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:
figured it out is 25
Step-by-step explanation:
hope this helps:)
Answer: (a) 0.006
(b) 0.027
Step-by-step explanation:
Given : P(AA) = 0.3 and P(AAA) = 0.70
Let event that a bulb is defective be denoted by D and not defective be D';
Conditional probabilities given are :
P(D/AA) = 0.02 and P(D/AAA) = 0.03
Thus P(D'/AA) = 1 - 0.02 = 0.98
and P(D'/AAA) = 1 - 0.03 = 0.97
(a) P(bulb from AA and defective) = P ( AA and D)
= P(AA) x P(D/AA)
= 0.3 x 0.02 = 0.006
(b) P(Defective) = P(from AA and defective) + P( from AAA and defective)
= P(AA) x P(D/AA) + P(AAA) x P(D/AAA)
= 0.3(0.02) + 0.70(0.03)
= 0.027
Answer:
D. 68 (APEX).........................................................................................
Solution:
Since the graph passes through the given points, (7, 20) & (-2, 11) are the solutions of the given equation <em>y = x + ?</em>.
⇒<em>(x, y)</em> = (7, 20); (-2, 11)
Substituting the variables with (7, 20),
20 = 7 + <em>?</em>
20 - 7 = <em>?</em>
<em>?</em> = 13
Similarly,
11 = -2 + <em>?</em>
<em>?</em> = 13
∴ <em>y</em> = 13