Question

0.1m+8-12n when m =30 and n =[1fraction[/4]

Answer 1

Answer:

Step-by-step explanation:

Root:

n≈0.00833333 m + 0.666667

Root for the variable n:

n≈-0.0833333 (-0.1 m - 8)

Derivative:

d/dm(0.1 m + 8 - 12 n) = 0.1

Indefinite integral:

integral(8 + 0.1 m - 12 n) dm = 0.05 m^2 - 12 m n + 8 m + constant

Definite integral over a disk of radius R:

integral integral_(m^2 + n^2<R^2)(0.1 m - 12 n + 8) dm dn = 8 π R^2 + 0

Definite integral over a square of edge length 2 L:

integral_(-L)^L integral_(-L)^L (8 + 0.1 m - 12 n) dn dm = 32 L^2 + 0