fr
wraith hinge
i got busted :P
dry copper
lol
dry copper
dz is not perpendicular to z is it
it is
if you ignore dĪø in the expression (cuz its just a number, like 0.001)
then dz = jz
wraith hinge
dot product of z with the relation dz = z1 - z0 isn't giving me 0 ?
dry copper
z rotated counter-clockwise by 90
dry copper
z = a + j b
dz = jz = ja - b
wraith hinge
this would be dz right ?
just dont understand why we have to show it only in the end
cause it effects the magnitude of dz ?
dry copper
the complex number z is a point in the complex plane
so when you change Īø, it gets changed to another point
wraith hinge
oh
dry copper
so dz must connect old point to new point
dry copper
youre looking at them as vectors, too much š
its the complex plane, its the complex world, its the complex realm
dry copper
aaand, its always like this with these differentials
area of circle A = Ļ rĀ²
dA = 2Ļr dr
means that if you change radius of circle by an amount dr
wraith hinge
I won't even try to visualise that
dry copper
area will change by 2Ļr * amount of change in radius
dry copper
I won't even try to visualise that
just grab the concept
Thank you too, nice problem
wraith hinge
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wraith hinge
It's good to visualise it
dry copper
,, z=a+jb = \begin{pmatrix} a \ b \end{pmatrix} \ \ dz = jz , d\theta = j , d\theta (a+jb) = -b , d\theta + j a , d\theta = \begin{pmatrix} -b , d\theta \ a , d\theta \end{pmatrix}
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Milena
wraith hinge
And I get why drheta is scalar
dry copper
do the dot product now
wraith hinge
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ā
wraith hinge
Its like rotating dz 90degrees and then moving it to starting point of z
Z1-Z0 .Z0 would give Z1.Z0
OHHHH
nvm
dry copper
you cant do it like that :p
wraith hinge
Yeah
dry copper
real part * real part + imaginary * imaginary
wraith hinge
I took Z0.Z0 as 0
dry copper
cant let them as z's and multiply
gotta expand to rectangular form
forget z0 and z1
those were just to explain old z and new z
wraith hinge
wraith hinge
dz=z1-z0
Dot product and we get
dz.z= z1.z0 - z0.z0
dry copper
dot product is defined between two vectors
dry copper
buuut, a complx number can be thought of as a vector with coordinates Re(z) and Im(z)
,, z_0 \cdot z_1 = Re(z_0) \cdot Re(z_1) + Im(z_0) \cdot Im(z_1)
solid kilnBOT
Milena
dry copper
dot product, not casual product
cuz z0 is represented as a vector (Re(z0) , Im(z0))
same for z1
hence the result
wraith hinge
I meant it that way
dry copper
okay noice šÆ
wraith hinge
The book said Z= ai+jb, without any harm we can remove the i and write it as a+jb,which makes z still as a vector
Misunderstanding
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dry copper
not remove the i
in this z=a+jb
j is the sqrt of -1
but in this z=ai + jb
i and j are the unit vectors
not the sqrt of -1
dry copper
okay then, good luck and ty!
wraith hinge
Thank you too
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lofty crown
who knows how to multiply rational expressions
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tranquil wave
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kindred pier
Can anyone help me with this
!status
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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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
3
kindred pier
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tranquil wave
2 loga(x) = loga(a) + loga(7x-10a)
2x = a(7x-10a)
(2-7a)x = -10a^2
x = 10a^2/(7a-2)
but the answer said 2a or 5a
wraith hinge
bro
wraith hinge
2x = a(7x-10a)
it's not 2x, it's x^2
wraith hinge
no problem dude
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elfin kite
I don't understand how to take the laplace transformation of (u(t-2)-u(t-4))(t-3).
elfin kite
in step 1-2, I perform a shift on the term (t-3) for the heaviside at c=2 and c=4 by plugging in (t-2) and (t-4) for t into the terms. Is this the correct approach?
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random niche
I suppose the reason why we plug in a and b is because we want to show, that the only way to get the same outputs is to have the same inputs.
for example
$f(x) = 2x + 1 \$
$2a + 1 = 2b + 1 \$
$a = b \$
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Tomi
limpid dawn
I suppose the reason why we plug in `a` and `b` is because we want to show, that...
