theres your answer
#help-13
coral jewel
honest cliff
what about arctg
honest cliff
ah, nice
Thanks
coral jewel
!done
cedar kilnBOT
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honest cliff
.close
peak prism
Hey guys, I'm trying to prove I1=I2, I was trying to find if I1-I2 = 0 but got stuck pretty quickly. is there something else easier that im missing maybe?
cedar kilnBOT
Hey guys, I'm trying to prove I1=I2, I was trying to find if I1-I2 = 0 but got s...
@peak prism Has your question been resolved?
hollow lantern
can someone help me with these
warm apex
How do you simplify a polynomial
cedar kilnBOT
How do you simplify a polynomial
warm apex
There was a multiple choices question that has the standard form and the answers were like... simplified
like (x+y)(x-y)
coral jewel
show said question?
warm apex
show said question?
i don't have a picture since no phones were allowed
coral jewel
i see
coral jewel
i think you meant "factor"?
warm apex
YES
that
we could try with this problem
x⁴ + 4x³ - 6x² + 4x - 3 = 0
@helper
help
wat
<@&286206848099549185>
so how to factorize
digital cliff
rational root theorem is often a good first step
then if you find roots do polynomial division and factor the rest
crimson sedge
I've found (x-1)(x³+5x²-x+3)
crimson sedge
then if you find roots do polynomial division and factor the rest
When I did this
cedar kilnBOT
@warm apex Has your question been resolved?
daring parcel
<@&286206848099549185>
state ur question please
mild spear
we could try with this problem
x⁴ + 4x³ - 6x² + 4x - 3 = 0
Try to take sum of coefficients of even power and odd power seperately and then take difference of them.
If it's zero, (x-1) is a factor of that polynomial
cosmic umbra
help me
vital wing
!status
cedar kilnBOT
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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
Available help channel!
lilac birch
does P(Z > 0.56) equal to 1 - P(Z < 0.56) in normal distrubution?
lilac birch
bump
fiery whale
ye
cedar kilnBOT
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soft jackal
Let a and b be two real numbers in the interval [2;4] We set A = (2a)/(2a + b)
-
Verify that: 1/A = 1 + b/(2a)
-
Determine a frame of A with amplitude 0.75
-
Give an approximate value of A to within 0.15
soft jackal
I need help with the second one :3
cedar kilnBOT
@soft jackal Has your question been resolved?
soft jackal
<@&286206848099549185>
cedar kilnBOT
@soft jackal Has your question been resolved?
chilly abyss
wanton sail
Let a and b be two real numbers in the interval [2;4] We set A = (2a)/(2a + b)
...
The wording of the question is a bit confusing to me. Is this the original question? Was it translated from another language?
Do you know what is meant by "frame"
cedar kilnBOT
@soft jackal Has your question been resolved?
soft jackal
The wording of the question is a bit confusing to me. Is this the original quest...
yesss
by frame it means
a<x<b
yk
wanton sail
No I don't know
I don't know what you're responding "yes" to
Is this the original question, or was it translated from another language?
Can you take a screenshot or something similar of the original question
Otherwise it's gonna be really difficult for anyone to help you
cedar kilnBOT
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dense iris
Good night, I been trying to solve this integral using Laplace transform , how can i do it?
dense iris
What do you mean?
dire geode
,w int 0 to inf exp(2t) t sin(t) dt
wraith daggerBOT
dire geode
typically when you're asked to take laplace transforms, integrals converge
show the original question and all context
opaque root
Isnt it -2t?
dusk goblet
probably
dense iris
show the original question and all context
It does converge tho
dusk goblet
🤔
dense iris
dusk goblet
^
dense iris
this is not the same I think
dusk goblet
,w \int_0^{\infty} e^{-2t}tsin(t) dt
wraith daggerBOT
dire geode
lmao
dusk goblet
typo
dense iris
TYPOOOO
dire geode
do a usub to get exp(-2t) to be exp(-t) then look up a table
dense iris
this is not the same also lmao
dire geode
probably a trig identity somewhere
dusk goblet
this is not the same also lmao
😟
dense iris
dusk goblet
dusk goblet
yikes
crimson hornet
can someone explain why its orthogonal?
cedar kilnBOT
can someone explain why its orthogonal?
hollow trail
a vector is orthogonal to another vector if their dot product is 0
crimson hornet
oh okay thanks so
if the dot product is 0, then they are orthogonal but if the cross product is 0 then they're parallel?
dusk goblet
cross product gives a vector
not a scalar
the cross product results in a vector orthogonal to the two vectors
which is what this question is demonstrating
crimson hornet
oh sorry yeah, if the cross product is like [0,0,0] in R3 then are the two vectors parallel?
