8. If a pendulum with length \( 169 cm \) has a frequency of \( 1 / 20 Hz \) , find the length of a pendulum that has frequency \( 1 / 5 Hz \) , given that you know that the frequency varies inversely with the square root of the length. If the answer is not an integer, enter it as a decimal. Round the decimal to the nearest tenth.
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Related Questions
Q:
Pick any number, multiply the number by \( 4 \) , add \( 12 \) to the product, divide the sum by \( 4 \) , and subtract \( 3 \) from the quotient. Complete parts a through d below
a) What is the relationship between the number you started with and the final number?
A. The final number is the same as the original number.
B. The final number is \( 4 \) times the original number.
C. The final number is \( 9 \) more than the original number.
D. The final number is \( \frac { 1 } { 4 } \) of the original number.
b) Arbitrarily select some different number and repeat the process, recording the original number and the result.
A. The final number is the same as the original number.
B. The final number is \( 4 \) times the original number.
C. The final number is \( 9 \) more than the original number.
D. The final number is \( \frac { 1 } { 4 } \) of the original number.
Q:
d) Try to prove, using deductive reasoning, the conjecture you made in part (c).
A. Pick a number \( n \) . Multiply the number by \( 4,4 n \) . Add \( 12 \) to the product, \( 4 n + 12 \) . Divide the sum by \( 4 , \frac { 4 n + 12 } { 4 } = \frac { n } { 4 } + 3 \) . Subtract \( 3 \) from the quotient, \( \frac { n } { 4 } + 3 - 3 = \frac { n } { 4 } \) .
B. Pick a number \( n \) . Multiply the number by \( 4,4 n \) . Add \( 12 \) to the product, \( 4 n + 12 \) . Divide the sum by \( 4,4 n + \frac { 12 } { 4 } = 4 n + 3 \) . Subtract \( 3 \) from the quotient, \( 4 n + 3 - 3 = 4 n \) .
C. Pick a number \( n \) . Multiply the number by \( 4,4 n \) . Add \( 12 \) to the product, \( 4 n + 12 \) . Divide the sum by \( 4 , \frac { 4 n + 12 } { 4 } = n + 3 \) . Subtract \( 3 \) from the quotient, \( n + 3 - 3 = n \) .
D. Pick a number \( n \) . Multiply the number by \( 4,4 n \) . Add \( 12 \) to the product, \( 4 n + 12 \) . Divide the sum by \( 4 , \frac { 4 n } { 4 } + 12 = n + 12 . \) Subtract \( 3 \) from the quotient, \( n + 12 - 3 = n + 9\)
Q:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Using the inspection method, what constant term must the numerator of the rational expression \(\frac { x ^ { 2 } + 8 x + 11 } { x + 6 } \) have so \( ( x + 6 ) \) is one of its factors?
For the numerator to have \( ( x + 6 ) \) as a factor, its constant term must be ____
Q:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Using the inspection method, what constant term must the numerator of the rational expression\(\frac { x ^ { 2 } + 8 x + 11 } { x + 6 } \) have so \( ( x + 6 ) \) is one of its factors?
For the numerator to have \( ( x + 6 ) \) as a factor, its constant term must be ___
Q:
Pick a number and add \( 3 \) to it. Find the sum of the new number and the original number. Add \( 7 \) to the sum. Divide the new sum by \( 2 \) and subtract the original number from the quotient. What is the final number?