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#help-49
rare musk
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rare musk
Did I approach this question correctly trying to use the double handle identity
grave summit
Did I approach this question correctly trying to use the double handle identity
is the question to prove cos 4w = LHS??
rare musk
yes
grave summit
because if so you can just use "compound angle formulae" by splitting into 2w and d2w and then call it a day
RHS --> LHS
rare musk
i have to make the lhs look like the rhs though
grave summit
does it FORCE u to say you go from LHS to RHS
cos usually in proofs you can go RHS to LHS as well??
wait it's not an identity
nvm
nvm
yh just use doduble angle with 2w
it's emantics
semantics
rare musk
did I do anything right in the left hand side expansion
rare musk
towards the end I felt as if I might be doing it wrong since i put v^2 and instead took the square out to the coefficient of v instead to make it equal
modern pendant
In physics why does contact velocity mean constant speed but constant speed does not equal constant velocity?
midnight plankBOT
In physics why does contact velocity mean constant speed but constant speed does...
unique pond
In physics why does contact velocity mean constant speed but constant speed does...
Velocity is a vector while speed is just a number that represents the length of that vector so if the velocity is constant the direction and speed are constant but if speed is constant than just the speed is constant but the direction is not given
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blissful tree
Hey guys, I'm new to this community and I'm looking for help, I just want to see if my answer is correct.
(The exercise is in Spanish, sorry, but it's my first language)
midnight plankBOT
Hey guys, I'm new to this community and I'm looking for help, I just want to see...
odd solar
Hey guys, I'm new to this community and I'm looking for help, I just want to see...
Hay q tener cuidado con las direcciones de las desigualdades. En el primer ejemplo tienes para el dominio [-2, 3] y eso esta correcto. Pero en forma de desigualdades, tienes que x es mas q -2 pero tambien mas q 3
blissful tree
Hay q tener cuidado con las direcciones de las desigualdades. En el primer ejemp...
¿Hablas Español? Gracias...
Tengo mis dudas, por que en la parte de "Agrupación", en Dominio tengo [-2, 3), y en Rango no supe que poner, me base en Y, y coloqué (-4, 5)
Mi mayor duda es en la parte de "Desigualdad", entiendo que debo usar la notación de desigualdades, pero no se que valor asignarle a X.
(I'm so sorry if we can't speak in Spanish in this server, but I don't undertand really well English)
odd solar
¿Hablas Español? Gracias...
Tengo mis dudas, por que en la parte de "Agrupación...
Mas o menos, creci en inglaterra asi q no estoy bien familiar con terminos especificos a las matematicas
Se ve como q has identificado q el dominio de x queda entre -2 y 3. En forma de desigualdades, sera -2 <= x < 3
Con el rango, yo diria q esta [-4, 5]
odd solar
Con el rango, yo diria q esta [-4, 5]
Con esto, me podras decir el rango en forma de desigualdades?
blissful tree
Mas o menos, creci en inglaterra asi q no estoy bien familiar con terminos espec...
Aprecio tu ayuda, mi profesor nunca me dio un valor a X, así que por el momento le estoy asignando 0.
Revisando nuevamente, lo corregí de la siguiente manera; Df = -2 > X < 3
Y lo que me comentas del rango [-4, 5], no entiendo por qué quedaría así, entiendo que "[" se usa cuando el valor es igual o mayor/menor, y "(" cuando el valor solo es mayor o menor, nunca igual, si pudieras aclararme eso estaría excelente.
odd solar
(I'm so sorry if we can't speak in Spanish in this server, but I don't undertand...
Esta bien hablar español, pero la mayoría hablan ingles asi q puede ser q hay q esperar mas para ayuda
Borro mi respuesta
Espera
Hay que extraer el valor de x del grafico y eso seria el dominio, los posibles valores de x aceptable
Y lo q dijiste del uso de [ y ( esta bien
Pero todavia con tu corregion esta incorrecto por los dirreciones de los desigualdades
Especificamente el primer desigualdad
blissful tree
Analizando mi situación directamente creo que no sé nada de leer gráficas.
Empecé a realizar el ejercicio 2, y me dio que en "Agrupación" Df = [-6, ∞)
Y en la parte de Rango, no sé si tomar el valor de 3 (tal y como lo indica la gráfica)
¿Te puedo pedir un favor? Explícame como realizar el ejercicio 2, con eso yo creo poder entender el tema mejor. 
blissful tree
> Df = [-6, inf)
Esto esta bien!
¿Sí? 😭
Pues el Rango es la distancia o los valores dentro de un conjunto de números, ej.
1 - 10
Su rango es 2, 3, 4, 5... 9
(Según yo)
Para realizar los ejercicios de las gráficas tomé como referencia el punto más alto y el más bajo (Y).
odd solar
El rango es todos los valores posible de Y para el dominio q corresponde
odd solar
Para realizar los ejercicios de las gráficas tomé como referencia el punto más a...
Si asi se hace
En el segundo caso la fecha es importante
Por que indica que la funcion contiua a subir (asi se dice?)
blissful tree
Entonces, mi siguiente respuesta en Agrupación es:
Rf = [-3, ∞]
Creo que acabo de entender tu punto de los "[]", en el Rango si tengo 1-9, mi rango usa 1, 2, 3, 4... 9, ¿Correcto?
blissful tree
Por que indica que la funcion contiua a subir (asi se dice?)
If you'd like I can speak English.
odd solar
Rf = [-3, inf]
Esta bien, solo q para infinidad siempre se usa )
No, tengo q practicar mi español
blissful tree
> Rf = [-3, inf]
Esta bien, solo q para infinidad siempre se usa )
Entonces, cuando es indefinido sería ")".
En este caso, en Rf de Agrupación es:
Rf = [-3, ∞)
blissful tree
Si, esta perfecto!
Voy entendiendo... Muchas gracias de verdad, no sabes lo mucho que lo aprecio.
En la forma de Desigualdad me comentaste que teníamos que sacar el valor de X, ¿Cómo se hace?
odd solar
Osa, no se saca el valor de x porque ya sabes que x es entre [-6, inf)
Solo hay q escribirlo en otra forma
En este caso es simple porque solo hay una (bound?) para x
Limite?