hollow trail
yes
cedar kilnBOT
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crimson sedge
cedar kilnBOT
crimson sedge
neon void
👍 seems legit
crimson sedge
Not sure if I set this up right. Cause at first I got 108 but I realized it said the last test is 2 test grades. I didn’t think that mattered when dividing by the number
.close
cedar kilnBOT
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grave charm
Modulus and Argument without using polar coordinates?
cedar kilnBOT
Modulus and Argument without using polar coordinates?
golden raven
You have to use angle and magnitude
dire geode
why can't you use polar coordinates
you can use binomial theorem but that's much longer
grave charm
why can't you use polar coordinates
cause our teacher hasn't taught it to us yet and he said we should be able to do all of these questions without polar
dire geode
what about binomial expansion
golden raven
imo your teacher is one of those okay
grave charm
what about binomial expansion
yea
dire geode
yea just do that twice then
grave charm
imo your teacher is one of those okay
he's teaching it to us tmrw
grave charm
yea just do that twice then
i got stuck on the cancellations
golden raven
i got stuck on the cancellations
which terms did you get cancel?
dire geode
just show all your work
dire geode
,rotate
wraith daggerBOT
dire geode
looks like there's a lot of simplifying you can do
dire geode
¯_(ツ)_/¯
grave charm
sry just been doing this hw for like 4 hours straight
because i thought i could cram it night before 💀
what is it
?
i know the argument is 0
but like
whats the modulus
@dire geode cld u just tell me pls
dire geode
looks like there's a lot of simplifying you can do
.
did you do any simplifying since i sent that?
grave charm
i honestly just cant see it
i know its probably very obvious
but ive just been staring at it for 20 minutes
i tried expanding the first few terms asw
cedar kilnBOT
@grave charm Has your question been resolved?
cedar kilnBOT
@grave charm Has your question been resolved?
quiet delta
Modulus and Argument without using polar coordinates?
Just show that a(n+3)=-8 * a(n), which is almost obvious as (1+-i sqrt(3))^3=-8
so, you get a(3k)=a(3k+1)=2*(-8)^k and a(3k+2)= -4 *(-8)^k for k=0,1,...
compact ice
can someone help me?
cedar kilnBOT
can someone help me?
compact ice
someone who know about complex numbers
cedar kilnBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
compact ice
imagine p=9
does it have imaginary part?
i've proved that it doesnt but i dont know where am i wrong
gritty viper
What's your proof?
gritty viper
Sure
compact ice
so we have this
1^x it doesnt matter the value of x that it wont have an imaginary part
something is wrong i dont know were
gritty viper
Ah yeah so this is exponent rules not really working properly for imaginary numbers
compact ice
can you find the mistake?
gritty viper
think about $((-1)^\f12)^2$
wraith daggerBOT
Dreyuk
gritty viper
first, what's -1 ^ 1/2 ?
wraith daggerBOT
Dreyuk
compact ice
yes
gritty viper
$=((-1)^2)^\f12$
wraith daggerBOT
Dreyuk
gritty viper
what's this?
compact ice
1
gritty viper
right
gritty viper
**Dreyuk**
So exponent laws don't always quite work for complex numbers
compact ice
okay
gritty viper
$(-1)^x$ should be real only when x is an integer
wraith daggerBOT
Dreyuk
gritty viper
So you have to check if the exponent is an integer
gritty viper
Yeah when you're dealing with complex numbers
compact ice
okay
gritty viper
So anything other than a positive real number for x
Since negative numbers raised to a non-integer exponent get you in the "complex numbers" territory
compact ice
thank you so much
gritty viper
Np
cedar kilnBOT
@compact ice Has your question been resolved?
nova solar
yo
nova solar
i have a math test coming up soon for geometry
and i was wondering
how come segment AB = segment AB for reflexive property, but for reflexive property segment AB = segment BA also
hollow trail
they are congruent, meaning they have the same length (not necessarily the same orientation)
cedar kilnBOT
@nova solar Has your question been resolved?
cloud vale
cedar kilnBOT
cloud vale
been 10 mins
cedar kilnBOT
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primal oriole
Does this look incorrect? I don't think it should diverge.
cedar kilnBOT
Does this look incorrect? I don't think it should diverge.
primal oriole
Also, for this, shouldn't the integral come out ot be -2e^(-rad(x)) + C?
acoustic quartz
Does this look incorrect? I don't think it should diverge.
This should be
primal oriole
This should be
1/2 e ^-t^2 goes to 0 for both infinity and -infinity right?
primal oriole
Also, for this, shouldn't the integral come out ot be -2e^(-rad(x)) + C?
Can you check the integral for this one?
acoustic quartz
Also, for this, shouldn't the integral come out ot be -2e^(-rad(x)) + C?
