2 Math Questions?

Question

Please answer with an EXPLANATION!

1. The minute hand of a clock measures 10 cm from its tip to the center of the clock face, and the hour hand from its tip to the center of the clock face is 5 cm. What is the sum of the distances, in meters, traveled by the tips of both hands in one twenty-four hour period? Express your answer to the nearest thousandth of a meter.

2. If Ella rolls a standard six-sided die until she rolls the same number on consecutive rolls, what is the probability that her 10th roll is her last roll express your answer as a decimal to the nearest thousandth.

Answer 1

In 24 hours the hands will go around twice. The problems breaks down to finding the circumfrence of two circle, one with radius 10 the other radius 5

The equation is 2piR

In the first case R (the radius) is 10cm, but remember we want meters. So it's .1m

C = 2pi(.1) = .2pi

Now this is the distance one time around, which would be 12 hours . but we want 24 so we need it to be twice that.

The final distance traveled by the minute hand is .4pi.

The same process can be done for the hour hand. and it is .2pi




The dice one is harder to explain.

So the first roll doesn't matter, the second is when the fun starts.
She has a 5/6 chance of not getting the same number.
On the third roll it's the same thing. 5/6 of not getting.
Fourth....you get the point.

We go until we get to the 10th and we want her to get this one so she has a 1/6 chance of getting it.

Now we just multiple them altogether.
5/6x5/6x5/6x5/6x5/6x5/6...x1/6

so eight 5/6 and on 1/6

that is 390625/10077696 or .0387613398 or 3.87613398%

So the final is 3.876%

Answer 2

1) first is to find the circumference of the minute hand circle and multiple by 24 then add the circumference of the hour hand.
pi = 3.141592
2*r*(pi)=Circumference
2*10(3.141592)= 62.83184 cm now multiple by 24 revolutions
62.83184 * 24 = 1507.96416 cm distance traveled by minute hand

2 * 5 * (3.141592)= 31.41592 cm now multiple by 2 revolutions
2 * 31.41592 = 62.83184 cm distance travel by hour hand

add the 2 together
1507.96416 cm + 62.83184 cm = 1570.796 cm

1570.796 cm = 15.708 meters