Answer:
5/24 kg
Step-by-step explanation:
5/6 ÷ 4/1 (keep-change-flip)
5/6 x 1/4 = 5/24
Answer:
x = 4 or x = 1 or x = -2 or x = -3/2
Step-by-step explanation:
Solve for x over the real numbers:
2 x^4 - 3 x^3 - 21 x^2 - 2 x + 24 = 0
The left hand side factors into a product with four terms:
(x - 4) (x - 1) (x + 2) (2 x + 3) = 0
Split into four equations:
x - 4 = 0 or x - 1 = 0 or x + 2 = 0 or 2 x + 3 = 0
Add 4 to both sides:
x = 4 or x - 1 = 0 or x + 2 = 0 or 2 x + 3 = 0
Add 1 to both sides:
x = 4 or x = 1 or x + 2 = 0 or 2 x + 3 = 0
Subtract 2 from both sides:
x = 4 or x = 1 or x = -2 or 2 x + 3 = 0
Subtract 3 from both sides:
x = 4 or x = 1 or x = -2 or 2 x = -3
Divide both sides by 2:
Answer: x = 4 or x = 1 or x = -2 or x = -3/2
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.