If this is about injectivity of f then yes
halcyon dome
some help me please how much heat is required to heat 10.0 g of liquid isobutane at-25c to 23c? the specific heat of liquid isobutane is 2.2j/(gxc) and the specific heat of gaseous isobutane is 1.6j/(gxc) the Boiling point of isobutane is --12c and the heat of fusion is 365j/g
random niche
some help me please how much heat is required to heat 10.0 g of liquid isobutane...
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random niche
If this is about injectivity of f then yes
cause in this case a and b are technically the same.
e.g quadratic functions would fail this test
limpid dawn
yea because aĀ² = bĀ² doesn't imply a = b e.g negative a and positive b
halcyon dome
how
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tepid junco
Original problem: x' = x -y
y' = y - 4x
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Original problem: x' = x -y
y' = y - 4x
tepid junco
Original problem: x' = x -y
y' = y - 4x
I have -(D^2 - 2D +1) [x] + 4x= 0
what now?
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bright quarry
if thereās kinetic friction then it isnāt balanced sir
because the weight of the two blocks on the table donāt affect the acceleration here
those forces are balanced by the table
look at the horizontal forces for them
this isnāt an atwood machine
yo youāre pending postgraduate?
what are you researching
your role
you said youāre studying postgraduate math
when you joined the server
šš
joined September 15th 2024
š¤š¤
well draw a FBD for each block
aye
yea sure
itās not that bad man
you can also just look at the entire system
i always did that
bright quarry
you can also just look at the entire system
just sum the three net forces
youāll get Fnet = (m1+m2+m3)a
because the acceleration will be the same for each block
you got it boss
just guess
iām kidding lol
well what direction is the tension going
thatās the direction the system wants to move
then which way is the friction
yep
it depends how you define your system
if you want to call the weight of the hanging block positive then the tension on that block is negative which means the tension on the other blocks is positive
and vice versa
you get to define direction
thereās 3 blocks
did you draw a FBD for each
draw the third
and you mightāve drawn the second one wrong
just a guess
send it
,rotate
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bright quarry
your labeling could use some work
also, why doesnāt the second mass experience friction
itās on the table
nah could use some work
not everyone knows what mass 1 2 and 3 are
label them in the middle of the block by their masses
2 kg 3kg 5kg
and donāt say Fg
because thereās 3 blocks
use m1g m2g m3g etc
bright quarry
2 kg 3kg 5kg
either that or m1 m2 m3 with a key that says which are which
same principle
Fn balances the vertical forces
so yes because thereās only one vertical force, mg
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rose nebula
I might be dumb but how do you Round to the nearest centimeter ā¬86,475
quiet island
I might be dumb but how do you Round to the nearest centimeter ā¬86,475
Hello!
That unit of measurement youāve put is not in cm. You put a Euro symbol š
About your question tho, you can only round to the nearest centimetre if there are decimals in the number you want to round off!
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sonic eagle
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sonic eagle
im so lost
lofty spade
you should start with a notation
tan^{-1} x becomes y
then you have sin(2y) which is what?
lofty spade
tan^{-1} x becomes y
also this means tan y = x
rugged latch
sonic eagle
I just dont get how cos appears
vale abyss
trig identity
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jagged wharf
I'm a bit rusty with linear algebra. I know how to compute the determinant of a matrix, but suppose all we are given is $T(x_1,\ldots,x_n)=(y_1,\ldots,y_n)$, e.g. \begin{align}T_1(x_1,\ldots,x_j,\ldots,x_n)&=(x_1,\ldots,cx_j,\ldots,x_n),\quad (c\neq0),\ T_2(x_1,\ldots,x_j,\ldots,x_n)&=(x_1,\ldots,x_j+cx_k,\ldots,x_n),\quad (k\neq j),\ T_3(x_1,\ldots,x_j,\ldots,x_k,\ldots,x_n)&=(x_1,\ldots,x_k,\ldots,x_j,\ldots,x_n).\end{align}How do I compute the determinant of $T_1,T_2$ and $T_3$?
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psie
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topaz musk
f(x)=2xātan(x) find the concavity
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f(x)=2xātan(x) find the concavity
topaz musk
for the second derivatie i got f''(x) = -2sec^2xtanx
but im not sure how to find the critical points
is it -2(1/cos^2x)(sinx/cos) = 0 ???
