Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.

Contour integral Subscript Upper C Superscript Baseline left parenthesis 3 x plus arctangent y squared right parenthesis dy minus left parenthesis 8 y squared plus hyperbolic sine x right parenthesis dx∮ C(3x+arctany2dy−8y2+sinhx)dx,

where C is the boundary of the square with vertices
left parenthesis 1 comma 5 right parenthesis comma(1, 5),
left parenthesis 2 comma 5 right parenthesis comma(2, 5),
left parenthesis 2 comma 6 right parenthesis comma(2, 6),
and left parenthesis 1 comma 6 right parenthesis (1,6)

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

16

step-by-step explanation: