a factory has a machine which bends wire at a rate of 8 units of curvature per second. how long does it take to bend a straight wire into a circle of radius 5?
To determine how long it takes to bend a straight wire into a circle of radius 5, we need to find out the length of the wire and divide it by the bending rate.
First, let's find the length of the wire. The circumference of a circle is given by the formula C = 2πr, where "C" represents the circumference and "r" represents the radius. In this case, since the radius is 5, we have C = 2π(5) = 10π units.
Since the wire is currently a straight line, its length is equal to the circumference of the circle it will form, which is 10π units.
Next, we divide the length of the wire by the bending rate to find the time it takes to bend the wire. The bending rate is given as 8 units of curvature per second.
Time = Length of wire / Bending rate
Time = 10π units / 8 units per second
Simplifying, we get:
Time = (10π / 8) seconds
Approximating the value of π to 3.14, we have:
Time = (10 * 3.14) / 8 seconds
Time ≈ 31.4 / 8 seconds
Time ≈ 3.925 seconds
Therefore, it takes approximately 3.925 seconds for the machine to bend the straight wire into a circle of radius 5.