Math Problem Statement
Solution
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8.117
What is the length of the side labeled "x" in each diagram?
a. A right triangle with a 60° angle and hypotenuse = 2.
b. A right triangle with a 45° angle and one side labeled "5√2".
8.119
Sketch the graph of each polynomial function below and identify all of the zeros.
a.
b.
8.124
Due to the worsened economy, mechanics in downtown Hollywood cannot afford to replace their outdoor light bulbs when they burn out. On average, about 1.8% of the lights burn out every month. Assuming there are now 1,000,000 outdoor lights in Hollywood, how long will it take until there are only 100,000 lights left?
8.125
Rewrite each expression as a single logarithm.
a.
b.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Polynomials
Logarithms
Exponential Decay
Formulas
Right triangle trigonometric ratios
Polynomial root finding
Logarithmic properties: log(a) + log(b) = log(ab), log(a) - log(b) = log(a/b)
Exponential decay formula: N(t) = N_0 * e^(-rt)
Theorems
Pythagorean theorem
Fundamental theorem of algebra
Properties of logarithms
Suitable Grade Level
Grades 10-12
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