A water wheel has a radius of 4 feet and the bottom of the wheel is 1 foot from the ground. One plank is painted white and it starts at the top of the wheel. The wheel is rolled forward through an angle of pi over 3 radians. How high from the ground is the white plank after this motion?

The height of the plank after the π/3 rotation motion is 8.464 ft

Step-by-step explanation:

The radius of the wheel = 4 ft

The elevation of the bottom of the wheel from the bottom = 1 foot

The angle to which the wheel is rolled = π/3 radians

The height of a rotating wheel is given by the following relation

f(t) = A·sin(B·t + C) + D

Where;

D = Mid line =  4 + 1 = 5 feet

B·t = π/3

C = 0

A = The amplitude = 4

Which gives;

f(t) = 4×sin(π/3) + 5 = 8.464 ft

The height of the plank after the π/3 rotation motion = 8.464 ft.

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4

y=20x

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hope this