Help me!!!! 30 points please just help so I can get it right!!!!!!
1 answer:
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Answer:
5/18
Step-by-step explanation:
When two cubes are rolled there are 36 possibilities
Each dice has 6 equally like outcomes so possibilities are
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Now we look at the pair that has sum equal to 9
(3,6) (4,5) (5,4) (6,3) that has sum of 9
Probability of sum is 9 =
we look at the pairs that has sum greater than 9
(4,6) (5,5)(5,6) (6,4)(6,5)(6,6)
Probability of sum greater than 9 =
Probability of sum 9 or higher = P(sum 9) + P(greater than 9)
=
Step-by-step explanation:
Use the identity
on the left side.
Now use the identity
on the left side.
It looks like the integral is
where <em>C</em> is the circle of radius 2 centered at the origin.
You can compute the line integral directly by parameterizing <em>C</em>. Let <em>x</em> = 2 cos(<em>t</em> ) and <em>y</em> = 2 sin(<em>t</em> ), with 0 ≤ <em>t</em> ≤ 2<em>π</em>. Then
Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on <em>C</em> nor in the region bounded by <em>C</em>, so
where <em>D</em> is the interior of <em>C</em>, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: .