P01 - and x ≥ is measured in appropriate units of...

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Project 1 MAC 2233 1. What do we call the set of all points whose distance from the point ( h,k ) is r ? Derive an equation for the graph using distance formula. Rewrite the following equations of circles by completing squares, draw the graphs, and label the points of intersection A and B . What is the distance between the centers of the circles? What is the slope of the line through the two centers? x 2 + y 2 - 2 x + 2 y - 8 = 0 x 2 + y 2 - 6 x - 4 y + 8 = 0 2. When the brightness x of a light source is increased, the eye reacts by decreasing the area R of the pupil. The experimental formula R = 40 + 24 x 2 / 5 1 + 4 x 2 / 5 has been used to model the dependence of R on x , where R is measured in square millimeters
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Unformatted text preview: and x ≥ is measured in appropriate units of brightness. Should the pupil have a larger area when x = 0 or when x = 32 ? How may times larger is it? The equation above can be solved for the variable x 2 / 5 . Show that x = ± R-40 24-4 R ² 5 / 2 . For what x-value will R be 10 square millimeters (round to the nearest tenth)? Note that x is not a real number for some R values because of the square root. Solve an inequality in order to determine the values of R for which there is a real solution ( x,R ) . What seem to be the smallest and largest possible areas R for the pupil?...
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