Yea
Dx = -2sqrtxdu
cedar kilnBOT
acoustic quartz
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coral jewel
hello, id like my proof checked please
cedar kilnBOT
hello, id like my proof checked please
sharp pike
Looks good to me
cedar kilnBOT
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raw oxide
Solve the following system of linear equations using the inverse matrix method.
2x-y+z=3
5x+2y-3z=1
2x+y-z=2
raw oxide
how far i've gotten
finally khud hi samaj me agaya bhais ki aakh yar bc mera dimag kharab hogya isko samjhte holy shit
tum sab ki ma ka
bc kisi ne ni help ki
bc
itna bada dimag hai mera
me khud pe hi phida hogya hu
cedar kilnBOT
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spiral prairie
cedar kilnBOT
spiral prairie
i dont see why its not 324k(pi)
because at the end of the integral, you get (324k[pi] +144k)-144k
.close
cedar kilnBOT
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gentle jackal
May I ask whether the derivative of this function can even be found?
cedar kilnBOT
@gentle jackal Has your question been resolved?
worldly chasm
u = √(1-y^2), du = 1/2√(1-y^2)
Our integral becomes int u^2 e^(xu)
@gentle jackal
gentle jackal
u = √(1-y^2), du = 1/2√(1-y^2)
Our integral becomes int u^2 e^(xu)
<@120803280...
hmmm, du not -y/√(1-y^2) dy ?
gentle jackal
😭
I think it is probably the teacher printed it wrong
sqrt(1-y^2) should be at below
then a lot easier
crimson sedge
but you dont have to integrate it
simple plume
cedar kilnBOT
simple plume
This is what I did
native rain
This is what I did
your solution overcounts combinations like [A, B] and [B, A], instead they should be considered the same combination
simple plume
Does the order not matter in this case 🤔
simple plume
your solution overcounts combinations like [A, B] and [B, A], instead they shoul...
There is mention of no right so the order should matter or am I not reading it correctly?
native rain
"... that can be pressed in any combination (including multiple buttons at a time)..."
If you pressed the 3 buttons A, B, and C, at the same time, how would you order that?
there is no order
there is no difference between pressing A,B,C at the same time and pressing B,A,C at the same time
they would be counted as the same combination
cedar kilnBOT
@simple plume Has your question been resolved?
tidal anchor
I need help with geometric sequence
cedar kilnBOT
I need help with geometric sequence
tidal anchor
I dont understand shit
like
5, 11, 17, 23,
I js need something
to do this
because im going insane
like
keen hound
5, 11, 17, 23,
This is an AP
5 + 6 = 11
11 + 6 = 17
17 + 6 = 23
What do you need help with?
tidal anchor
wdym ap
armethic sequence?
wait
bro
my brian is not braining
so how do i write in a formula
that describes the sequence
cedar kilnBOT
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tidal anchor
.close
cedar kilnBOT
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north sage
hmhmm to find the area, do i use intergration? but then how do i intergrate an inverse trigo mmhhmhm
steel heart
Integration by parts, if you don't directly know how to integrate an inverse trig function
north sage
is that the only way? because i havnt learnt it yet hmhm
steel heart
the area under that curve is ∫ydx
obtuse mango
is that the only way? because i havnt learnt it yet hmhm
think about what happens if we reflect the curve in the line y=x
north sage
.close
cedar kilnBOT
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outer canopy
When the angle of elevation of the Sun is 62°, a telephone pole that is tilted at an angle of 8°
directly away from the Sun casts a shadow 20 feet long. Determine the length of the pole.
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outer canopy
<@&286206848099549185>
jade vessel
Hi, why is this?
cedar kilnBOT
Hi, why is this?
jade vessel
cant use Taylor's expansion btw
I can use first order of it maybe its enough
ok it works by three sequences and ln approximation $\frac{x}{x+1} \leq \ln(1+x) \leq x$
wraith daggerBOT
zzzz
jade vessel
.close
earnest geyser
this is just a whimsical question
cedar kilnBOT
this is just a whimsical question
earnest geyser
solution for x=x-1
like there is no real solution to it
is there any imaginary solution?
jade vessel
is there any imaginary solution?
nope
earnest geyser
i see
jade vessel
as long as $-1 \neq 0$ there is no sol
wraith daggerBOT
zzzz
cedar kilnBOT
@earnest geyser Has your question been resolved?
opal stirrup
Which inequality corresponds to the following interval?
cedar kilnBOT
Which inequality corresponds to the following interval?
pastel vault
Which inequality corresponds to the following interval?
|x - 5| means the distance between x and 5 (on the number line)
the distance between x and 5 for this interval is..... ?
opal stirrup
the distance between x and 5 for this interval is..... ?