Porque x es -6 o mas
blissful tree
Limite?
¿Podrías darme la respuesta de la Desigualdad de Df?
Y si se puede explicado, por qué a partir de aquí ya me confundí un poco... 
odd solar
Df = x > -6
blissful tree
Df = x > -6
Entonces en Rf es:
Rf = x > -3
odd solar
Si!
Porq x > -6 significa ‘x es mas que -6’
A pero tiene q ser >= porq es mas o igual
Asi q Df = x >= -6
blissful tree
Entonces, simplemente para confirmar voy a volver a hacer el ejercicio 1:
Agrupación:
Df = [-2, 3]
Rf = [-4, 5]
Desigualdad
Df = x > ?
Rf = x > ?
En Desigualdad volví a tener dudas, en Df tengo que mi X vale [-2, 3], ¿Con qué debería comparar mi X?
blissful tree
Asi q Df = x >= -6
¿Entonces Rf también aplica con >= por ser inf?
odd solar
Por ser inf no
Es porque x es mas o igual a -6
Es lo mismo q [ contra (
Pero en otra forma
odd solar
Entonces, simplemente para confirmar voy a volver a hacer el ejercicio 1:
Agrup...
Este primer ejercicio tiene un limite de arriba, no va a inf, asi que hay dos desigualdades
blissful tree
Este primer ejercicio tiene un limite de arriba, no va a inf, asi que hay dos de...
Entonces, en Desigualdad, Df = -2 ? X ? 3
Aquí tengo que asignarle un numero a X, ya sé que X = [-2, 3]
¿Pero que hago aquí?
odd solar
X queda entre -2 y 3, x = [-2, 3), asi q ‘x es mas o igual a -2 y menos que 3’
.> es ‘mas que’, < es ‘menos que’
Ayuda eso?
blissful tree
X queda entre -2 y 3, x = [-2, 3), asi q ‘x es mas o igual a -2 y menos que 3’
...
Entonces, X es un valor random entre -2 y 3:
Df = -2 < X < 3
blissful tree
Con <=
¿Sí? Pero es [-2, 3], ambos son numeros cerrados, según yo no puede ser igual.
odd solar
Hey guys, I'm new to this community and I'm looking for help, I just want to see...
El dominio es todos los valores de x en la linea naranja
odd solar
¿Sí? Pero es [-2, 3], ambos son numeros cerrados, según yo no puede ser igual.
Es [-2, 3), -2 incluido, 3 no
blissful tree
Es [-2, 3), -2 incluido, 3 no
Ya ví por que, en el 3 no se muestra que sea ni cerrado ni abierto, entonces se toma con un ), ¿Correcto?
blissful tree
Por la linea puntado
¿Con esa línea significa que es cerrado?
odd solar
En mi opinion, no es claro
Porque lineas puntados normalmente no corresponden a cerrado
blissful tree
Hmm, una solución que yo creo sería:
Df = -2 > X < 3
No uso = debido a que al ser numeros cerrados, no pueden ser iguales.
odd solar
Pero en este caso se ve como q lo usan para indicar q esta incluido
Pero el -2 definitivamente esta incluido
Seria Df = -2 <= X < 3
blissful tree
Pero el -2 definitivamente esta incluido
¿Por qué esta incluido?
¿No se supone que cuando tiene el . completamente cerrado significa que no puede ser igual?
odd solar
Porque, leyendolo izquerda a derecha, -2 es menos o igual a X y X es menos q 3
Esta incluido por el circulo ne
Gro
Borra mis mensajes cuando digo black
blissful tree
Entonces, cuando el circulo es completamente cerrado, ¿Puede ser =>/<=?
Si el circulo es abierto, ¿Es >/<?
odd solar
Exactamente
odd solar
Porque, leyendolo izquerda a derecha, -2 es menos o igual a X y X es menos q 3
Y por esto significa q Df = -2 <= X < 3
blissful tree
Uy...
Df = -2 <= X => 3
blissful tree
Y por esto significa q Df = -2 <= X < 3
Hmm, ¿Hay algún problema si decido tomarlo como X => 3? Tengo mis dudas respecto a tomarlo como ( [.
odd solar
De nuevo, no es claro. Normalmente se usa circulos para indicar si esta cerrado o no
Asi q preguntale a tu prof
Yo creo q 3 no esta incluido
Porque la linea esta puntado
blissful tree
De nuevo, no es claro. Normalmente se usa circulos para indicar si esta cerrado ...
Por lo mientras voy a tomarlo como X => 3.
blissful tree
Entonces:
Rf = -4 <= X <= 5
odd solar
O tambien 3 >= X esta correcto
blissful tree
Cuidado con la direccion
Lo acabo de ver, gracias.
odd solar
Entonces:
Rf = -4 <= X <= 5
Si esta perfecto esto
Si hay que tener mucho cuidado con las direcciones cuando combinas los desigualdades
blissful tree
Oof... Creo que ya entendí, tengo otros 2 ejercicios, voy a intentar hacerlos por mi cuenta.
De verdad, no sabes lo mucho que aprecio tu ayuda, la verdad es que no tengo muchas clases de matemáticas en mi nuevo horario y mi examen es en pocos días, estoy tratando de sacar el conocimiento que pueda.
blissful tree
Si hay que tener mucho cuidado con las direcciones cuando combinas los desiguald...
Si, noté que me falla un poco, gracias por recordarmelo nuevamente.
odd solar
Mandame mensaje si nadie te ayuda y cuando estoy libre te puedo ayudar
blissful tree
Mandame mensaje si nadie te ayuda y cuando estoy libre te puedo ayudar
Muchas gracias, vuelvo en un momento para verificar si mis respuestas por mi cuenta de los nuevos ejercicios han sido correctas. 
odd solar
Puede ser q me quedo dormido, me tengo q levantar temprano en la mañana
Pero lo puedo chequear en la mañana si me quedo dormido
blissful tree
Puede ser q me quedo dormido, me tengo q levantar temprano en la mañana
De hecho ya resolví uno, lamento mucho las molestias.
