1. A scalar field is given by the function . a. Find at the point (3, 5). b. Find the component of that makes a angle with the x axis at the point (3, 5). 2. If the fluid of density in Problem...

1. A scalar field is given by the function

.

a. Find

at the point (3, 5).

b. Find the component of

that makes a

angle with the x axis at the point (3, 5).

2. If the fluid of density

in Problem 1.3 obeys the perfect gas law, obtain the equation of state of the mixture, that is,

Will this result be valid if a liquid is present instead of a solid?

Problem 1.3

For a fluid of density

in which solid particles of density

are uniformly dispersed, show that if

is the mass fraction of solid in the mixture, the density is given by