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.

Statements reasons 1. ab ? cd; ad ? bc 1. given 2. ac ? ac 2. reflexive property 3. ? adc ? ? cba 3. ? 4. ? dac ? ? bca; ? acd ? ? cab 4. cpctc 5. ? dac and ? bca are alt. int. ? s; ? acd and ? cab are alt. int. ? s 5. definition of alternate interior angles 6. ab ? cd; ad ? bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?

The product of sin 30 degrees and sin 60 degrees is same as the product of

Identify the slope an intercept of the following linear equation y = 1/5x - 6 a. slope: 1/5; intercept: -6 b. slope: 5; intercept: -6 c. slope: -1/5; intercept: 6 d. slope: 1/5; intercept: 6