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.
To solve this problem, let us recall that the formula for
probability is:
Probability = total number of successful events / total
events
Where in this case, an event is considered to be successful
if the sum is 3 on the pair of six sided dice.
First, let us calculate for the total number of events. There
are 6 numbers per dice, therefore the total number of combinations is:
total events = 6 * 6 = 36
Next, we calculate for the total number of combinations
that result in a sum of 3. We can identify that there are only two cases that
result in sum of 3. That is:
1st case: first dice rolls 1, second dice
rolls 2
2nd case: first dice rolls 2, second dice
rolls 1
Hence, total number of successful events = 2. Therefore the
probability is:
Probability = 2 / 36 = 1 / 18 = 0.0556 = 5.56%
The scale ratio of a point A to another point B is the division of the length of B by the length of A. The best equation that models the situation is: 
The page dimension is:
The length and the width of Uche's book are equal; this means the pages of Uche's book have the shape of a square
The margin of 0.75 on either sided means the usable dimension is:
The dimension of India is:
The longest side in India's dimension is:
From Uche's book, the longest dimension is:
So, the scale equation is:
k * longest length of Uche's book = longest side of India
This gives:
Read more about scale ratio at:
brainly.com/question/16192120
Answer:
185
Step-by-step explanation:
firstly you calculate all in brackets
(280+20)÷3
300÷3
100-15
85
now you calculate 10×5=50
2×50=100
85+100=185
so firstly deal with problem inside the brackets, then you got multiplication and division outside their brackets and finally get 85 +100 =185
We know the rate of the change, 3 meters per hour. And we want to know how long it will take to reach 12 meters. Say we need to reach 6 meters instead 12.
How long will that take? 2 hours! Because we divide 6 m by 3 m/h.
Now let us do the same thing will 12 meters.
12 m / 3 m/h = 4 hours
It will take 4 hours to reach the 12 meters height.
