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Chapter 1: Problem 6
Plot the given point in a rectangular coordinate system. $$(-4,-2)$$
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Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$(y+1)^{2}=36-(x-3)^{2}$$
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.
A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at this point of contact. Write an equation in point-slope form for the line tangent to the circle whose equation is \(x^{2}+y^{2}=25\) at the point (3,-4).
Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$g(x)=\left|4-x^{2}\right|$$
In your own words, describe how to find the midpoint of a line segment if its endpoints are known.
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