A carousel horse travels on a circular path with a radius of 15 ft. How many feet does the horse travel over an angle of 2π3 radians? Round to the nearest foot.

2π3 radians =

The horse travels 31 feet over an angle of radians

Step-by-step explanation:

∵ A carousel horse travels on a circular path

- That means the distance that the horse travels is the length

   of an arc of the circular path

∵ The radius of the circular path is 15 feet

∴ r = 15 ft

∵ The horse travel over an angle of radians

- Let us change it to degree by multiply it by

∵   × = = 120°

- use the formula above to find the distance

∵ d = × 2πr

∵ x = 120°

∴ d = × 2π × 15

∴ d = 10π

∴ d = 31.41592654 feet

- Round it to the nearest foot

∴ d = 31 feet

The horse travels 31 feet over an angle of radians

option: d is correct

step-by-step explanation:

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".