Let σ be portion of the paraboloid z = x 2 + y 2 − 9 lying on and below the xy-plane. Let σ have downward orientation. Let C be
its boundary curve, oriented positively with respect to σ. Let F = x − y, x 2 z, y . (a) Evaluate R C F • T ds as a line integral. (b) Use Stokes’ theorem to evaluate R C F • T ds by evaluating an appropriate surface integral.
1 answer:
Answer:
See explaination
Step-by-step explanation:
Stoke theorem proposes that the surface integral of the curl of a function over any surface bounded by a closed path is equal to the line integral of a particular vector function round that path.
The Stoke Theorem can be used if you see a two dimensional region bounded by a closed curve, or if you see a single integral ie a line integral.
See attached file for further solution.
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Answer:
The width of the garden bed must be less than or equal to 4 feet.
Explanation:
Given that;
She has 20 feet of boards to make the sides.
The perimeter of the garden bed must not be more than 20 feet
Given;
The length is 6 feet;
To get the inequality for the width w, let us substitute the value of the length into the inequality above and simplify;
Therefore, the width of the garden bed must be less than or equal to 4 feet.