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Chapter 2: Problem 76
In your own words, describe how to find the midpoint of a line segment if its endpoints are known.
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 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 \((3,-4)\)
Explaining the Concepts Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?
Does \((x-3)^{2}+(y-5)^{2}=0\) represent the equation of a circle? If not, describe the graph of this equation.
The regular price of a computer is \(x\) dollars. Let \(f(x)=x-400\) and \(g(x)=0.75 x\) a. Describe what the functions \(f\) and \(g\) model in terms of the price of the computer. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the computer. c. Repeat part (b) for \((g \circ f)(x)\) d. Which composite function models the greater discount on the computer, \(f \circ g\) or \(g \circ f ?\) Explain.
Find all values of x satisfying the given conditions. $$f(x)=2 x-5, g(x)=x^{2}-3 x+8, \text { and }(f \circ g)(x)=7$$
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