Find the jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables. if x = f(u, v, w), y = g(u, v, w), and z = h(u, v, w), then the jacobian of x, y, and z with respect to u, v, and w is ∂(x, y, z) ∂(u, v, w) = ∂x ∂u ∂x ∂v ∂x ∂w ∂y ∂u ∂y ∂v ∂y ∂w ∂z ∂u ∂z ∂v ∂z ∂w . spherical coordinates x = ρ sin φ cos θ, y = ρ sin φ sin θ, z = ρ cos φ

Ahypothesis is: a the average squared deviations about the mean of a distribution of values b) an empirically testable statement that is an unproven supposition developed in order to explain phenomena a statement that asserts the status quo; that is, any change from what has been c) thought to be true is due to random sampling order da statement that is the opposite of the null hypothesis e) the error made by rejecting the null hypothesis when it is true