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.
X = height of pole (in meters)
With respect to the 50 degree angle, the side x is the opposite leg. It is the leg furthest from the reference angle. The hypotenuse is 5 meters.
The trig function sine ties together the opposite and hypotenuse
sin(angle) = opposite/hypotenuse
sin(50) = x/5
5*sin(50) = x .... multiply both sides by 5
x = 5*sin(50)
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Since x = 5*sin(50) isn't listed as an answer choice, let's try using cosine. We can't use it right away because we don't know the adjacent side. What we can do is change the reference angle. The missing angle of the triangle is 90-50 = 40 degrees. Let's make the 40 degree angle the reference angle
So x is now the adjacent side with respect to the 40 degree reference angle. The hypotenuse is always the longest side. The hypotenuse stays at 5.
cos(angle) = adjacent/hypotenuse
cos(40) = x/5
5*cos(40) = x
x = 5*cos(40)
This expression is listed. The answer is choice B
Answer:
For 4 years the money was in the account .
Step-by-step explanation:
Formula
As given
Bonita deposited 1300 into a bank account that earned 5.75% simple interest each year.
She earned $299 in interest before closing the account.
Principle = $1300
Rate = 5.75%
Simple interest = $299
Putting all the values in the formula
Time = 4 years
Therefore for 4 years the money was in the account .
Answer:
I think its 2 kg anyone correct me if I'm wrong!
All integer numbers are either even or odd. So, the complement to the set B (to the set of all even integers) is the set of all odd integers, that is D.
The integer number of the form 2x is always even, because it is always divided by 2, so the set C is the empty set.
Numbers 1, 3, 5, 7 are odd, therefore they belong to the set D.
