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What combination of transformations is shown below
2 answers:
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Answer:
Q = 52.5
Step-by-step explanation:
given P is directly proportional to Q then the equation relating them is
P = kQ ← k is the constant of proportion
to find k use the condition Q = 30 when P = 40 , then
40 = 30k ( divide both sides by 30 )
=
= k
P = Q ← equation of proportion
when P = 70 , then
70 = Q ( multiply both sides by 3 to clear the fraction )
210 = 4Q ( divide both sides by 4 )
52.5 = Q
Proof:
Let . As we chose
in
we know that
. Since
by transitivity we get:
.
If is the empty set, we already have that
. But if
is not empty, that means that it can't be subset of
, because
is already subset of
, and those sets do not share any element. In other words:
As can't be subset of
, then
.
was an arbitrary element, and
Thus, , where we conclude that
