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.
Answer:
168
Step-by-step explanation:
The vertex will be when the velocity is equal to zero:
df/dx=-12x+24 (using the power rule for differentiation)
df/dx=0 only when:
-12x+24=0 add 12x to both sides
12x=24 divide both sides by 12
x=2, we find the y value to be:
y(2)=-6(2^2)+24*2-20
y(2)=-24+48-20=4
So the vertex is the point (2,4)
And the axis of symmetry is the line x=2
Now if you do not yet do calculus...
The vertex will occur midway between the two zeros.
6x^2-24x+20=0 (using the Quadratic Formula for simplicity)
x=(24±√96)/12
x≈(1.1835, 2.8165)
Now the vertex occurs at the average of the zeros...
x=(1.1835+2.8165)/2=2 (as we saw earlier)
y(2)=4
Vertex is at (2,4) and axis of symmetry is the vertical line x=2
Answer:
x=7
Step-by-step explanation: