Consider crho ∂u ∂t = ∂ ∂x k0 ∂u ∂x ! + αu, where c, rho, k0 and α are functions of x, subject to u(0, t) = 0, u(l, t) = 0, u(x,0) = f (x). assume that appropriate eigenfunctions are known according to the results included in the box on p.157. (a) show that the eigenvalues are positive if α < 0. (b) solve the initial-boundary value problem. (c) discuss lim t→[infinity] u(x, t).

step-by-step explanation:

it will be a cylinder. with a diameter of 8 and 4 single pieces high

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

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