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limpid dawn
but im not sure how to find the critical points
You can do that
Since cosine must not be 0 anyway
Then the left side is only 0, if sine is 0
topaz musk
so x = npi ??
limpid dawn
Yup
topaz musk
it says the critical points and va is plus minus pi/4 and pi/2 tho š
limpid dawn
You went from concavity to critical points
For the critical points of f, you consider f'(x) = 0
2-secĀ²(x) = 0
2 = secĀ²(x)
cosĀ²(x) = 1/2
topaz musk
wait but
i thought for concavity u had to find the critical points for the second derivative
limpid dawn
f"(x) = 0 tells you the intflection points of f
f'(x) = 0 tells you the critical points of f
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icy hedge
Can someone help me with LU decomposition? The U matrix is fine but the L matrix Iām confused on
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Can someone help me with LU decomposition? The U matrix is fine but the L matrix...
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sharp crest
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placid valve
empty wyvern
Say we get a graph like this and I specify an interval or intervals on a graph, like 0 < x < 20. My question is do I have to specify that it is LESS THAN OR GREATER TO
empty wyvern
I know open circles = <, and closed circles = less than or greater than yfm
But what if it's just the line yfm
bright quarry
you donāt assume itās an open circle unless they explicitly draw one
this is just 0<x<65
empty wyvern
So always assume it's a closed circle, so [] and <=
bright quarry
with equality
bright quarry
So always assume it's a closed circle, so [] and <=
yes
but it isnāt really necessary
unless thereās more context
to the question
empty wyvern
Word
bright quarry
that would give that away
topaz musk
i think im doing something very wrongn
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sly pewter
i think im doing something very wrongn
Why are you setting the derivative and function equal
Nvm
Looks right for that
There is a horizontal tangent at x =-2 what about the second derivative tho
topaz musk
the full question is to find f when f is increasing and decreasing using first derivative test
i dont think we can use the second derivative for that right
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twin yoke
One message removed from a suspended account.
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frozen plover
do you know the product rule?
twin yoke
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frozen plover
yep then just use it and sub the values
twin yoke
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haughty ingot
also need help on this š
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also need help on this š
shell quest
Hoi
U got a diagram
If no draw one
If yes, think
You have an angle, another right angle, and a side
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mortal folio
Hello guys, can sb help me with this task? I tried to sum up this three equations and I got that a+b+c=x+y+z
mortal folio
???
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main spire
hellloooooo
ig someone asked the same qn few days ago
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mortal folio
???
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late laurel
sen(60Āŗ + x)*cos(60Āŗ + x) = 1/2
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sen(60Āŗ + x)*cos(60Āŗ + x) = 1/2
late laurel
help me with this equation pls
wraith hinge
use sin2a = 2sinacosa
wraith hinge
angle is 60+x
wraith hinge
npnp
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marsh forum
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marsh forum
So I have to prove $10 \mid (a-b) iff 2 \mid (a-b) \land 5\mid (a-b)$
solid kilnBOT
A dense set
marsh forum
We first wish to prove that $10 \mid (a-b) \implies 2 \mid (a-b) \land 5 \mid (a-b)$
\
We thus have $(a-b)\frac{5 \cdot 2} =k_1; k_1 \in \Z$. We thus have $\frac{a-b}{5}=2k_1$. As integers are closed under multiplication, $5 \mid (a-b)$. We similarly have $ 2 \mid (a-b)$.
solid kilnBOT
A dense set
marsh forum
We first wish to prove that $10 \mid (a-b) \implies 2 \mid (a-b) \land 5 \mid (a-b)$
\
We thus have $\frac{(a-b)}{5 \cdot 2} =k_1; k_1 \in \Z$. We thus have $\frac{a-b}{5}=2k_1$. As integers are closed under multiplication, $5 \mid (a-b)$. We similarly have $ 2 \mid (a-b)$.
\
\
We now wish to prove $2 \mid (a-b) \land 5 \mid (a-b) \implies 10 \mid (a-b)$
\
to do so, we wish to prove that $a \mid c \land b \mid c \implies (ab) \mid c; a \neq b$.
\
Let's assume to the contrary that $(ab) \nmid c$. We then have $c=(ab)q+r; 0<r<ab$
\
We now divide across by $a$ . We thus have $k_1= bq_1 + \frac{r}{a}$.
\
$k_1 \in \Z$, we also know that $bq \in \Z$. We thus now need $\frac{r}{a} \in\Z$. This can only happen if $r=0$ or if $r=a$.
