Give conditions on the constants a, b and c that ensure that the flux integral integral_s f middot ds, where f = ai + bj + ck and s is the lower half of the unit sphere centered at the origin and oriented downward, is positive. (for each, if there is no restriction on the constant select = and enter anything for the value.)

Parameterize by

with and . The downward normal vector to is

Then the flux of across is

Only the last term of the integrand contributes to the integral; we have

so that the flux is . In order for this to be positive, we must have . and can be any constants.

536

step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.