Afluid has density 810 kg/m3 and flows with velocity v = z i + y2 j + x2 k, where x, y, and z are measured in meters and the components of v in meters per second. find the rate of flow outward through the cylinder x2 + y2 = 9, 0 ≤ z ≤ 4.

Denote the cylindrical surface by , and its interior by . By the divergence theorem, the integral of across (the outward flow of the fluid) is equal to the integral of the divergence of over the space it contains, :

The given velocity vector has divergence

Then the total outward flow is

Converting to cylindrical coordinates gives the integral

3.4 pizzas

step-by-step explanation:

given is a scatter plot showing number of pizzas sold during weeks for different issues of coupon

y represents number of pizzas sold and x number of coupons issued

y is marked verticaly and x horizontally

the trend line is given as

y =3.4x+43

this says that even when no coupon is issued pizzas sold will be 43

and rate of change of pizza sold for 1 unit of coupon = slope = 3.4

i.e. when x increases by 1 unit y increases by 3.4 units

hence for each additional coupon issued 3.4 pizzas more will be sold

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.