\
\
We now once again assume $(ab) \nmid c$
\
We thus have $c = q(ab)+r_2$
\
We now divide across by $b$.
\
this gives us
\
$k_2 = aq_2+\frac{r}{b}$.
\
The only way this can be an integer is if $r= 0$ or $r=b$
vagrant marsh
good so far
solid kilnBOT
A dense set
vagrant marsh
what condition must a and b have so that a|c, b|c => ab|c
marsh forum
We first wish to prove that $10 \mid (a-b) \implies 2 \mid (a-b) \land 5 \mid (a-b)$
\
We thus have $\frac{(a-b)}{5 \cdot 2} =k_1; k_1 \in \Z$. We thus have $\frac{a-b}{5}=2k_1$. As integers are closed under multiplication, $5 \mid (a-b)$. We similarly have $ 2 \mid (a-b)$.
\
\
We now wish to prove $2 \mid (a-b) \land 5 \mid (a-b) \implies 10 \mid (a-b)$
\
to do so, we wish to prove that $a \mid c \land b \mid c \implies (ab) \mid c; a \neq b$.
\
Let's assume to the contrary that $(ab) \nmid c$. We then have $c=(ab)q+r; 0<r<ab$
\
We now divide across by $a$ . We thus have $k_1= bq_1 + \frac{r}{a}$.
\
$k_1 \in \Z$, we also know that $bq \in \Z$. We thus now need $\frac{r}{a} \in\Z$. This can only happen if $r=0$ or if $r=a$.
\
\
We now once again assume $(ab) \nmid c$
\
We thus have $c = q(ab)+r_2$
\
We now divide across by $b$.
\
this gives us
\
$k_2 = aq_2+\frac{r}{b}$.
\
The only way this can be an integer is if $r= 0$ or $r=b$
solid kilnBOT
A dense set
marsh forum
from this I want to somehow conclude that $r=0$ , thus arriving at a contradiction
solid kilnBOT
A dense set
marsh forum
Or is this the wrong way to approach it
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marsh forum
<@&286206848099549185>
marsh forum
<@&286206848099549185>
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gusty estuary
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sage scarab
I need help with this
what steps do I take, can someone list it š
wary basin
split chasm
also your selection for the dropdown is incorrect
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wraith hinge
How do I find the domain in B
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How do I find the domain in B
wraith hinge
<@&286206848099549185>
wraith hinge
All real values are allowed
ohh right I see it
so itās all dependent on the denominator and I donāt have to take the numerator in consideration right?
lofty elk
Mhm
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lofty elk
Although, is x=i considered a vertical asymptote
wraith hinge
what about this? how do I continue to solve for finding the vertical asymptote
lofty elk
what about this? how do I continue to solve for finding the vertical asymptote
Wat
Factorise the bottom
wraith hinge
Although, is x=i considered a vertical asymptote
itās imaginary so idk
lofty elk
itās imaginary so idk
There should be no vertical asymptotes
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lucid dove
Lmao I made u switch channels
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orchid wagon
do not do this
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kind island
okokok
kind island
i might crashout here
i need someone to help me justify why my answer is the way it is
becuase im deadass confused
i just generally also wanna know why my answer is my answer
my answer: F is orange
f is blue
fā is black
i need some big boy explinations
crisp zodiac
I mean, derivative of a parabola is a straight line
because essentially you're converting a quadratic polynomial to the format of y=mx+c
crisp zodiac
ye
crisp zodiac
you can if you want, its not necessary
kind island
ok bet thanks a lot
crisp zodiac
yeye np
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verbal canopy
tried this like 7-8 times, really not sure what to do. thx for any help
hidden dew
How did you get x as 75 ?
verbal canopy
cuz i thought if 2x is 150 then x is 75
hidden dew
cuz i thought if 2x is 150 then x is 75
The mistake is from here you didnāt subtract 150 from both sides
verbal canopy
could you visualize that or explain how id do that
hidden dew
Like at the step
2x+150=180
for both sides to be equal we need to take from both sides the same amount
so we take from (subtract) both sides 150
2x+150-150=180-150
Left side becomes
2x and right side becomes 30
verbal canopy
so then one x is just 15
hidden dew
Yep
verbal canopy
@hidden dew the question changes as u get it wrong
i tried again i just cannot work it out
can u maybe reexplain with my new workings
hidden dew
Process was right you just used the wrong numbers
You subtracted 150 when the question stated
2x+130=180
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bronze hound
conceptually speaking, how can you have a second derivative at one point
zinc ginkgo
derivative of derivative 
clear cloud
f'(x+h) - f'(x) / h
bronze hound
the slope doesnt change at one point, how can it have a second derivative
tribal pond
the slope doesnt change at one point, how can it have a second derivative
well isn't the derivative, in some cases, a function itself?