So |x-5| > 3 is correct?
pastel vault
So |x-5| > 3 is correct?
yes
cedar kilnBOT
opal stirrup
.reopen
cedar kilnBOT
✅
opal stirrup
I also struggle with comparing this two.
First one is obviously 1.
Second... IDK
pastel vault
I also struggle with comparing this two.
First one is obviously 1.
Second... ID...
ah, so by change of base $\log_{0.5} \frac{1}{3} = \frac{\log 1/3}{\log 0.5}$
we can use log base 10 or log base e, it doesn't matter
what matters is that log(0.5) < 0
wraith daggerBOT
south
opal stirrup
So the answer is less than or equal? Or am I getting it wrong?
pastel vault
So the answer is *less than or equal*? Or am I getting it wrong?
well they can't be equal
pastel vault
So the answer is *less than or equal*? Or am I getting it wrong?
since log(1/2) > log(1/3), log is an increasing function if we use log base 10 for example
now divide both sides by log(0.5), which is negative
so......
pastel vault
I don't get them logs at all, sorry for being slow. Is it *less than*?
what is less than
which one do you think is the smallest
opal stirrup
log 1/2
wraith daggerBOT
south
pastel vault
do you want me to explain why?
opal stirrup
That would be fabulous
pastel vault
since log(1/2) > log(1/3), log is an increasing function if we use log base 10 f...
dividing by a negative number flips the sign
hence $\frac{\log 1/2}{\log 0.5} < \frac{\log 1/3}{0.5}$
or just $\log_{0.5} (1/2) < \log_{0.5} (1/3)$
wraith daggerBOT
south
cedar kilnBOT
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random grove
how would you use the method of moments to assess the fit of a distribution? I am trying to see if a dataset I have fits the exponential distribution. My plan work out my estimated parameters and then compare the 2nd moments using the estimate and the actual data and see how close they are
cedar kilnBOT
how would you use the method of moments to assess the fit of a distribution? I a...
@random grove Has your question been resolved?
cedar kilnBOT
@random grove Has your question been resolved?
cedar kilnBOT
@random grove Has your question been resolved?
cedar kilnBOT
@random grove Has your question been resolved?
dire geode
how would you use the method of moments to assess the fit of a distribution? I a...
your "observed" is the data (x_i, y_i)and "expected" is the distribution value at that datapoint x_i
random grove
oh thank you very much, my assignment says this. I was thinking of using qqplots and getting an estimated parameter using MoM. This only assumes 1st year stats knowledge as well btw
thank you for the lnik though
drowsy tulip
!done @random grove
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cedar kilnBOT
cedar kilnBOT
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trim wagon
what does N mean
cedar kilnBOT
what does N mean
hollow trail
natural numbers usually
cedar kilnBOT
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rough osprey
Why y = x + 3 when switched becomes -x = 3 - y not -x = 3 / y ?
dire geode
y/y = 1, not 0
dire geode
And also there is this symbol ±
```
(-x + 1)² = 64
-x + 1 = ± 8
```
Because (-8)^2 = 64
So when taking the square root of a square, you need to take absolute value
$\sqrt{x^2} = |x|$
wraith daggerBOT
riemann
rough osprey
y/y = 1, not 0
I see
cedar kilnBOT
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vapid grotto
Looking for somebody to check my work since my teacher did not post the answer key
cedar kilnBOT
Looking for somebody to check my work since my teacher did not post the answer k...
@vapid grotto Has your question been resolved?
vapid grotto
No
And I’m really confused about these
I have a test on Friday and don’t understand at all and I don’t think we can use a calucltor and I’m really panicking
Because I cannot do 4x4x4 even with writing it out and a lot of these I would have to guess and multiplying like that would take five minutes for one guess since I have to double check
ornate rune
Looking for somebody to check my work since my teacher did not post the answer k...
You can check your work on the graphing part using a graphing calculator
vapid grotto
I don’t understand how 😭
And honestly I’m mainly worried about the equations and the thing above
I’m super screwed for the converting stuff
ornate rune
I don’t understand how 😭
Input the function at the graphing calculator then hover your mouse
ornate rune
And I’m really confused about these
In what part are you confused on here
vapid grotto
In what part are you confused on here
The whole thing mainly fractions
I really don’t understand
vapid grotto
Like how do I know when to put this
ornate rune
Like how do I know when to put this
What's the given
vapid grotto
What's the given
And I’m not sure how to square root and cube root and whatever root without a calucltor
dire geode
,tex .exp rules
wraith daggerBOT
riemann
vapid grotto
I understand that
But idk how to convert between them
And how to square root without a calculator
I have no idea how we got to eight
Because 16^3 is not equal to 2^3
ornate rune
What's the 4th root of 16?
ornate rune
Aren’t we supposed to do the expoient thats attached to the number first
U mean cube 16 first?
