Answer:
7
Step-by-step explanation:
The function can be written in vertex form as ...
f(x) = -(x +1)^2 +7
The vertex is then identifiable as (-1, 7). The y-coordinate is 7.
_____
Vertex form is ...
f(x) = a(x -h)^2 +k
where "a" is the vertical scale factor, and (h, k) is the vertex point. It is convenient to arrive at this form by factoring "a" from the first two terms, then adding and subtracting the square of the remaining x-coefficient inside and outside parentheses.
f(x) = -(x^2 +2x) +6
f(x) = -(x^2 +2x +1) + 6 -(-1) . . . . completing the square
f(x) = -(x +1)^2 +7 . . . . . . . . . . . . vertex form; a=-1, (h, k) = (-1, 7)
Consider the point P where the gears meet. When the smaller gear rotates clockwise, the larger one will rotate counterclockwise.
Through one rotation of the smaller gear, P will have traveled the circumference of the smaller gear, which is 
in.
At the same time, a point P' on the larger gear traverses the same distance along the larger gear's circumference. This point traces out an arc that is subtended by some angle 
. The arc is as long as the smaller gear's circumference.
The measure of a circle's interior angle subtended by an arc is proportional to a complete revolution, i.e. an angular displacement of 
radians:
For part 2, we apply the same reasoning to the larger gear. In one full rotation of the larger gear, the point P' traverses the circumference 
in, and so does the point P on the smaller gear.
A full rotation is 360 degrees, so the smaller gear would have rotated 
times.
The width is 12.8 and when u round it is 13 foot