that maps an X to an unique Y in the codomain (the slope)
bronze hound
what, can you dumb it down a bit for me
tribal pond
what, can you dumb it down a bit for me
the derivative can be a function itself
and it coul dbe a differentiable function
like say f(x) = x^2
then f'(x) = 2x
now g(x) = f'(x) is a function itself
and we can see it's differentiable everywhere
bronze hound
but like im just thinking about this logically though
for example, the derivative at x = 1 is 2
like that point has a constant slope right
the second derivative means the first derivative is changing right
bronze hound
but if the slope there is constant, shouldnt the second derivative just be zero
bronze hound
why not, dont you agree that a point can only have 1 slope value
tribal pond
think of your derivative as a function
tribal pond
why not, dont you agree that a point can only have 1 slope value
well if the derivative exists at that point yes
bronze hound
ok so the second derivative is 2, meaning that the slope increases, but at that point the slope is just 2
so it doesnt increase, its just constant
tribal pond
ok so the second derivative is 2, meaning that the slope increases, but at that ...
mhm
so the second derivative is a constant function
bronze hound
i get that the neighboring point can have an increased slope
but my point is that point, cannot
as that point is simply a constant value
if you say an interval close to that point has a second derivative, i agree
like we say between [1,1.000000001]
lets say this interval has a second derivative
i get that, because the values now have different slopes right
but i dont get how simply one point which has a constant slope can now have a changing slope
tribal pond
but i dont get how simply one point which has a constant slope can now have a ch...
no
we look at MULTIPLE points
f'(x) can be a function
itself
bronze hound
ya i get that
ok so the derivative of the function f'(x) will look at neighboring points at some x value correct?
tribal pond
ok so the derivative of the function f'(x) will look at neighboring points at so...
yes
but sometimes the function f'(x) will not be differentiable
for some reason
(discountinies or left and right hand limit does not exist or equal each other)
etc
bronze hound
ok so then my point is, isnt it imprecise to say the second derivative at a certain point, wouldnt it be more precise to say the second derivative at points near this certain point
near and including the point
tribal pond
ok so then my point is, isnt it imprecise to say the second derivative at a cert...
is it not the second derivative at a certain point
ur still looking at the same neighborhood
bronze hound
i mean it is the derivative at the point, but like its more of an interval than a point right?
tiny river
A point does not have a constant derivative
bronze hound
what
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ruby heron
any ideas how to start this one?
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odd tapir
How is momentum conserved in an inelastic collision given the fact that kinetic energy is lost, and so since p = mv (momentum is equal to mass x velocity) and velocity is lowered (kinetic energy is lost) then how come momentum is convserved?
silent canyon
Maybe kinetic energy is passed in the collision?
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random quest
hey guys, I feel silly for now knowing how to do this, but I need to figure out how to solve for x for a personal project of mine.
assuming I have the length of the largest side of a triangle (3), the angle opposite to that side (135*), and the length of one other side of said triangle, how would I solve for the unknown length of the other side (X)?
exotic pine
cos rule
exotic pine
or sin rule works aswell
exotic pine
congruence??
wraith hinge
you can't fix a triangle by knowing two sides and an angle opposite to one of the two sides, can you?
Otherwise ASS would have been a criterion
Angle-Side-Side
exotic pine
nah only 1 positive
wraith hinge
oh
random quest
thanks guys, I haven't had a maths class in like 5 years so I was giving myself a brain bleed trying to figure this out
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wraith hinge
I had asked this earlier.
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I had asked this earlier.
wraith hinge
I don't think I got a satisfactory answer
Prove by induction that the product of r consecutive integers is divisible by r!
hollow tangle
I remember this lol
visual trench
That is, r!|(n)(n+1)(n+2)(n+3)(n+4)..........(n+r-1)
it is a binomial coefficient. you can prove it is integer in many ways. One is combinatorial as a number of combinations. Another one by recurrence from Pascal triangle. Another way is to use prime factorization formula for factorials.
