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Fractional Equations II
Problem 213: Solve for : (1) Solution: We will start by factoring the denominators. (2) Now we get the denominator for the fractions so that we can add them. That is, (3) Now we can get rid of the denominator by multiplying both side by it. (4) That is, and ….
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Fractional Equations
Problem 212: Solve for : (1) Solution: Let’s start with writing the term with constant coefficient. (2) One can now find a common denominator in order to add the two fractions. Also, we can multiply by both sides in order to simplify. (3) That is, . The last step is to check…
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Growth and Decays III
Problem 211: Maria, a biologist, is observing the growth pattern of a virus. She starts with 100 of the virus that grows at a rate of 10% per hour. She will check on the virus in 24 hours. How many viruses will she find? Solution: One can find the amount of viruses can be found…
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Growth and Decays II
Problem 210: A research at the Center for Disease Control and Prevention, Lisa, is studying the growth of a bacteria. She starts his experiment with 50 of the bacteria that grows at a rate of 15% per hour. She will check on the bacteria every 8 hours. How many bacteria will he find 8 in…
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Growth and Decay
Problem 209: Chris is a researcher at the Center for Disease Control and Prevention and he is trying to understand the behavior of a new and dangerous virus. He starts his experiment with 100 of the virus that grows at a rate of 25% per hour. He will check on the virus in 24 hours….
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Application of Logarithm (Decibel Level of Sound)
Problem 208: Extended exposure to noise that measures 85 dB can cause permanent damage to the inner ear which will result in hearing loss. What is the decibel level of music coming through ear phones with intensity watts per square inch? Solution: The loudness level measured in decibels, of a sound of intensity, , measured…
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Application of Logarithm (Earthquake Intensity)
Problem 207: In 1906, San Francisco experienced an intense earthquake with a magnitude of 7.8 on the Richter scale. Over 80% of the city was destroyed by the resulting fires. In 2014, Los Angeles experienced a moderate earthquake that measured 5.1 on the Richter scale and caused $108 million dollars of damage. Compare the intensities…
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Trigonometric Equation III
Problem 206: Solve the equation . Solution: We will use some trigonometric properties to solve this equation. (1) Notice that this is a quadratic equation. Let so that Using the quadratic equation we have (2) Thus or . However, -1.618 is not an option because this value is not in the…
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Trigonometric Equation II
Problem 205: Solve the equation . Solution: We will use arccosine to solve this problem. Notice that (1) since . This means that (2) But these are not the only solutions. In general we have, (3) Hence, (4)
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Trigonometric Equation
Problem 204: Solve the equation . Solution: When solving trigonometric equation, we use the same method as solving algebraic equations i.e., solving for . Thus (1) That is, . However, these are not the only solutions since any other multiple of will also be a solution. Hence,
One Problem at a Time
