Looks like we're given
which in three dimensions could be expressed as
and this has curl
which confirms the two-dimensional curl is 0.
It also looks like the region 
is the disk 
. Green's theorem says the integral of 
along the boundary of is equal to the integral of the two-dimensional curl of over the interior of :
which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of by
with 
. Then
Answer:
2: 0.65
Step-by-step explanation:
<h3>
Answer: Yes they are equivalent</h3>
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Work Shown:
Expand out the first expression to get
(a-3)(2a^2 + 3a + 3)
a(2a^2 + 3a + 3) - 3(2a^2 + 3a + 3)
2a^3 + 3a^2 + 3a - 6a^2 - 9a - 9
2a^3 + (3a^2-6a^2) + (3a-9a) - 9
2a^3 - 3a^2 - 6a - 9
Divide every term by 2 so we can pull out a 2 through the distributive property
2a^3 - 3a^2 - 6a - 9 = 2(a^3 - 1.5a^2 - 3a - 4.5)
This shows that (a-3)(2a^2 + 3a + 3) is equivalent to 2(a^3 - 1.5a^2 - 3a - 4.5)
Answer:
5) 27/70
6) 90
Step-by-step explanation:
5) The first step in this problem is to figure out the amount of total spins. To do so, add up all of the numbers in the column "Frequency".
18 + 15 + 27 + 10 = 70.
Now, look at the amount of times the spinner landed on green. This is 27 times. So, the ratio of green spins to total spins is 27:70, or 27 out of 70 spins. Converting this to a fraction, we get the final answer, 27/70.
6) To solve this problem, we have to first do the same steps as the previous problem, but with the color red. There are 70 total spins, and 18 red spins. Therefore, the ratio is 18:70. However, this problem wants the total number of spins to be 350. In other words, 70 needs to become 350. To do this, multiply each side of the ratio by 5. The ratio becomes 90:350. Using this ratio, we can determine that a solid prediction is 90 red spins out of 350 total spins.
Answer:
Range of 
is (−5,11).
Step-by-step explanation:
Given the invertible function Ф(x) which has the domain (−5,11) and the range (−12,1).
Invertible function is the function that inverses another function i.e if y=Ф(x) then x=g(y) where g is called the inverse of Ф and denoted by
Given Ф(x) the function whose domain is (−5,11) and range is (−12,1). Therefore, by definition of invertible function there exist a function g with domain (−12,1) and range (−5,11) which is called the inverse function denoted by
Hence, Range of is (−5,11)