(n)(n+1)(n+2)(n+3)(n+4)....(n+r-1)/r! is a binomial coefficient C(n+r-1, r)
wraith hinge
This is the first exercize of the book.
visual trench
Ok, you can prove by induction that C(n,k) is integer because C(n,k)=C(n-1,k)+C(n-1,k-1). Starting from C(1,0)=C(1,1)=1 which is integer.
wraith hinge
I don't get the notation
visual trench
where C(n,k)=n!/((n-k)!k!)
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orchid wagon
This is the first exercize of the book.
hammack?
wraith hinge
I'll try and tell
orchid wagon
book of proof by richard hammack?
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jagged portal
spiral ocean
Extended remainder theorem for non-linear divisor; how do i deal with it?
spiral ocean
For example, let ${f(x) = x^{2011} - ax + 3}$ and ${f(x)}$ yields the remainder of -3 when divided with ${x^2 - 1}$. Then what is ${a}$?
solid kilnBOT
k
spiral ocean
so i know that if ${f(x) = x^{2011} - ax}$ should be divisible by ${x^2 - 1}$. So, ${x(x^{2010} - a)}$
so i know that if ${f(x) = x^{2011} - ax}$ should be divisible by ${x^2 - 1}$. So, ${x(x^{505} - a)(x^2 - 1) \implies a = 1}$
spiral ocean
Extended remainder theorem for non-linear divisor; how do i deal with it?
this brought me to ths
is there a shortcut for this kind of problems?
nova spire
For example, let ${f(x) = x^{2011} - ax + 3}$ and ${f(x)}$ yields the remainder ...
you're sure the remainder isn't 3?
also yes you can use that since (x-1) and (x+1) both divide x^2-1 and remainder is of degree 0 < 1
f(1) = remainder and f(-1) = remainder
so 1 - a + 3 = remainder and -1 + a + 3 = remainder
nova spire
For example, let ${f(x) = x^{2011} - ax + 3}$ and ${f(x)}$ yields the remainder ...
so yeah if remainder isn't 3 the problem should be false
but 1 - a + 3 = 3 gives a = 1
and same for -1 + a + 3 = 3
if for example you had that f(x) when divided by x^2-1 gives remainder of x + 4
f(x) divided by x-1 has same remainder as x+4 divided by x-1
so f(x) divided by x-1 gives remainder of 5
f(1) = 5, then repeat with x+1
it can be a powerful tool sometimes
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dull pulsar
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dull pulsar
not sure if i'm overthinking or misunderstanding the notation. we are given already, so just fgind g(x)^2? Not sure how to
shell gust
I think the answer is just 8
oak fractal
I think the answer is just 8
Ye
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dull pulsar
Thanks
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harsh siren
if we are given three complex point in a plane then angle at z2 will be?
harsh siren
is it (z1-z2)/z2-z3 ?
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acoustic flint
is it (z1-z2)/z2-z3 ?
(z_1 - z_2) / (z_3 - z_2)
Convert to polar form before dividing that way you can just subtract the arguments
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boreal berry
can someone please help me with this question
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can someone please help me with this question
boreal berry
i donāt get what i am doing
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unique harness
hi i am having trouble with how to start these two problems
modern hamlet
think of them as squares and triangles
and add up the areas
then take into acount the interval
and devide it by the length of the interval
to get an average
modern hamlet
yes
modern hamlet
yes
modern hamlet
yes
modern hamlet
all good
unique harness
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floral atlas
my question is that how to find domain and range f(x) = sqrt(x + 1) . the answer that my friend gave me is Dom g = [-1 , +infinty ) and Range g = [0 , +infinity] and he also don't know how he got these answer a year ago
floral atlas
and also please tell me how to find domain and range of a function in general
spring summit
a negative number in a sqrt would give u an imaginary number
floral atlas
please explain further
spring summit
so u can't have a negative number in a sqrt
which means values of x must be -1 or bigger
for it not to be negative
floral atlas
and why are we excluding infinity in domain
spring summit
domain of a function is a set of all possible inputs for this function
spring summit
and why are we excluding infinity in domain
we're not
+infinity is greater than -1
floral atlas
so we should use ] instead of )
floral atlas
so in domain he is excluding + infinity but i should include it??