Sure you can do that, you'll still get the correct answer
vapid grotto
How do you know when to do that method
ornate rune
Try doing it, you'll see why did they took a different route
vapid grotto
Also why for the equations that look like this ( 64^(1/2) ) do we get 8 but 8 is not haft of 64
ornate rune
Also why for the equations that look like this ( 64^(1/2) ) do we get 8 but 8 is...
64^(1/2) is sqrt(64)
ornate rune
Square root
ornate rune
64^(1/2) is sqrt(64)
That fractional power doesn't mean you divide it
ornate rune
**riemann**
It is basically this rule
vapid grotto
So 1/3 is x^3
ornate rune
No
ornate rune
**riemann**
Rule
vapid grotto
I’m so confused then why would we get the square root or cubed root of the number then
ornate rune
**riemann**
In simple terms, basically when you have a^(x/y) the y (denominator) would be the nth root and the x (the numerator) would be it's integer power
ornate rune
Also how would postive 64^(1/2) equal 1/8
First rewrite that to square root
Then take square root of that
ornate rune
Wouldn’t the exponent be negative
Why?
vapid grotto
First rewrite that to square root
It’s 8 not 1/8
ornate rune
**riemann**
The rule doesn't state that
vapid grotto
My teacher said that
ornate rune
It’s 8 not 1/8
Correct
ornate rune
My teacher said that
Are you sure?
ornate rune
That's correct
ornate rune
Also how would postive 64^(1/2) equal 1/8
If you mean by this 64^-(1/2) = 1/8 then yes that's trur
vapid grotto
It’s how it’s done for every other problem similar to it
ornate rune
Uh tbh idk where are you confused
ornate rune
soo?
vapid grotto
Why would it be a postive 1/2?
The answer key says it’s postive but I thought it’s negative
vapid grotto
vapid grotto
Yea I’m having a lot of trouble
ornate rune
And checking if you applied the rules correctly
vapid grotto
I’m fine with everything else in the unit
I just cant get it in my brain and idk where to get extra pratice
Bevause I can memorize these numbers but that only helps me if the same numbers are on the test
ornate rune
And you got the items where the top part is given correctly
ornate rune
At 1/8 part you got it wrong
It is supposed to be raised to a negative exponent
How do you know? Something raised to a negative exponent means reciprocal
ornate rune
Here you can see 64^(1/2) = 8
vapid grotto
Yea
ornate rune
Therefore you can conclude that 1/8 = 64^-(1/2)
vapid grotto
So when it’s 1/8 the expoinet should be negative
vapid grotto
I’m going to make a Quizlet with the pratice ones I have so hopefully that helps
And I’m going to see if I can guilt trip my teacher into letting me use a calculator…
ornate rune
And I’m going to see if I can guilt trip my teacher into letting me use a calcul...
Uh yk you don't need a calculator for those
quaint berry
So when it’s 1/8 the expoinet should be negative
1/8=8^-1
cedar kilnBOT
@vapid grotto Has your question been resolved?
vapid grotto
Uh yk you don't need a calculator for those
To be fair yea but it takes me five minutes to cube stuff and depending on the number squaring also
Like 9x9 I would break it up into 4x4 and 5x5
scarlet token
cedar kilnBOT
scarlet token
whatever the fuck this is
quaint berry
What question do you have doubt on
left heart
for the first one, it describes a curve where as you get closer and closer to x = 1, the curve looks like it goes towards 2. but the actual value at x=1, is 1.
scarlet token
What question do you have doubt on
b) tiill d)
i understand thr first but other than that i don't understand what they're saying
especially c)
left heart
as x approaches 3, y approaches infinity.
meaning, the closer you get to 3, the larger y gets, so much so that it never actually reaches 3.
quaint berry
especially c)
In c when x is just after 2 its -1 when just before 2its 3
scarlet token
wait i can see it now so for b) the line just shoots upwards near vertically but never reaching 3
scarlet token
i thought it's a straight line with a discontinuity at x=2
left heart
it can be anything with a discontinuity at x=2.
scarlet token
it can be anything with a discontinuity at x=2.
oh
left heart
its just "a function with this property"
scarlet token
since function arent implicitly stated i see
left heart
yeah
scarlet token
yeah
wait if it can be anything how do you draw it
anything as long as discontinuity at x=2?
left heart
and a point at (1, 1)
scarlet token
so this is correct i presume?
scarlet token
wait i understand that but i drew the discontinuity wrong i think
left heart
the discontinuity is at y=2 the point is at y=1
scarlet token
should the discontinuity be at (1,1) ?
left heart
u have it backwards
left heart
no
"lim x -> 1 f(x) = 2"
not f(x) = 2
the limit isnt a separate statement
its part of one expression
left heart
the actual point at f(1) is 1
scarlet token
oh
left heart
hence the discontinuity
scarlet token
okay i understand
scarlet token
i understand2
left heart
ye
scarlet token
so for c, then as x approaches 2, theres a sudden discontinuity at -1, then from the other side as x approaches -2 theres a sudden discontinuity at 3?
left heart
yeah
scarlet token
when it has small plus and minus sign
so wait graph should look like this right
top is discontinuity at y=3
and bottom is discontinuity when y=-1
am i correct?
left heart
yes
scarlet token
ok so for d) e) what does it means when x-> infinity?
means all value of positive x?
so means theres a graph at negative side of x with the right side at y=-2 completely undefined?
left heart
ok so for d) e) what does it means when x-> infinity?
it means as x gets larger, y approaches -2. maybe at x = 10, y= -1. x = 1000, y = -1.8, x = 10^100, y = -1.99 etc.
left heart
is it correct or
you said "am i correct" and i said yes idk what u want
scarlet token
so means theres a graph at negative side of x with the right side at y=-2 comple...
for this i mean lol
is my statement correct
sorry for confusion
scarlet token
it means as x gets larger, y approaches -2. maybe at x = 10, y= -1. x = 1000, y ...
i see
so the graph should be almost horizontal but approaching y=-2 but never reaching y=-2
so for e)as x get negatively larger then y approaches negative infinite soo
left heart
y = x satisfies e
if y gets lower as x gets lower, and there's no asymptote, then its correct for e)
scarlet token
if y gets lower as x gets lower, and there's no asymptote, then its correct for ...
ooh
scarlet token
if y gets lower as x gets lower, and there's no asymptote, then its correct for ...
thanks so much for the help ! really appreciate them
left heart
ye
opal garden
nice!
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inland helm
How do I solve number 20?
cedar kilnBOT
How do I solve number 20?
ripe bane
How do I solve number 20?
lmk if this makes sense
coral jewel
!nosols
cedar kilnBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
inland helm
Is the picture irrelevant to the question? I see how it makes sense.
ripe bane
Is the picture irrelevant to the question? I see how it makes sense.
i mean you don’t need to use it so its kinda useless
inland helm
Okay, so it's just there to throw you off then?
ripe bane
As a helper, please do not give out answers that could be copied as a homework s...
should i delete it
coral jewel
yes you should
ripe bane
oki then,but ion have the time to explain each step so imma leave it to someone then
inland helm
No, I assume something with x.
inland helm
wdym
coral jewel
No, I assume something with x.
yeah
in general, if you have an integral in this form
$\int\frac{\dd x}{x^n + a^n}$
wraith daggerBOT
coral jewel
your trig sub will be x = atan(u)
scenic heron
this isnt a trig sub
inland helm
I know I'm supposed to use an inverse
scenic heron
i checked
coral jewel
this isnt a trig sub
?
scenic heron
i can send the ss but its the solution
inland helm
It's supposed to be a derivative of an inverse trig function
scenic heron
see what you get :)
1/(u^2 + 1) is a common integral
coral jewel
i mean sure if you want to get 16 out and do u = x/16, then go ahead
jade plume
Why do we have letters in math?
coral jewel
but im aiming for a more general solution
either way, lets not argue over such trifle
scenic heron
but im aiming for a more general solution
i see well as long as it works it doesnt matter ig
coral jewel
go somewhere else to ask that question
inland helm
How do you go from 1/(a^2+x^2)dx to 1/a arctan(x/a)?
coral jewel
your trig sub will be x = atan(u)
inland helm
I just don't get it in general.
coral jewel
well you surely know what a u-sub means right?
ripe bane
well you surely know what a u-sub means right?
its ok if they don’t
coral jewel
no it is not
if they got to trig sub without knowing what u-sub means, that's a problem
ripe bane
I just don't get it in general.
bro check it on yt there are many explanations
ripe bane
if they got to trig sub without knowing what u-sub means, that's a problem
yeah but they can always learn
its alright if they don’t know now
ripe bane
you are completely missing my point
ok mb
coral jewel
either way, let's not argue
ripe bane
I just don't get it in general.
i gtg now so hopefully you get it
inland helm
I know how u sub works its just setting it up is the problem. That's how it's always been for me is just the set up.
Each problem is different so it always throws me off on how to set it up.
coral jewel
okay, let's look at this integral shall we?
what i want you to do is to substitute x = a*tan(u)
fill in the blank, thus dx = ...?
!occupied
cedar kilnBOT
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jade plume
Oops wrong channel
inland helm
fill in the blank, thus dx = ...?
