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Chapter 1: Problem 33
Evaluate each function at the given values of the independent variable and simplify. \(f(r)=\sqrt{r+6}+3\) a. \(f(-6)\) b. \(f(10)\) c. \(f(x-6)\)
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding \(h\) and \(k,\) I place parentheses around the numbers that follow the subtraction signs in a circle's equation.
Find the area of the donut-shaped region bounded by the graphs of \((x-2)^{2}+(y+3)^{2}=25\) and \((x-2)^{2}+(y+3)^{2}=36\).
Determine whether each statement makes sense or does not make sense, and explain your reasoning.I used a function to model data from 1990 through 2015 . The independent variable in my model represented the number of years after \(1990,\) so the function's domain was \(\\{x | x=0,1,2,3, \dots, 25\\}\).
Graph \(y_{1}=x^{2}-2 x, y_{2}=x,\) and \(y_{3}=y_{1} \div y_{2}\) in the same [-10,10,1] by [-10,10,1] vicwing rectangle. Then use the TRACE l feature to trace along \(y_{3}\). What happens at \(x=0 ?\) Explain why this occurs.
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+x+y-\frac{1}{2}=0$$
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