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naive aurora
hey im not into this topic, or a math guy or smthin
but using the basic idea you can get from this ,
use congruency
before that,
do you know how to find the length of the 3rd side of a scalene triangle,
given 2 sides, and the angle between them?
lets say here a = 80 , b = 100 , angle O = 60 deg
the formula for 3rd side c is
so if u substitute the value for that, youll get c = 91.65 which is approx 91.7
but well never mind that, this is just random n not correct approach
but idk if this is math question or physics
coz if its physics then id say you can use relative velocity formula, since this can be considered vector
say v1 = 80km/hr n v2 = 100km/hr and angle between them is 60 deg
again thats goes to the same logic
we do the same thing, and can say that the rate is 91.6515
its relative velocity formula
for rate of separation
using law of cosines, coz they are vectors with a direction and an angle between them
wispy vigil
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wispy vigil
I know that sin /=/ 1
So it cant be pi/2
and cos cant be 0
so it cant be 0 or pi
but why cant it be 0,-1
270deg
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wispy vigil
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how do i do this?
molten comet
Create cases for when each abs is pos and neg
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cedar fiber
Hello?
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full hull
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full hull
did i do something wrong?
restive pewter
Fundamental Theorems for Normed and Banach....
Please send me viva questions and help me š
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tardy ledge
can i get help with this
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can i get help with this
tardy ledge
I worked out the probabilities 1 is 1/6 2 and 6 is 2/6 and 5 is 1/6
i can't seem to figure out the next step
bright quarry
did you work out how it could add up to 6
naive otter
did you work out how it could add up to 6
Is there any such way ?
bright quarry
Is there any such way ?
yes
naive otter
Except 2,2,2
bright quarry
Except 2,2,2
no
tardy ledge
ok yeah i got that far now
so the probabilitiy of roling a 2
3 times
is
1/36
wait
no
bright quarry
there are multiple 2s
thorn otter
You shouldnāt calculate it that way
naive otter
there are multiple 2s
I was questioning him, sry i tagged you lol !
tardy ledge
2/6 probability each time, 3 independent events, wouldn't it just be (2/6)(2/6)(2/6)
naive otter
2/6 probability each time, 3 independent events, wouldn't it just be (2/6)(2/6)(...
It would be
tardy ledge
the answer is 1/27 š
naive otter
1/3Ā³ = 1/27
naive otter
2/6 = 1/3
naive otter
and 6^3 = 256
216
tardy ledge
oh ya its 216
right
ok
also
how come my ti-84 doesn't always convert into fraction when i do math frac
naive otter
,calc 8/216-1/27
naive otter
@thorn otter You mean, he should write the possible event set and calculate š
thorn otter
Your way of calculating this is wrong, you should count how many configurations of the dice that add up to 6, and then divide that by 6^3
thorn otter
<@896953469808832532> You mean, he should write the possible event set and calcu...
You just have to calculate the length of it, not write it all down
naive otter
You just have to calculate the length of it, not write it all down
Yes !!
tardy ledge
Your way of calculating this is wrong, you should count how many configurations ...
theres only 1 config isn't there?
thorn otter
You have to divide it into 3 cases:
- 3 dice are different to each other
- 2 dice are the same, the other is different
- 3 dice are the same
For the first case, you only have 1+2+3 = 6
thorn otter
theres no 3
Yeah, so that solution is out
tardy ledge
but your not dividing by 6^3
thorn otter
Yes, I have :)
tardy ledge
how
number of configs / 6^3 isn't it?
oh
wait
there is 3
possible ways of getting 2,2,2
thorn otter
The prob of getting a 2 is 1/3, right? Now we have to have 3 2ās in a row, so weāre taking the third power :)
tardy ledge
no there is 8
silver glade
you can do 2^3 / 6^3 or (1/3)^3, it's the same
tardy ledge
yeah ok
thorn otter
number of configs / 6^3 isn't it?
Sorry, I thought this problem isā¦ another problem
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quick garnet
In a regular hexagonal pyramid with base edge a = 1 cm and peripheral edge l = 2 cm is constructed an intersection that passes through the largest diagonal of the base and is perpendicular to it. The area of the intersection?
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In a regular hexagonal pyramid with base edge a = 1 cm and peripheral edge l = 2...
@quick garnet Has your question been resolved?
mystic iris
In a regular hexagonal pyramid with base edge a = 1 cm and peripheral edge l = 2...
