Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x, y) = 8 sin(xy), (0, 3).

If a substance is in the gas phase, which of qualities of the gas will stay constant? a: volume b: mass c: shape d: position of particles

1. how to locate the image in converging(concave) mirror and diverging (convex) mirror with salt. 2. how to locate the image in a converging (convex) lens and diverging (concave) lens with salt.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)