Answer:
a. a[1] = 3; a[n] = 2a[n-1]
b. a[n] = 3·2^(n-1)
c. a[15] = 49,152
Step-by-step explanation:
Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.
The first term is 3, and the common ratio is 2.
<h3>(a)</h3>
The recursive rule is ...
a[1] = 3
a[n] = 2×a[n-1]
__
<h3>(b)</h3>
The explicit rule is ...
a[n] = a[1]×r^(n-1)
a[n] = 3×2^(n-1)
__
<h3>(c)</h3>
The 15th term is ...
a[15] = 3×2^(15-1) = 3×2^14
a[15] = 49,152
Answer:
Part A) see the explanation
Part B) 
Step-by-step explanation:
Part A)
we know that
A relationship between two variables, x, and C, represent a proportional variation if it can be expressed in the form 
or 
Let
C ---> is the total cost (represent the output or dependent variable)
x ----> is the number of books (represent the input or independent variable)
In this problem
we have a proportional relationship between the variables x and C
Part B) we know that
The linear equation is given by
The constant of proportionality k is the same that the slope or unit rate of the linear equation
In this problem the constant k is given
so
For x=12 books
substitute in the equation and solve for C
In function notation
Answer: 41 1/4
Step-by-step explanation: 160/4=40
5/4= 1 1/4
LIKE IF CORRECT
Answer:
1813.137 KJ
Step-by-step explanation:
potential energy of the body = mgH
where m is mass in Kg , g= 9.81 m/sec^2 and H= height in m
here m= 1000 kg, g= 9.81 m/s^2 and H= 607 feet = 607×0.305= 185.135 m
hence the potential energy p= 1000×9.81×185.135= 1813137.2 J
= 1813.137 KJ
hence the potential energy associated with 1 m^3 of water at 607 feet tall taking the mass as 1000 kg is = 1813.137 KJ