Have you tried like drawing it
quick garnet
Not really I'm confused bcs the intersection is supposed to be an equilateral triangle
mystic iris
Not really I'm confused bcs the intersection is supposed to be an equilateral tr...
Yes it is but why does it make it more difficult
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wheat torrent
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wheat torrent
Is there any way I can determine the magnitude/length of vector D efficiently without finding each individual component of A B & C?
digital bolt
Is there any way I can determine the magnitude/length of vector D efficiently wi...
no
it's pretty quick to find the individual components though
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serene crane
Quick question, should I foil this then multiply by 5v?
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Quick question, should I foil this then multiply by 5v?
trim musk
Quick question, should I foil this then multiply by 5v?
im sorry but whats foil?
trim musk
oh expand
serene crane
yes
trim musk
yes you can do that but there is a faster and simpler way
serene crane
What would that be?
trim musk
substitution
serene crane
explain?
trim musk
have you not learnt it?
u sub
let the thing inside the brackets be = u
so v^2 + 4 = u
now differentiate
trim musk
u sub in integration
oh well then you can just expand
its going to be a bit painful though
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valid beacon
Quick question, should I foil this then multiply by 5v?
you could avoid foiling actually
valid beacon
nvm i think they mention u-sub
earlier at least
but if you let u = v^2 + 4
you get du = 2v dv
you have a 5v in front
but you could just multiply the whole integral by 5/2 and replace the 5 with a 2
and its all good
trim musk
yeah he hasnt learnt it yet
mystic iris
u sub is so satisfying once youve learned it
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radiant crow
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radiant crow
how do i long division that divided by a + b
restive vortex
how do i long division that divided by a + b
What you wanna find the quotient or the remainder?
empty orchid
how do i long division that divided by a + b
you mean, prove that $\frac{a^p+b^p}{a+b}=a^{p-1}+a^{p-2}b...+b^{p-1}$?
solid kilnBOT
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empty orchid
mayb idk
radiant crow
What you wanna find the quotient or the remainder?
remainder
radiant crow
I though Clyde want to divide a^(p-1).... By a+b
ye
empty orchid
i tried long division but i'm dumb
hmm
maybe we can use remainder theorem here
$\frac{a^p+b^p}{(a+b)^2}$
solid kilnBOT
;(
empty orchid
maybe try this
radiant crow
maybe we can use remainder theorem here
wym am dumb
idk how to use remainder theorem when there r 3 variables
empty orchid
idk how to use remainder theorem when there r 3 variables
which is why i opted for the simplifcation
restive vortex
If a = -b
The (-b)^p+b^p
If p even then (a+b)^2 will not fully divide that expresion
radiant crow
p is odd
radiant crow
If p even then (a+b)^2 will not fully divide that expresion
also there's a remainder
restive vortex
p is odd
If p is odd then it will fully divide
Because (-b)^p+b^p
If p is odd ,for example 7
(-b)^7 + b^7
Is 0
radiant crow
a, b are coprime
restive vortex
a, b are coprime
So a can't be equal to b
Then yeah uhhh this is harder
What is the question again
restive vortex
What is the question again
I mean the full version of the question
radiant crow
p is an odd prime
a, b are coprime
prove that the gcd of
a + b, (a^p + b^p)/(a + b) is either 1 or p
radiant crow
i jst need the remainder of this divided by a + b
restive vortex
p is an odd prime
a, b are coprime
prove that the gcd of
a + b, (a^p + b^p)/(a +...
Lcm*gcd = a^p+b^p
This form might help
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radiant crow
the remainder should jst be pb^(p-1)
so gcd(a + b, pb^(p-1))
since a + b and b^(p-1) are coprime
it will be
gcd(a + b, p)
which is either p or 1
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uncut bough
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uncut bough
Can someone help me make the geometric interpretation for 0<x<1 ?
This is what I got
empty orchid
Can someone help me make the geometric interpretation for 0<x<1 ?
for F, or f?
uncut bough
But Iām confused how to get X-x^2/2 using geometric interpretation
empty orchid
or which part of the questions are you stuck on?
uncut bough
for F, or f?
For F
uncut bough
or which part of the questions are you stuck on?
It is 1b
empty orchid
But Iām confused how to get X-x^2/2 using geometric interpretation
because look at the shape of the linear graph.
we haev that $F(x)=\int_0^x f(t)dt$
solid kilnBOT
;(
