Eber ran 3 miles. He stopped to take a break every {3}{4) mile.How many times did Eber stop, including his final stop at the end
2 answers:
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Answer:
The counterclockwise circulation is and the outward flux is
Step-by-step explanation:
We are given the field . A picture of the region and the path we are considering is attached. Recalll the following theorems.
Given a field of the form F(x,y)=(f(x,y),g(x,y) with f,g having continous partial derivates, C is a closed path counterclockwise oriented, R is the region enclosed by C and n is the normal vector pointing outwards of the path C. Then
(this one calculates the counterclockwise circulation)
(This one calculates the outward flux)
Then, recall that in our case f(x,y) = 7xy, g(x,y)=2y^2[/tex]. Then
.
Note that we just need to describe our region R. The region R lies between the parabola y=x^2 and the line y=x. Thus, one way to describe the region is as follows . Then, using the previous results, we get that
(circulation)
(flux)
Answers:
Domain = [-3, 3]
Range = [-1, 2]
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Explanation:
The domain is the set of all allowed x inputs. Visually, the left-most point is when x = -3, so -3 is the smallest allowed x input. We have a closed circle at this endpoint, so this endpoint x value is included. In contrast, if you had an open circle, then you would exclude the endpoint.
Similarly, we have a closed endpoint at the other side as well when x = 3. This is the largest allowed x value. The domain is the set of x values such that meaning x is between -3 and 3, including both endpoints. This translates to the interval notation of [-3, 3]. The square brackets say "include the endpoint".
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The range is the set of possible y outputs of a function. The lowest the function goes is when y = -1, and the highest is when y = 2. We include both endpoints. The range as a compound inequality is which converts to the interval notation of [-1, 2]