Let f= 6(x+y)i + 6 sin(y)j,. find the line integral of f around the perimeter of the rectangle with corners (50) traversed in that order.

line integral =

333.04656

Step-by-step explanation:

F can be rewritten as

The path C on which we are going to evaluate the integral is

All the paths can be parametrized with parameter t (0≤ t≤ 1)

Parametrization of

r(t) = (5,0)+t((5,7)-(5,0)) = (5,0)+t(0,7) = (5,7t)

Parametrization of

r(t) = (5,7)+t((-3,7)-(5,7)) = (5,7)+t(-8,0) = (5-8t,7)

Parametrization of

r(t) = (-3,7)+t((-3,0)-(-3,7)) = (-3,7)+t(0,-7) = (-3,7-7t)

Parametrization of

r(t) = (-3,0)+t((5,0)-(-3,0)) = (-3,0)+t(8,0) = (-3+8t,0)

Finally

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.