2x?
coral jewel
you should probably watch this https://www.youtube.com/watch?v=ocgjfF2AboA
wouldnt be productive to just start teaching you trig sub all over again
inland helm
I appreciate it, I'll see. I'm just screwed all around at this point.
cedar kilnBOT
@inland helm Has your question been resolved?
cedar kilnBOT
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vestal sandal
my channel now
cedar kilnBOT
my channel now
vestal sandal
isnt their answer wrong
the Area of plate is pi capital R square - pi small r squared
as it is said in the question the mass of this plate
the plate with the hole
is M
cedar kilnBOT
@vestal sandal Has your question been resolved?
cedar kilnBOT
@vestal sandal Has your question been resolved?
slim anchor
hi
vestal sandal
ih
cedar kilnBOT
@vestal sandal Has your question been resolved?
acoustic plank
Hi
silver oxide
aight so whats the largest common factor that u can pull out
acoustic plank
6
acoustic plank
right, so u now have 6(x^2 - 4) right?
How did you get that
silver oxide
so like u said 6 is the largest factor in both terms
acoustic plank
Yes
silver oxide
so we take out the 6 from 6x^2 and since 24 is 6x4 we also take the 6 out of that
and leave the 4
acoustic plank
Why would it not be 6x(x-4x)
cedar kilnBOT
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acoustic plank
Oh right
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@acoustic plank Has your question been resolved?
dire radish
I’m looking at my answer key here, “Find solution of the differential equation that satisfies the initial condition” problem 14
dire radish
Can someone explain to me the second to last step
Isn’t there suppose to be a 2
Divide by the right side
I don’t know where it went
My work if u want to see
Don’t I divide by 2 and square other side
But the answer key is different
Skull
Figured it out
They did do it
.close
cedar kilnBOT
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Available help channel!
inner solar
Let there be matrix $A:\mathbb{R}^m\rightarrow\mathbb{R}^n$, whose $rank(A)=m$ and matrix $B:\mathbb{R}^n\rightarrow\mathbb{R}^m$, whose $rank(B)=m$. How can i show that $AB$ is invertible?
wraith daggerBOT
Slowaq
inner solar
i know that rank(AB)≤min{rank(A),rank(B)} but dunno how that helps
dire geode
maybe try applying rank-nullity theorem to AB
https://brilliant.org/wiki/rank-nullity-theorem/
actually probably not new information than the rank(AB) <= min inequality you already stated
fallen jetty
Is that sentence actually true?
If you take $A \in \operatorname{L}(\mathbb{R},\mathbb{R}^2)$ given by $A(x) = (x,0)$ and $B \in \operatorname{L}(\mathbb{R}^2,\mathbb{R})$ given by $B(x_1,x_2) = x_2$, then we have $\operatorname{rank}(A) = 1$, $\operatorname{rank}(B) = 1$, and $AB(x_1,0) = 0$ for all $x_1 \in \mathbb{R}$
Or did I miss something?
wraith daggerBOT
ucheo
fallen jetty
Sorry for the edits ^^
prisma laurel
yeah I would guess you need to assume $\operatorname{image}(A)\cap \ker(B)={0}$ or something
wraith daggerBOT
derivada.schwarziana
cedar kilnBOT
@inner solar Has your question been resolved?
dire geode
Let there be matrix $A:\mathbb{R}^m\rightarrow\mathbb{R}^n$, whose $rank(A)=m$ a...
can you show the original question. picture or screenshot
inner solar
can you show the original question. picture or screenshot
its in czech so dunno if it helps but translation should be correct
but yes these is mistake
wraith daggerBOT
Slowaq
inner solar
we were supposed determine whether its treu or not
but yea i overlooked the correct answer and its not correct
dire geode
dire geode
If you take $A \in \operatorname{L}(\mathbb{R},\mathbb{R}^2)$ given by $A(x) = (...
they gave you the answer here
cedar kilnBOT
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earnest garden
cedar kilnBOT
earnest garden
can someone please check if this proof is right?
cedar kilnBOT
@earnest garden Has your question been resolved?
prisma laurel
Always the proofs that get ignored :(
yeah it's more effective to ask about proofs in the topic channels, maybe #linear-algebra in this case
lemme check this one rq though
prisma laurel
yeah your proof is correct
earnest garden
aaah thank you very much
earnest garden
yeah it's more effective to ask about proofs in the topic channels, maybe <#5402...
oooh okay ill do that next time then :)
prisma laurel
earnest garden
.close
cedar kilnBOT
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crisp mantle
how is this not rounded correctly lmao
cedar kilnBOT
how is this not rounded correctly lmao
muted timber
cuz it's not computed correctly
you're given a 6% interest annually for two years.
