Consider the velocity field of a fluid at time t given by F(x, y, z) = (x^3 , y^3 , z^3) . Consider the fluid flux through the surface ∂E of the closed cone E = {(x, y, z)|x^2 + y^2 = z^2 , 0 ≤ z ≤ 1} Flux = double integral ∂E F · N dS. Use the Divergence Theorem to express the flux through ∂E
in terms of a triple integral.

Now switch to cylindrical coordinates to evaluate the triple integral

Abuyer pays a deposit to the seller in advance before completing the transaction. which term best defines this? a. down payment b. earnest money c. mortgage application fee

Colby and jaquan are growing bacteria in an experiment in a laboratory. colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours. jaquan starts with 80 of a different type of bacteria that doubles every 3 hours. let x equal number of days. colbys experiment follows the model: a.) y=50*2^x b.) y=50*2^8x c.) y=50*2^12x jaquans experiment follows the model: a.)80*2^x b.)80*2^8x c.)80*2^12x

As voters exit the polls, you ask a representative random sample of voters if they voted for a proposition. if the true percentage of voters who vote for the proposition is 63%, what is the probability that, in your sample, exactly 5 do not voted for the proposition before 2 voted for the proposition? the probability is