Question

Considere uma barra de 45 cm e com condutividade térmica igual a 4, cuja distribuição inicial de temperatura é dada pelo gráfico abaixo.



CI

Assinale a alternativa que apresenta a lei de formação da função que descreve essa distribuição inicial de temperatura, e a equação completa do calor associada.

Escolha uma:
a. 15 u subscript x y end subscript equals u subscript tu left parenthesis 0 comma space t right parenthesis equals u left parenthesis 45 comma space t right parenthesis equals 0u left parenthesis x comma space 0 right parenthesis equals open curly brackets table row cell x comma space x element of left square bracket 0 comma 15 right square bracket end cell row cell 15 comma space x element of left square bracket 15 comma space 30 right square bracket end cell row cell 15 minus x comma space x element of left square bracket 0 comma space 30 right square bracket end cell end table close
b. 16 u subscript x x end subscript equals u subscript tu left parenthesis 0 comma space t right parenthesis equals u left parenthesis 45 comma space t right parenthesis equals 0u left parenthesis 0 comma space x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 16 comma space x element of left square bracket 15 comma space 30 right square bracket end cell row cell x plus 45 comma space x element of left square bracket 30 comma space 45 right square bracket end cell end table close
c. 16 u subscript x x end subscript equals u subscript tu left parenthesis 0 comma space t right parenthesis equals u left parenthesis 45 comma space t right parenthesis equals 0u left parenthesis x comma space 0 right parenthesis equals open curly brackets table row cell x comma space x element of left square bracket 0 comma 15 right square bracket end cell row cell 15 comma space x element of left square bracket 15 comma space 30 right square bracket end cell row cell 45 minus x comma space x element of left square bracket 30 comma space 45 right square bracket end cell end table close
d. u left parenthesis t comma space 0 right parenthesis equals u left parenthesis 45 comma space t right parenthesis equals 0u left parenthesis y comma space 0 right parenthesis equals open curly brackets table row cell x comma space x element of left square bracket 0 comma 15 right square bracket end cell row cell 10 comma space x element of left square bracket 15 comma space 30 right square bracket end cell row cell x minus 10 comma space x element of left square bracket 30 comma space 45 right square bracket end cell end table close
e. u subscript x x end subscript equals u subscript tu left parenthesis 0 comma space t right parenthesis equals u left parenthesis t comma space 45 right parenthesis equals 0u left parenthesis x comma space 0 right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell x comma space x element of left square bracket 0 comma 15 right square bracket end cell row cell x minus 15 comma space x element of left square bracket 30 comma space 45 right square bracket end cell end table close

Answer 1

Corrigido pelo AVA:

u(x, 0) = x, x, E (0, 15)

            15, x E (15, 30)

            45 - x, x E (30, 45)

15u xy = ut

u(0, t) = u(45, t) = 0