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Radicals and Rational Exponents and Applications of Logarithms

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include an example of an equation easier to solve as a rational exponent rather then a radical sign.

2)The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear.
How is sound measured. The formula for measuring sound.
What would be a specific sound, give me the decibels of the sound, and please explain what this measurement means. If you have a reference I would like to see it and check it out also)

3)Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related the arithmetic sequence?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence?
I need to find at least two real-life examples of a sequences or series. One example, I know is arithmetic, and the second is geometric. How can I explain these examples would affect me personally.

1) Solve the following equations.
a)
Answer:

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b) .
Answer:

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c) .
Answer:

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2) Is an identity (true for all values of x)?
Answer:

Explain your answer in this space.

3) For the equation , perform the following:
a) Solve for all values of x that satisfies the equation.
Answer:

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b) Graph the functions and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

Graph

c) How does the graph relate to part a?
Answer:

4) A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides' measurements are 3 feet and 4 feet.
Answer:
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5) Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? North and east can be considered the directions of the y- and x-axis respectively.

Answer:
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6) The volume of a cube is given by V = s3. Find the length of a side of a cube if the Volume is 729 cm3.
Answer:
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Radicals and Rational Exponents and Applications of Logarithms are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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