Agrupación:
Df = (Inf, 6]
Rf = (Inf, -3]
Desigualdad:
Df = <= 6
Rf = X <= -3
odd solar
Tienes q indicar si va negativo inf o no
Y el numero menor siempre va al lado izquierda
blissful tree
Tienes q indicar si va negativo inf o no
En este caso, sería:
Agrupación:
Df = (-Inf, 6]
Rf = (-Inf, -3]
Desigualdad:
Df = 6 => X
Rf = -3 => X
odd solar
El rango va a +inf, porque sube la Y
blissful tree
El rango va a +inf, porque sube la Y
Agrupación:
Df = (-Inf, 6]
Rf = (Inf, -3]
Desigualdad:
Df = 6 => X
Rf = -3 => X
odd solar
Rf =[-3, inf), numero menor a la izquierda
blissful tree
Rf =[-3, inf), numero menor a la izquierda
Agrupación:
Df = (-Inf, 6]
Rf = [-3, Inf)
Desigualdad:
Df = 6 => X
Rf = -3 => X
odd solar
Agrupación:
Df = (-Inf, 6]
Rf = [-3, Inf)
Desigualdad:
Df = 6 => X
Rf = -3 =>...
Ahi se ve bien 🙂
Cuando hay solo un desigualdad, es comun a poner el variable a la izquierda, pero igual esta bien
blissful tree
Dios... Yo era bueno con las matemáticas hasta que metieron a X, muchas gracias nuevamente por tu ayuda, de verdad lo aprecio.
Descansa, buenas noches. 
odd solar
Buenas noches!
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mighty hare
The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly's reasoning is correct or incorrect?
She is incorrect because systems may have only complex solutions which are not visible on a graph.
She is incorrect because the solutions may have multiplicity greater than 1.
She is correct because all solutions are intersection points of the graphs.
She is correct because the solutions are irrational.
midnight plankBOT
The graphs of two polynomial equations do not intersect. Kelly concludes that th...
mighty hare
i thought it was d idk tho
hearty rune
by d do you mean the 'irrational' one? That wouldnt be the answer
mighty hare
by d do you mean the 'irrational' one? That wouldnt be the answer
yeah
hmm
then if it aint that one i assumw A ??
hearty rune
why
mighty hare
ik theres like complex solutions in some graphs that aint seen
i just dont know if it woukd apply to graphs that dont intersect
hearty rune
it would
consider y=x^2 and y=2x^2+1
if we're purely speaking in terms of real numbers then there are no solutions, we see this graphically because on the xy plane they dont intersect
but if you solve x^2=2x^2+1, it does have complex solutions
mighty hare
ohhh okok i see, so A is right
modern pendant
This possible?
midnight plankBOT
This possible?
modern pendant
Like that’s a really damn big number
fallow scarab
why does it matter if it's big
modern pendant
I mean anything ^50 is gonna be kinda hard to even get a number for
modern pendant
why does it matter if it's big
Rieman you didn’t give me a sum 🗿
fallow scarab
I mean anything ^50 is gonna be kinda hard to even get a number for
you're supposed to give an exact value
modern pendant
But the software doesn’t even give me the option for the notation to even make this bearable to type out
Yeah no wait this can’t be serious I gotta email my prof or something
fallow scarab
show your work and try inputting the exact value
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zinc kelp
Do you guys know how to run doom in a calculator
midnight plankBOT
Do you guys know how to run doom in a calculator
@zinc kelp Has your question been resolved?
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@zinc kelp Has your question been resolved?
waxen linden
Do you guys know how to run doom in a calculator
lol
if you're still wondering
what calculator
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icy jungle
To get line 6 the correct rule would be addition using line 4 right?
midnight plankBOT
To get line 6 the correct rule would be addition using line 4 right?
dreamy lichen
what is that?
icy jungle
discrete math
dreamy lichen
what are premises?
it looks like a random sequence of statements
is that sequence supposed to mean something?
dreamy lichen
okay
line 6 follows from line 5
I thinnk
by disjunction introduction or similar rules
idk what set of rules are you working with
A entails A v B
icy jungle
Equvalence rules and Inference rules
dreamy lichen
Equvalence rules and Inference rules
Yeah, the thing is that there are many derivation system and each one has different set of inference rules
dreamy lichen
A entails A v B
^ do you have a rule like that?
icy jungle
let me check my notes rq
dreamy lichen
if you don't, then please send all the rules you have
icy jungle
1.Modus Ponens
2.Modus Tollens
3.Hypothetical Syllogism
4.Disjucntive Syllogism
5.Addition
6.Inconsistency
7.COmmutitive
8.Associative
9.Distibutive
10.De Morgans Law
11.Implication
12.Controposition
13.Double Negation
14.Equivalence
15.Exportation
icy jungle
if you don't, then please send all the rules you have
^ these are all the rules
icy jungle
so pretty much I add the D prime to the H prime
dreamy lichen
yes
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graceful ferry
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fallow scarab
maybe try finding a basis for U?
graceful ferry
Wait i did sum let me write it down
How do i find for which value of a is r(A)>=2
dawn dagger
How do i find for which value of a is r(A)>=2
You need at least 2 linearly independent vectors
I guess you could do the reverse and ask for which a is r(A) < 2 which is the same as r(A) = 1
graceful ferry
Wait i think my matrix is wrong its U+W
How do i find the intersection of U and W
dawn dagger
iirc you write the linear combinations of U and V and equate them
frail carbon
U is not the span of {1+x^2, i+x^3, -i+x, 1+x^4} btw
Ignoring a sign error in the last one, -i+x and i+x^3 aren't even in U because they aren't polynomials with real coefficients
fallow scarab
Whats U then
e.g. x^2 + 1 is in U
there could be others, not sure, but you should find them via gram schmidt or otherwise
graceful ferry
Im sorry i dont know gram schmidt
frail carbon
You can show that every polynomial in U is divisible by x^2+1
And from there somehow show it has dimension 3
btw while i+x^3 isn't in U, x+x^3 is which with 1+x^2 and -1+x^4 would be a basis for U
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last slate
Hello! Can someone help me understand these radical problems?
midnight plankBOT
Hello! Can someone help me understand these radical problems?
last slate
hearty rune
what have you done so far?
last slate
Nothing so far, I’ve picked some I thought I’d have trouble with I’m on a newer level with these
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last slate
I think this is all I really know what to do for radicals
last slate
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worthy kestrel
midnight plankBOT
worthy kestrel
how do we know the highlighted part?
http://abstract.ups.edu/aata/struct-section-finite-abelian-groups.html
agile lichen
what is it exactly you don't understand?
worthy kestrel
why aH has order p
agile lichen
this is true by the induction hypothesis
the order of G/H is strictly smaller than G, therefore there exists an element in G/H whose order is p.
worthy kestrel
sorry what is the induction hypothesis
agile lichen
sorry what is the induction hypothesis
do you know how to prove something by induction?
worthy kestrel
yea
agile lichen
the induction hypothesis is in this case: assume the assertion has been proven for all k < n
think of k = |G/H| < n
agile lichen
where does the induction step take place
the induction step would be to prove the case n which is what that paragraph is about
this is the initial case n = 1 and the induction hypothesis:
worthy kestrel
can we use a specific example
say Z6
how does this method show that it has an element of order 3
pick H=<3>
G/H contains g+H
how does induction hypothesis show that g+H has order 3
agile lichen
how does this method show that it has an element of order 3
assume for groups of order < 6 the assertion has been proven. Consider the prime p = 3 which divides |Z6|. For the Subgroup H we know that 3 doesn't divide |Z2|. Therefore is must divide Z6/H. By the induction hypotheis we can find an element in Z6/H whose order is 3, because |Z6/H| < 6.
worthy kestrel
assume for groups of order < 6 the assertion has been proven. Consider the prime...
sorry how did u get the first line where we assume that the assertion is true for order <6. ive only seen it been proven for when order is <1 (which never happens)
agile lichen
sorry how did u get the first line where we assume that the assertion is true fo...
that is the induction hypothesis. You prove the case n = 1 (initial case), and then prove that if for any natural number n, if A(k) is true for all natural numbers k < n (the induction hypothesis), then A(n) is true (induction step). This is just proof by induction.
worthy kestrel
that is the induction hypothesis. You prove the case n = 1 (initial case), and t...
yea but where did we show that if An is true for all n<k, Ak is true?
agile lichen
you don't show that, you show that IF it is true for all k < n then this implies A(n) is true.
worthy kestrel
sorry my statement was the same as yours. i accidentally reversed a and k
worthy kestrel
you don't show that, you show that IF it is true for all k < n then this implies...
where did we show that in this case?
agile lichen
just like how in normal induction you assume the case A(n - 1) is true and then SHOW that this implies A(n)
agile lichen
where did we show that in this case?
that is what the entire rest of the proof is about
worthy kestrel
that is what the entire rest of the proof is about
is it covered in the subsequent lemmas?
agile lichen
i suggest brushing up on your proof by induction skills. Maybe watch a couple of youtube videos or look at a few examples, ideally about STRONG induction
agile lichen
is it covered in the subsequent lemmas?
this is the entirety of the proof
the proof is self contained, it might make references to PREVIOUS lemmas, not subsequent ones
agile lichen
np
worthy kestrel
sorry it took me so long
worthy kestrel
i think like
i needed a more explicit breakdown of the cases
or that would help at least
anyway i got it still
tyty
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orchid dust
The answer is 17 seconds but I don't understand how to get there. I tried solving for final velocity of the first ship and got 34.3 meters per second and that's as far as I've gotten.
midnight plankBOT
The answer is 17 seconds but I don't understand how to get there. I tried solvin...
last slate
so we have 2 objects with 2 velocities, displacements, and accelerations each
using the kinematic equation $x_f = x_i + V_i \cdot t + 0.5 \cdot a \cdot t^2$ we can find this t value
grand pondBOT
Farside29 forever
orchid dust
using the kinematic equation $x_f = x_i + V_i \cdot t + 0.5 \cdot a \cdot t^2$ w...
So 200 = 0 + 5 • t + 0.5 • 3 • t² ?
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orchid dust
Please I don't understand. This is my last problem and the test is tomorrow and I just want to go to sleep. I'm sorry I'm not smart 😭😭😭
orchid dust
<@&286206848099549185> Pardon me but it's been 20 minutes. I've consulted everyone else I can, I'm just not understanding.
orchid dust
Wait what is 66.6 m/s?
fallow summit
Thought it was 16.68 seconds
last slate
No, 200/3
orchid dust
Ah, how do you get there though? In this class we're given the answers but we must figure out how to get there
fallow summit
What class is this
orchid dust
Physics. Not AP, just normal
orchid dust
A friend showed me how to represent this equation on a graph and the answer is where the lines cross but I cannot use graphs on tests
orchid dust
I thought so 😭
Yeah I'm not the brightest math wise
orchid dust
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young summit
brazilian air force exam question
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brazilian air force exam question
young summit
can someone help me?
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young summit
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twilit field
Here would I have to prove every real number can be expressed as the product of two real numbers
midnight plankBOT
Here would I have to prove every real number can be expressed as the product of ...
twilit field
do I prove that there exists a $\lambda \in \R$ such that $\lambda a =b$ , $b \in \R$
grand pondBOT
Veni, vidi, perii
junior flower
and is it not so obvious that you don't even need to mention it
twilit field
and is it not so obvious that you don't even need to mention it
It is
Will probably prove this in a RA course
fast estuary
I think that it would be easier to show any non zero subspace of R has at least one non zero vector in it which could be a basis of U then show the span of that = R
junior flower
1*a = a for any a
twilit field
**Veni, vidi, perii**
again, that would depend on this fact, no?
fast estuary
Because any non zero subspace has at most dimension less than or equal to R
Well any subspace does
twilit field
Haven't done dim yet
fast estuary
Ohh hmm can't appeal to dimension arguments then
I think the best way to approach may depend on your availabile theorems in part
twilit field
hmm, okay
as RA is a sem 3 course, I could probably take this fact for granted for now
fast estuary
Normally a 1st year linear class would cover that just maybe not yet
twilit field
Normally a 1st year linear class would cover that just maybe not yet
hmm, yeah
okay
fast estuary
The best thing to do is use closure under addition properties to show any element of U is in R and vice versa
Something like that
junior flower
**Veni, vidi, perii**
i think what you wanted to say is:
fix a, nonzero. then for every b in R, there exists lambda in R such that lambda*a = b
twilit field
yeah
junior flower
that's different than
every real number can be expressed as the product of two real numbers
and the texit message
twilit field
I see
junior flower
i think what you wanted to say is:
fix a, nonzero. then for every b in R, there ...
but yes, the proof is easy with this
twilit field
how
junior flower
if U is a subspace and not {0}, then U has an element a \neq 0 in it
now you use the definition (or a characterization of the definition, or some properties) of subspace to show every real number is in U
you might think about by saying:
let b be a real number. then b is in U because....
twilit field
there exists a number $\lambda$ such that $\lambda a=b$
grand pondBOT
Veni, vidi, perii
junior flower
yep
midnight plankBOT
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Available help channel!
cinder crescent
can someone help me with this?
midnight plankBOT
can someone help me with this?
cinder crescent
I can do it using u-sub and trig sub but everytime I try IBP I get to a dead end
wise dirge
Show your working for IBP
cinder crescent
tried doing u=x^3 and dv = sqrt(1+x^2)
I get to a dead end trying to find the antiderivative or v
wise dirge
Use the tabular method, much easier lol
X^3 should disappear after taking derivatives 4 times, so the algorithm must terminate
midnight plankBOT
cinder crescent
.reopen
midnight plankBOT
✅
cinder crescent
wait
i run into the same problem though
taking the integral of sqrt(1+x^2)
using trig sub I get to sec^3(x) but I can't find a way out
midnight plankBOT
@cinder crescent Has your question been resolved?
wise dirge
using trig sub I get to sec^3(x) but I can't find a way out
So you’re having trouble integrating sec^3 ?
cinder crescent
yeah
wise dirge
You need to do another integration by parte lo
Lol
Or consult a standard integrals table xd
cinder crescent
what would u and dv be
wise dirge
For sec^3 in particular, you need to use the iterated integral trick
cinder crescent
u = sectheta and dv = sec^2theta?
cinder crescent
alr lemme try that
wise dirge
Diff sec since
cinder crescent
For sec^3 in particular, you need to use the iterated integral trick
we haven't learned iterated integrals yet
wise dirge
For this one, use the IBP FORMULA since you want to rewrite it
wise dirge
we haven't learned iterated integrals yet
Dw, it’s very simple in this case
Because at some point, you’re gonna run into a “loop”
Because notice that both the u and dv terms are trig terms
cinder crescent
ye
wise dirge
So you need to do a trick
Do it once, then name the entire integral expression as “I”, then integrate again
cinder crescent
alr
wise dirge
After integrating again, see if you can spot ‘I’ in your new expression
Now rearrange for ‘I’, which should hopefully cancel out all the integral terms
Also, I’m pre sure you need to use tan^2 = sec^2-1 somewhere
cinder crescent
yeah i did use that
I got secθtanθ - 1/2(sec^2(θ)) - ln(abs(secθ))
so then i js need to convert it back into x and integrate again?
wait i think i did smth wrong
midnight plankBOT
@cinder crescent Has your question been resolved?
scarlet thicket
midnight plankBOT
daring mulch
could you send a larger pic?
scarlet thicket
I’ll try
daring mulch
non continuous function so gint functions graph ig
daring mulch
i think -3 if x belongs to (-4,-1)
uncut cloud
,rccw
grand pondBOT
daring mulch
much better
daring mulch
f(x) = 4 if x belongs to (-1,2]
scarlet thicket
Ok
daring mulch
and - 4 if x belongs to [2,5]
scarlet thicket
They’re both not included ?
daring mulch
They’re both not included ?
which?
yes they are
they both are non negative so they are included
which is why [] is added
scarlet thicket
daring mulch
yes i suppose
scarlet thicket
What ?
daring mulch
What ?
i said that this is the answer accord to me
oh wait
it showss which is correct
rip got 2 wrong
scarlet thicket
Well I try the two again for full points if I get it right this next time
daring mulch
but how is (-4,-1) wrong?
daring mulch
Well I try the two again for full points if I get it right this next time
yea
can you show me the answer key to that question
oh i think since the dots are not hollow
then
[-4,-1]
yes
scarlet thicket
Yeah that’s what o was trying to say earlier
daring mulch
yeaa
daring mulch
then the last questions ans is (2,5]
daring mulch
yes sorr
scarlet thicket
It’s ok
daring mulch
i thought that the numbers in negative ranges are taken by () brackets
but it depends on the dots
nice
scarlet thicket
Yeah I just learned that earlier too haha
daring mulch
haha i wont forget that now
midnight plankBOT
@scarlet thicket Has your question been resolved?
daring mulch
,rccw
grand pondBOT
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last slate
I don't quite understand how to solve questions like this can someone walk me through it please?
midnight plankBOT
I don't quite understand how to solve questions like this can someone walk me th...
@last slate Has your question been resolved?
carmine sigil
@last slate you can set up two equations, one that comes directly from the givens.
EBF = ABF - ABE
The other is a little tricky.
Notice that EBC = 180 - ABE and also EBC = 2EBH = 2HBC
So 2(FBH + EBF) + ABE = 180
If we let FBH = a then we have two equations and two variables. We can solve this system of equations.
midnight plankBOT
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rustic tartan
for a 2D vector we have to apply the pythagorean theorem once to get the length
for a 3D vector we have to apply the pythagorean theorem twice to get the length
can this be generalized as for a xD vector the pythagorean theorem has to be applied x-1 times to get the length?
midnight plankBOT
for a 2D vector we have to apply the pythagorean theorem once to get the length
...
feral sedge
for a 2D vector we have to apply the pythagorean theorem once to get the length
...
yes
recall the formula of magnitude of a vector
rustic tartan
ohhh, i had not seen the formula noted with 3 values under the root, interesting
.close
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radiant lotus
Is this right so far?
last slate
what's the question?
last slate
right
give me a min
just to let u know, there's a much easier way of doing this with suvat equations
radiant lotus
Kinematic equations?
I was trying that early, but was told to ude integration. Just looked at it again though and was debating trying it again* it right as you mentioned it 😅
last slate
right
so a = dv/dt
a = (0.032)(15-t)= dv/dt
rearrange
so integral of ((0.032)(15-t)) dt = integral of 1 dv.
what you have missed though is that you must integrate both 15 and -t with respect to time
1 dv is just v, not vx -6.6. you will evaluate your limits in the next step
radiant lotus
I thought the bottom number was supposed to be the initial v?
last slate
it is the initial v. there is nothing wrong with how you've set up the integral. there are issues with the actual integration though
radiant lotus
1 dv is just v, not vx -6.6. you will evaluate your limits in the next step
-6.6 is the initial v
or wait
last slate
no, it is 6.6
radiant lotus
or yeah, misspoke
it is 6.6 but thats why in subtracting it is what I was trying to explain
guessing youre just saying that the line (converted integrade?) on the top equation is indicating that so I shouldnt have it there
radiant lotus
so integral of ((0.032)(15-t)) dt = integral of 1 dv.
what you have missed thou...
Im not sure how this works though
last slate
right hand side is good, left hand side is still wrong though
radiant lotus
im working on it now, think I might know actually
last slate
what is the integral of (1+x) dx
radiant lotus
1x+(x^2/2)
last slate
right, so what is integral (15-t) dt
radiant lotus
Im confused about how to use the power rule here. I'm assuming:
(-0.032(15t-t^2))/2
last slate
just the (t^2) is over 2
you can take (-0.032) out of the integral, then break it into the sum of 2 integrals S15 dt and S tdt
the S is a bad integral sign
∫-tdt + ∫15dt
last slate
yo ill get some pen and paper
radiant lotus
basically that would just be the next step in the equation. if it was (15-t) instead of just (t) it would be
(2.9(15t) - ((2.9t^2)/2)
last slate
radiant lotus
last slate
Yes
But we don’t know what Vx is. But we want to know what x is, and we know what t is
Vx can be expressed in these terms
radiant lotus
last slate
My bad lol
The equation on the right is correct
On the left
The v=Vx dx/dt is wrong
radiant lotus
wasnt sure how else to symbolize the equation
last slate
Yeah this stuff isn’t easy don’t worry
But your right hand side stuff is correct. Now take the integral with your limits
last slate
Is the lower bound of x 0?
last slate
Everything else is good
radiant lotus
I got 38.667 but its wrong?
last slate
Give me a min
last slate
You should have
radiant lotus
Then Im not sure what I did wrong...
radiant lotus
Is my work wrong?
radiant lotus
yeah
last slate
Try 44
radiant lotus
Got that earlier
didnt work
Its not constant acceleration
suvant/kinematics dont work
radiant lotus
No clue
radiant lotus
My pc will be around, but may get up so just @ me when you find something. Also appreciate the help. :)
last slate
My pc will be around, but may get up so just @ me when you find something. Also ...
45.333
radiant lotus
but how?
last slate
Right answer?
radiant lotus
no
radiant lotus
nope
last slate
38.66666
radiant lotus
Tried that one already
last slate
My thinking is that 15 must have units of time tho?
radiant lotus
last slate
Because 0.032 has units of ms-3
And a had units of ms-2
I’ll redo with this idea in mind
Final answer, 126.66666. After that, I give up
last slate
wtf
I’ll just dm u if I get an answer from anyone else. This is why you don’t do maths with units until the very end
radiant lotus
I’ll just dm u if I get an answer from anyone else. This is why you don’t do mat...
Appreciate it. Didnt have this issue with the last one so not sure hwats going on.
last slate
Science says it can not be done
summer terrace
Appreciate it. Didnt have this issue with the last one so not sure hwats going o...
i found 100/3
radiant lotus
as the answer?
summer terrace
idk how you guys integrate
i integrated twice, and substituted t=10
write the expressions of a(t), v(t), x(t) that you have
i will compare with mine
radiant lotus
This is my paper.
radiant lotus
V(t)=-0.032(15t-(t^2)/2)
summer terrace
omg.. i expected it lol
why the hell did you leave the acceleration as -0.032 (15 - t)
its difficult
why not distribute and make it easier
a(t) = 0.032 t - 0.48
isnt it better! 😛
radiant lotus
a(t) = 0.032 t - 0.48
im not sure how you got that
radiant lotus
oh ok
summer terrace
you dont have to lock yourself to what youre given
you can always change the form to what suits you!
summer terrace
V(t)=-0.032(15t-(t^2)/2)
also, i ask you
how did you accept this as your velocity
it cant be the velocity
youre given that v(0)=6.6
if you put t=0 in your expression you dont get v=6.6
summer terrace
a(t) = 0.032 t - 0.48
so try to start from this one, this time
and make use of the initial conditions given!
radiant lotus
Yeah, thats what im doing now
summer terrace
x(0)=-14 and v(0)=6.6
radiant lotus
V(t)=-0.032(15t-(t^2)/2)
Oh I just realized
This is from earlier, but I did work based off v(0)=6.6
last slate
how did you accept this as your velocity
so where did it go wrong?
radiant lotus
last slate
-0.032* integral(15+t)dt still makes sense, right?
because -0.032 is just a constant multiplier
summer terrace
yess
summer terrace
noice
radiant lotus
summer terrace
yeah, noice
radiant lotus
Maybe wasnt distributing the negative sign correctly?
summer terrace
dunno, but anyway
radiant lotus
summer terrace
i have a suggestion
a side note, dont always exhaust your brain doing the dv, dt, a, dx stuff
they have fixed formulas
$v(t) = v_0 + \int_{0}^{t} a(\tau) , d\tau \ \ x(t) = x_0 + \int_{0}^{t} v(\tau) , d\tau$
grand pondBOT
Emily
radiant lotus
Im for some reason not understanding what youre referring to
last slate
apply directlyyy
w8 so what is different about the approach you used to our approach? am i just stoopid or something lol
summer terrace
**Emily**
i dont integrate this way
i prefer doing like $v(t) = \int a(t) , dt + C$
grand pondBOT
Emily
summer terrace
and then i determine the constant C
using initial conditions
to avoid any mistake
summer terrace
w8 so what is different about the approach you used to our approach? am i just s...
nothing much, just initial conditions didnt come to play
or Ousel forgot to account for v(0)=6.6
radiant lotus
or Ousel forgot to account for v(0)=6.6
No I did. Im still not sure what I did wrong
last slate
yeah, we took integrals between initial condition and pointx conditions im pretty sure
summer terrace
its okayyy, dont sweat it guys 😛
radiant lotus
No I did. Im still not sure what I did wrong
I know how to do it correctly now tbc
radiant lotus
**Emily**
am trying to figure this out but I think I got it, just gotta test it to make sure
summer terrace
this is the general way, even if you're not given initial conditions at time t=0
just integrate whatever you have, and then determine the integration constant
using them given initial conditions
which can be at any time, not necessarily 0
like t=1, t=2, t=π/2 lol
summer terrace
is the +c `-14` technically?
no, the C was v0 = 6.6
in the equation of the velocity
and in the equation of the position, it was x0 = -14
radiant lotus
Idk what that is
last slate
what year are u in
radiant lotus
Calculus based Physics I
Supposed to take it after Calc I but Im taking them at the same time
radiant lotus
Yeah, got throwin into the deep end 😅
short hill
I'd use power rule for a and chain rule for b right?
midnight plankBOT
I'd use power rule for a and chain rule for b right?
nimble copper
Pretty much
midnight plankBOT
topaz lily
I'd use power rule for a and chain rule for b right?
yes man
topaz lily
I'd use power rule for a and chain rule for b right?
what you mean chain rule/ just use product
short hill
what you mean chain rule/ just use product
Don’t troll ping me thx
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Available help channel!
hollow cobalt
hi i would appreciate if anyone could help
midnight plankBOT
hi i would appreciate if anyone could help
hollow cobalt
i have absolutely no clue what to do
last slate
hi i would appreciate if anyone could help
is this a test ?
hollow cobalt
is this a test ?
its one of teh questions in my worksheet
honestly i just need help with the first part
the other 3 are fine for me
midnight plankBOT
@hollow cobalt Has your question been resolved?
last slate
the other 3 are fine for me
you could use the formula (theta / 2pi) *2pir = length of rope on smaller circle
midnight plankBOT
@hollow cobalt Has your question been resolved?
twilit field
Prove that every even function f can be written as f(x)= g(|x|) for infinitely many functions g
midnight plankBOT
Prove that every even function f can be written as f(x)= g(|x|) for infinitely m...
twilit field
I'm not even sure I get what this means
barren onyx
I'm not even sure I get what this means
same
grand pondBOT
Veni, vidi, perii
twilit field
where $h=|x|$
grand pondBOT
Veni, vidi, perii
barren onyx
where $h=|x|$
what grade is this btw
barren onyx
oh
twilit field
for probably year 1 to year 2 of uni
mental tide
Have you tried anything yet?
mental tide
You pretty much just wrote down the definition but yeah it looks like it
Do you know the definition of an even function?
mental tide
So the best idea would be to construct at least one example g
mental tide
f is given to be even in the problem
twilit field
f is even
mental tide
I'm ngl I didn't notice that it required infinitely many functions
Give me a second to think
twilit field
I'll send a pic of the problem
modern sapphire
I expected g to be a family of functions that are basis for the function space for f
mental tide
Okay so here's part of it, what do you know about the domain and range of h?
twilit field
12(d)
twilit field
Okay so here's part of it, what do you know about the domain and range of h?
Domain is R
The range is really hard to determine
mental tide
range is just going to be all values that it takes on
mental tide
Think of the range as the "height" the graph of the function can achieve
So at h(0), it'll be 0, and for h(x) where x > 0, it'll be x
twilit field
I think what's troubling me is if f(x)= g(|x|) for all x
atleast for all x>0, f(x) and g(x) are identical
mental tide
What about for x < 0?
hollow oyster
for g(x) when x<0 g can be whatever you want it to be
mental tide
Yeah, it's best to look for the most obvious counterexamples or solutions you can find
If you try to look for a very nice continuous family of solutions you probably are going to have a lot of trouble with so little information
twilit field
for g(x) when x<0 g can be whatever you want it to be
Realised , just when you sent that message
twilit field
If you try to look for a very nice continuous family of solutions you probably a...
Guess I learn something from evey problem
Thanks
mental tide
Just make sure to spend a lot of time on it before asking for help
hollow oyster
you can consider g to be a family of curves such that g will equal to f when x >= 0 and anthing else for x<0
mental tide
Asking for help is fine but it's really best to spend the time grinding through the problems on your own
twilit field
Asking for help is fine but it's really best to spend the time grinding through ...
I work better when I feel I'm being judged so I work here
sorry
mental tide
Your good
twilit field
dont say sorry if you didnt do anything wrong
sorry
twilit field
.close
midnight plankBOT
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chilly cobalt
Let f_0(x) = e^x, and for natural number n, f_n(x) = x f'_n-1(x) and P_n(x) = f_n(x) e^(-x) prove that P_n is an n degree polynomial
chilly cobalt
i know than f_n would be some polynomial multiplied by e^x but how do i prove it
fallow scarab
Induction?
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civic moth
midnight plankBOT
civic moth
Question number 4
My answer is not matching
Ans=19π/2 in book
<@&286206848099549185>
hollow oyster
!15mins
midnight plankBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
civic moth
Ok
midnight plankBOT
@civic moth Has your question been resolved?
civic moth
<@&286206848099549185>
midnight plankBOT
@civic moth Has your question been resolved?
twilit field
midnight plankBOT
twilit field
so I can simplify this to $2 \cdot \frac{(2n-1)(2n-2) \dots (n+1)}{(n-1)!}$
grand pondBOT
Veni, vidi, perii
twilit field
oops
tawdry laurel
Parity argument
twilit field
Suppose that $n \in \N$.
\
then $ \binom{2n}{n} = 2 \cdot \frac{(2n-1)(2n-2) \dots (n+1)}{(n-1)!}$
\
which is equivalent to
\
\
$2 \cdot \frac{(2n-1)(2n-2) \dots (n+1)n!}{(n-1)!n!}$
\
\
which is
\
$2 \binom{2n-1}{n}$
\
which is trivially divisble by 2.
\
thus we have proven
$\binom{2n}{n}$ is even
grand pondBOT
Veni, vidi, perii
twilit field
How's this
quiet hinge
If you have the set S={1,2,..,2n} and any choice of n elements of S, say A={a1,a2,..,an}, then A can be paired up with another choice of n things, namely S-A.
visual tiger
How's this
this works well if you use the factorial definition
quiet hinge
this works well if you use the factorial definition
That expression has been obtained by the factorial definition
visual tiger
That expression has been obtained by the factorial definition
which is what I said
i was gonna say that the combinatorial definition is a clever proof too
quiet hinge
which is what I said
👍 i thought you were suggesting using the factoial definition
olive matrix
i was gonna say that the combinatorial definition is a clever proof too
factorial bashing is sacred
quiet hinge
The proof is correct in every way but I feel like using the factorial expression removes the understanding that comes by using a combinatorial argument
twilit field
Thanks
twilit field
The proof is correct in every way but I feel like using the factorial expression...
I don't know any other defn
quiet hinge
If you have the set S={1,2,..,2n} and any choice of n elements of S, say A={a1,a...
You can formalise this by defining a relation on S and whatnot
quiet hinge
I don't know any other defn
Well an alternative definition of \binom{n}{k} is the number of ways to choose k things from n things
twilit field
Yes, which is what I've used
quiet hinge
You have used a large expression with factorials that is derived from the definition, to be precise
My point was that combinatorial arguments are also something to be on the lookout for
midnight plankBOT
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Available help channel!
cerulean arch
midnight plankBOT
midnight plankBOT
@cerulean arch Has your question been resolved?
cerulean arch
.
twilit field
midnight plankBOT
twilit field
Suppose : $n \in \N \land n \geq 2$.
\
let $\exists k st 2\leq k\leq n$.
\
$n!= 1 \cdot 2 \cdot 3 \dots \cdot k \cdot (n-1) \cdot n$
\
$n!+k = 1 \cdot 2 \cdot 3 \dots \cdot k \codt (n-1) \cdot n+k$
\
\
$n!+k (1 \cdot 2 \cdot 3 \dots k \dots (n-1) \dots n)$
\
Which proves that $n!+k$ is atleast divisible by $k,1 , 1 \cdot 2 \cdot 3 \dots k \dots (n-1) \dot n).$
\
\
thus any number of the form $n!+k$ is composite
tribal temple
What’s that fifth line supposed to be?
grand pondBOT
Veni, vidi, perii
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
twilit field
What’s that fifth line supposed to be?
oops
Suppose : $n \in \N \land n \geq 2$.
\
let $\exists k st 2\leq k\leq n$.
\
$n!= 1 \cdot 2 \cdot 3 \dots \cdot k \cdot (n-1) \cdot n$
\
$n!+k = 1 \cdot 2 \cdot 3 \dots \cdot k \cdot (n-1) \cdot n+k$
\
\
$n!+k= k (1 \cdot 2 \cdot 3 \dots (n-1) \dots n+1)$
\
Which proves that $n!+k$ is atleast divisible by $k,1 , 1 \cdot 2 \cdot 3 \dots k \dots (n-1) \dot n).$
\
\
thus any number of the form $n!+k$ is composite
grand pondBOT
Veni, vidi, perii
twilit field
That's it?
tribal temple
Good enough 
halcyon trellis
Pretty much.
twilit field
How else would I do this
tribal temple
There are some style comments to be made - e.g. I wouldn’t put that “there exists” for k
halcyon trellis
I mean ... for 2<=k<=n, k | n! so k | n! + k.
Is basically what you did so I don't think there's any easier way
midnight plankBOT
hard umbra
Is basically what you did so I don't think there's any easier way
are you patrolling the help channels again
midnight plankBOT
Available help channel!
deft bough
i have the following problem, and my work:
midnight plankBOT
i have the following problem, and my work:
deft bough
and the textbook says that this is the answer:
i'm not entirely clear on where the h came from
in the examples in the text, with the proofs, the book never used an h (always a G(t))
midnight plankBOT
@deft bough Has your question been resolved?
midnight plankBOT
@deft bough Has your question been resolved?
midnight plankBOT
@deft bough Has your question been resolved?
twilit field
Find a function $f$ other than the constant function, such that $|f(y)-f(x)| \leq |y-x|$
midnight plankBOT
Find a function $f$ other than the constant function, such that $|f(y)-f(x)| \le...
grand pondBOT
Veni, vidi, perii
twilit field
I was thinking of f(t)=t
twilit field
So does my example work?
strong lava
ofc
twilit field
Thanks
worthy wing
The identity works
twilit field
Isn't it too simple though
worthy wing
Then do f(t)=-t lol
strong lava
Isn't it too simple though
you expected hard exercises?
Go read Spivak/Rudin instead then
twilit field
you expected hard exercises?
Go read Spivak/Rudin instead then
This is from spivak
strong lava
oof
twilit field
I meant simple as in this example
strong lava
you can also propose sin or cos then
midnight plankBOT
strong lava
or 1/(1+x²)
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tacit veldt
I need help in the last question. the answere is 1.362 meters. i tried finding the 40% by dividing 1.4 (50%) by 5 and then subtracting the result from 1.4. I got 1.12 but the value is not the same as the answere.
midnight plankBOT
I need help in the last question. the answere is 1.362 meters. i tried finding t...
@tacit veldt Has your question been resolved?
olive mantle
I need help in the last question. the answere is 1.362 meters. i tried finding t...
have you tried eating the paper
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tacit veldt
have you tried eating the paper
I tried but it is a PDF file
midnight plankBOT
I tried but it is a PDF file
tacit veldt
.close
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wintry eagle
My question is about how to implement Cauchy Reimann's integral formula. I don't really understand how to rearrange this in a way which makes it okay to use his formula
midnight plankBOT
My question is about how to implement Cauchy Reimann's integral formula. I don't...
worthy kestrel
cant u just use it?
wintry eagle
I do not think so, since I have more than one singalurity
wintry eagle
how do you see that?
wintry eagle
hmm okay
is there any more simple method than partial fraction? or is that standard
wintry eagle
okay, I'll read it in the book then, I saw it somewhere in there
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