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3 years ago

The minute hand of a clock is 7 in. Long how far does the point of the hand travel in 60 minutes?

Mathematics

1 answer:

Semmy [17]3 years ago

4 0

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

$C=2\pi r$

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

$C=2\pi (7)$ 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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3 years ago

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3 years ago

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3 years ago

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3 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: