What is the period of the function F(x) = -4sec (1/2 x) A. 4 pi
B. pi
C. pi/2
D. 2 pi

4piR^2

Step-by-step explanation:

A) 4π

Step-by-step explanation:

The period of a secant function, f(x)=a*sec(bx+c)+d, is defined as 2π/|b| where b is the distance of the period. Since we know b=1/2 given by the function, then the period is 2π/|1/2|=2π/(1/2)=2π(2/1)=4π.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752