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Carryonlearning <3
The number of subsets of a set is 256, and the number of subsets of a set is 128. If | ∪ | = 2 × | ∩ |, then what is the value of | ∩ |? and what will be the number of subsets of the set ∩ ?
Differentiate the given solution:
Substitute 
and 
into the ODE:
and it's easy to see the left side indeed reduces to 0.
Cross-multiply so that 8(3x + 1) = 14(2x)
Distribute the 8 and 14 into the parentheses:
24x + 8 = 28x
Subtract 24x from both sides:
8 = 4x
Divide both sides by 4:
x = 2
Answer: option D is the correct answer.
Step-by-step explanation:
The given sequence is a geometric sequence because the consecutive terms differ by a common ratio.
The formula for determining the nth term of a geometric progression is expressed as
an = a1r^(n - 1)
Where
a1 represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a1 = 36
r = 12/36 = 4/12 = 1/3
Therefore, the formula for the nth term of the sequence is
an = 36 × 1/3^(n - 1)
an = 36 × 3^-1(n - 1)
an = 36 × 3^(-n + 1)
an = 36 × 3^(1 - n)
