Use Stokes' theorem for both parts, which equates the surface integral of the curl to the line integral along the surface's boundary.
a. The boundary of the hemisphere is the circle 
in the plane 
, where the curl is 
. Green's theorem applies here, so that
which means the value of the line integral is 3 times the area of the circle, or 
.
b. The closed sphere has no boundary, so by Stokes' theorem the integral is 0.
Answer:
$372.330
Step-by-step explanation:
if 1 mile = $0.45 and you want to find out 827.4 miles
you should multiple $0.45 × 872.4
1 mile : $0.45
827.4 × $0.45 = 372330
827.4 : $372.330
I assume you are calculating the total area to be painted.
Then 3 x 8.3 x 7.5 = 186.75 sq. ft.
Answer:
k = 575
Step-by-step explanation:
let d be distance and h time.
Given d varies directly as h then the equation relating them is
d = kh ← k is the constant of variation
To find k use the condition d = 2875, h = 5, then
2875 = 5k ( divide both sides by 5 )
k = 575
