Use stokes' theorem to change ∫∫∇×⋅∫∫s∇×f⋅nds to an equivalent surface integral and evaluate it, where =++=xi+y2j+xyzk, is the upward unit normal, and is the part of the paraboloid z=4−x2−y2z=4−x2−y2 with z≥0z≥0.

positive

step-by-step explanation:

the quadrant is facing upwards

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:

answer: 72: 111

step-by-step explanation: