Evaluate the surface integral modifyingbelow integral from nothing to nothing integral from nothing to nothing with upper s f (x comma y comma z )ds using a parametric description of the surface. f (x comma y comma z )equalsx squared plus y squared, where s is the hemisphere x squared plus y squared plus z squared equals 36, for zgreater than or equals0 the value of the surface integral is nothing. (type an exact answers, using pi as needed.)

Parameterize by

with and . Take a normal vector to ,

which has norm

Then the integral of over is

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

-6 is the correct option from the above given options