Sebastian writes the recursive formula f(x+1)=4f(x) to represent a geometric sequence whose second term is 12.

which explicit formula can be used to model the same sequence?

a. f(x)=12(4)x
b. f(x)=3(4)^x-1
c. f(x)=4(12)^x
d. f(x)=4(3)^x-1

B. f(x)=3(4)^x-1

Step-by-step explanation:

In order to know which explicit formula can be used to model the same sequence you have to calculate f(x) in:

f(x+1) and 4f(x)

and prove if they have the same results in both sides (f(x+1) = 4f(x))

Then, if you take

1. f(x+1)

=

2. 4f(x)

==

if you evaluate both sides (f(x+1) and 4f(x)) for x=0, x=1, x=2, you have:

x=0

==3

===3

x=1

==12

===12

x=2

==48

===48

Then you can say for: f(x)=3(4)^x-1 is fulfilled that f(x+1) = 4f(x)

72 is the answer to this problem

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47