Without knowing exactly what
is, this is impossible to do. So let's assume
. Then the line integral over the given rectangle will correspond to the "signed" perimeter of the region.
You don't specify that the loop is complete, so in fact the integral will only give the "signed" length of three sides.
Parameterize the region by first partitioning the contour into three sub-contours:
where
for each sub-contour. Then the line integral is given by
with
. You have
Then the integral over the entire contour would be
. Note that if the loop is complete, then the last leg of the contour would evaluate to -5, and so the total would end up as 0. This result would also follow from the fact that
is conservative, i.e.
for some scalar field
, and so the line integral is path independent. Its value would depend only on the endpoints of the contour, which in the case of a closed loop would simply be 0.
Rewrite the system of equations in matrix form.
This system has a unique solution so long as the inverse of the coefficient matrix exists. This is the case if the determinant is not zero.
We have
so the inverse, and hence a unique solution to the system of equations, exists as long as m ≠ -4.
Answer:
? = 3
Step-by-step explanation:
To find the value of ?, substitute one of the ordered pairs from the table [except (0, 0)] into the given formula and solve for ?.
Given formula:
Substitute x = 1 and y = 3 into the formula:
To isolate ? divide both sides by 1:
Therefore, ? = 3:
Check by inputting another value of x from the table into the found formula and comparing the calculated y-value:
Answer:
A.
Step-by-step explanation:
Determine the area of all the faces of the and then devide by 0.15