$10000$=PV\cdot (1+0.06)^2$
wraith daggerBOT
LordFelix
muted timber
also, a 6% compound yearly is not the same as a 3% compound every six months, which is what you appear to have done
wraith daggerBOT
cedar kilnBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
wraith daggerBOT
muted timber
the idea is not for you to give the result just because, ago
like literally everything else in maths
lol no, what
those of us who actually teach properly ask our students to actually learn the formulas and how to obtain them, in case they cant remember them, or they arent given.
Also, again, you should not just straight up give the answers to the problems. If you want to help, you need to help the guy asking understand how to do it themselves
crisp mantle
wait ive been using the compund interest formula on previous examples and getting it correct i dont seem to know what is diff ab this one besides the fact i have to find P this time.
muted timber
wait ive been using the compund interest formula on previous examples and gettin...
as i said before, the mistake is that you assumed that it was four payments at 3% interest
when it is two payments at 6% interest, or four payments at 2.9563...% interest
you got a 6% annual
so anually, you multiply your capital by 1.06
so every six months, you dont multiply your capital by (1.06)/2, you multiply it by sqrt(1.06)
wraith daggerBOT
cedar kilnBOT
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muted timber
well, since the first three are marked as correct when they arent, you definetly didnt get it properly taught
crisp mantle
wait sorry im a little confused is the formula that im using is P(1+r/n)^n*t the same as what ur doing?
muted timber
wait sorry im a little confused is the formula that im using is P(1+r/n)^n*t th...
what is r, n and t there?
crisp mantle
thats literally what im trying to doo..?
since when did asking someone a qs on this seerver come wirh a side of sass?
this was the example i went off of im not entirely sure what u guys are saying tbh
muted timber
okay, so apparently you're using the interest used in advertisement instead of the equivalent interest
...
9%/100 = 0.0009
ago, please stop
im not teasing you. I'm telling you to shut up
anyways rain, with that formula you were given, your result is still not correctly computed
you'd have the following:
$10000$=PV\cdot(1+0.03)^4$
wraith daggerBOT
LordFelix
muted timber
which gives you a PV of 8884.87(047) instead of what you wrote of 8888.47
muted timber
it does ask to round up
and that's why i added the other decimal places. Rounding up, you'd have 8884.88
wraith daggerBOT
muted timber
<@&268886789983436800> can we get someone to stop @molten basin spamming crap please?
crisp mantle
<@&268886789983436800> can we get someone to stop <@971531002310713424> spamming...
clock it
crisp mantle
and that's why i added the other decimal places. Rounding up, you'd have 8884.88
oh so regardless of the 3 deciaml place im still gonna round up?
crisp mantle
oh i see i shouldve just read teh question more carfeully mb
muted timber
i very much dislike tests in computer because they have a ton of bullshit like "if you dont input the answer in whatever draconic way we want it's wrong no matter if you know how to do the thing"
crisp mantle
i still dont really know what u gusy were talking ab in the begining
muted timber
It's basically on how you understand the compunding
if you use the "true" interest, it would be the one i've mentioned
if you use the "advertisement" interest, it would be the formula you were given
crisp mantle
i don t think ive leaned the other
muted timber
dont worry about it
it's basically understanding it as "per payment" instead of "per time"
crisp mantle
ohhh
muted timber
it's pretty obvious if you go with easier numbers
for example, let's say you have a 20% interest.
First payment will multiply your shit by 1.2
Second payment by 1.44
if we go by true interest
let's say we now use the "advertisement" 20% interest, but paid every half year. So "in theory", you'd get 10% (as you were given
your "half" payment would multiply your shit by 1.1 each time
but 1.1*1.1=1.21, not 1.2
muted timber
to have the equivalent real interest, you would multiply your shit by sqrt(1.2)=1.0954... so you'd really only have a 9.54% interest
that's why banks have in small letters the annual equivalent interest
and in big ass letters the advertisement one
and you'll notice that the advertisement one is always higher
crisp mantle
but i dont thnk theyre planning onteaching us that . what im learning now is the most theyr eteachig up to
muted timber
and that's perfectly fine
as long as you understand which one you're asked about
it is a linguistic difference, after all
cedar kilnBOT
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formal river
cedar kilnBOT
wraith daggerBOT
formal river
So now that I have values of y wheee p’s slope = 0
How would I do second derivative test to determine if it’s a relative max or min if it’s values of y
crimson sedge
b or c ?
formal river
B
Would I set dp/dt = to 0 and 180
Get values of t then do derivative test
That won’t help me
Idk
crimson sedge
we are to find when P grows most rapidly
we know that the growth of p = $\frac {dP}{dt}$
wraith daggerBOT
crimson sedge
most rapidly means $\frac {dP}{dt}$ should be maximum
wraith daggerBOT
crimson sedge
which means you have to find $\frac{d^2 P}{dt^2}$
wraith daggerBOT
