The minute hand of a clock is 7 in. Long how far does the point of the hand travel in 60 minutes?
1 answer:
Answer:
Step-by-step explanation:
60 minutes is one hour, which is all the way around the outside of the clock one time. This distance is represented by the circumference of a circle, assuming that the clock is in fact circular. The formula for the circumference of a circle in terms of the radius is
Our radius is 7, so the distance around the outside of that particular clock (and how far the minute hand travels if it goes around the clock one time) is
or
C = 14π
If you want the decimal equivalency for that, multiply in pi as 3.1415 and round to whatever place you need. In decimal form, that is
C = 43.9 inches
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To simplify the calculations, we start by calculating the fourth root of r:
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Then, we calculate the arguments of the trigonometric functions:
We can now calculate for each value of k:
Answer:
The four roots in exponential form are
z0 = 18^(1/4)*e^(i*π/8)
z1 = 18^(1/4)*e^(i*5π/8)
z2 = 18^(1/4)*e^(i*9π/8)
z3 = 18^(1/4)*e^(i*13π/8)