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The minute hand of a clock is 4.5 cm long. How far does the tip of the minute hand travel in 80 minutes?

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Distance = Rate x Time

How far does the tip of the Hour Hand move in 60 minutes?

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Start your 7-day free trialDistance = Rate x Time is not the formula you need. There is no rate in this problem. You also do not need trig. The formula you need is more basic and is very common.

There are different ways to solve a problem. It can be the formula. The rate (cm/hour) can be determined easily.

Some hints were offered, so I think to proceed with this thread, you need to show us what you have so far. If you have questions on the hints, then why not ask about them?

From what I got from this problem it went something like this:

t = theta

s = r*t

r = 4.5 cm

t = 80 / 60

2*pi = 60

Because 2*pi counts as a full rotation such as 60 mins = 1 hour with a remainder to 20 minutes left thus making...

t/2*pi = 4/3

Doing some math that gives us... 8*pi/3

Now we just substitute that back into the original equation and...

s = 4.5 (8*pi/3) = 36*pi / 3 = 12*pi

Now I just don't know if i'm correct...

- the tip travels in a circle;

- in 80 minutes, the tip travels around the circle 80/60, or 4/3 times;

- the circumference of a circle is 2 * pi * r;

- hence the distance traveled is

(4/3) * 2 * pi * 4.5cm

= (4/3) * 2 * 4.5 * pi cm

= (4/3) * 9 * pi cm

= 12 pi cm

C=2 pi r

Rate = C/60 (cm/min)

Distance = Rate * time = Rate * 80 = (C/60) * 80 = 4C/3 = 4(2 pi r)/3 = 8/3 * pi * r = 12 pi (cm)

==========

Another way (Angular speed/displacement):

Angular speed, omega (radians/minute) = (2 pi radians) / (60 minutes) = (pi/30) radians/minute

angular displacement, theta = omega * t = (omega radians/minute) * (80 minutes) = (80 * omega) radians

distance = r * theta = r * (80 * omega) = r * 80 * (pi/30) = 8/3 pi r = 12 pi (cm)

Math / Science

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it is a violation of the member agreement.

please post what you have tried and we can help assist