Modifiers

[1] Resumptive modifiers ( Sahils)

Since the 1930’s aircraft manufacturers have tried to build airplanes with frictionless
wings, shaped so smoothly and perfectly that the air passing over them would not
become turbulent.
(A) wings, shaped so smoothly and perfectly
(B) wings, wings so smooth and so perfectly shaped
(C) wings that are shaped so smooth and perfect
(D) wings, shaped in such a smooth and perfect manner
(E) wings, wings having been shaped smoothly and perfectly so
B is the correct answer.
Wings is required to unambiguously convey the meaning of the sentence.
A resumptive modifier picks up a word or phrase from a sentence that seems to be
finished and then adds information and takes the reader into new territory of thought.


In a crowded, acquisitive world, the disapperance of lifestyles such as those once
followed by southern Africa's Bushmen and Australia's aborigines, requiring vast wild
spaces and permitting little accumulation of goods, seem inevitably doomed.
(B) requiring vast wild spaces and permitting little accumulation of goods, seems to be
inevitably doomed
(C) which require vast wild spaces and permit little accumulation of goods, seems to be
inevitably doomed
(D) life-styles that require vast wild spaces and permit little accumulation of goods, seem
inevitable
(E) life-stlyes requiring vast wild spaces and permitting little accumulation of goods,
seems inevitable
E is the correct answer.


Proponents of artificial intelligence say they will be able to make computers that can
understand English and other human languages, recognize objects, and reason as an
expert does—computers that will be used to diagnose equipment breakdowns,
deciding whether to authorize a loan, or other purposes such as these.
(A) as an expert does—computers that will be used to diagnose equipment
breakdowns, deciding whether to authorize a loan, or other purposes such as
these
(B) as an expert does, which may be used for purposes such as diagnosing
equipment breakdowns or deciding whether to authorize a loan
(C) like an expert—computers that will be used for such purposes as diagnosing
equipment breakdowns or deciding whether to authorize a loan
(D) like an expert, the use of which would be for purposes like the diagnosis of
equipment breakdowns or the decision whether or not a loan should be
authorized
(E) like an expert, to be used to diagnose equipment breakdowns, deciding
whether to authorize a loan or not, or the like
C is the answer.

[2] S+V+O+verb-ed/verb-ing+Blah Blah(Manhattan)
S+V+O+verb-ed+blah...
S+V+O+verb-ing+blah...

"verb-ed" and "verb-ing" modify the object O.
My question is when should I use verb-ed? when should I use verb-ing?
(Ron Purewal)
the distinction you're talking about is that between the PRESENT PARTICIPLE (that's the '-ing' form) and the PAST PARTICIPLE (that's the form that usually ends in '-ed', although there are plenty of exceptions, like written, known, etc.)

i won't go on at length about the distinction between the two, because it's so fundamental that you can find literally thousands of thorough internet sources with one search. just type "present participle" "past participle" (including the quotes), and perhaps english, into google and read one of the huge number of explanatory pages that you'll find.

i will, however, point out one thing of enormous importance that you haven't addressed here at all, which is the presence/absence of a COMMA after the main clause (the thing you've written s+v+o).
if there's NO COMMA before a participle, then the participle creates an adjective phrase that modifies the noun immediately preceding.
if there's a COMMA before a participle, then the participle creates an adverb phrase that modifies the action of the preceding clause.
examples:
joe picked the fruit hanging from the tree. <-- joe, who was probably on solid ground, picked the fruit that was hanging from the tree. joe picked the fruit, hanging from the tree. <-- joe was hanging from the tree while he picked the fruit. for instance, i think that the following sentence is perfectly fine: the pedestrian was hit by a car, sustaining multiple major injuries
although it would probably be better written as
the pedestrian was hit by a car and sustained multiple major injuries

i think that, as long as the 'verb-ing adverb phrase' refers properly to the action in the main clause (whether that action is in the active or the passive), you're fine.

well, i don't like to endorse any statement involving the word 'always', especially when it comes to english grammar - but here are a couple of guidelines:

if the participial phrase comes before the verb of the main clause, then you usually can check it with the rule that you're propounding:
(1) joe, racing down the wet sidewalk, slipped and fell.
(2) racing down the wet sidewalk, joe slipped and fell.
either of these sentences means the same thing as 'joe slipped and fell as/while he was racing down the wet sidewalk'. by contrast, trying to place the participle after the verb - joe slipped and fell, racing down the sidewalk - yields a sentence that doesn't make any sense.

on the other hand, if the participial phrase comes after the verb of the main clause, then it usually expresses a result and thus can't be checked with your rule:
(3) the bodybuilder ate a 3000-calorie dinner, bringing his calorie intake for the day to 7000.