The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below. f (l) = 2 pi StartRoot StartFraction l Over 32 EndFraction EndRoot, where l is the length of the pendulum in feet What is the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth?

46.08 feet.

Step-by-step explanation:

Given that, for length, feet, the time period, , of the pendulum is

.

As the time period equals the time taken by the pendulum in one back and forth motion, so, actually, the given seconds to swing back and forth is the time period.

Let feet be the length of the pendulum for the time period seconds, so

[squaring on both the sides]

Hence, the approximate length of a pendulum that takes seconds to swing back and forth is 46.08 feet.

22 and 22

step-by-step explanation:

10 plus 12 equals 22.

12 plus 10 also equals 22 because regardless of what order they're in, they're gonna equal the same thing.

(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