If a weight hanging on a string of length 5 feet swings through 6° on either side of the vertical, how long is the arc through which the weight moves from one high point to the next high point? \

  1.047 ft

Step-by-step explanation:

The length of an arc is given by ...

  s = rθ

where s is the arc length, r is the radius, and θ is the central angle in radians. Your arc subtends an angle of 12° = (12·π/180) = π/15 radians. The length of the arc is then ...

  s = (5 ft)(π/15) = π/3 ft ≈ 1.047 ft

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x