Complete the table by entering the correct value in each blank. (Enter fractional answers like
1 answer:
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Answer:
Step-by-step explanation:
To solve this problem, we will use the following two theorems/definitions:
- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by
- (Gauss' theorem)Given a closed surface S, the following applies
where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.
Let us, in our case, calculate the divergence of the given field. We have that
Hence, by the Gauss theorem we have that
So, we must calculate the volume V bounded by the cube S.
We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.
Take the vertices (1,1,1) and (1,1-1). The distance between them is given by
.
Hence, the volume of V is . Then, the final answer is
Step-by-step explanation:
there 5^(n+1) + 5^(n+2) = 5^n x 5^1 + 5^n x 5^2 breaking them as x^(a+b) = x^a x x^b
then taking common 5^n from both terms
