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Chapter 11: Q. 3 (page 713)
If a system of equations has no solution, it is said to be _______.
If a system of equations has no solution, it is said to be inconsistent.
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Kelly has \(20,000 to invest. As her financial
planner, you recommend that she diversify into three investments: Treasury bills that yield 5% simple interest, Treasury bonds that yield 7% simple interest, and corporate bonds that yield 10% simple interest. Kelly wishes to earn \)1390 per year in income. Also, Kelly wants her investment in Treasury bills to be $3000
more than her investment in corporate bonds. How much money should Kelly place in each investment?
If Bruce and Bryce work together for hour and minutes, they will finish a certain job. If Bryce and Marty work together for hour and minutes, the same job can be finished. If Marty and Bruce work together, they can complete this job in hours and minutes. How long will it take each of them working alone to finish the job?
Constructing a Box: A rectangular piece of cardboard, whose area is 216 square centimeters, is made into an open box by cutting a 2-centimeter square from each corner and turning up the sides. See the figure. If the box is to have a volume of 224 cubic centimeters, what size cardboard should you start with?
Descartes鈥檚 Method of Equal Roots: Descartes鈥檚 method for finding tangents depends on the idea that, for many graphs, the tangent line at a given point is the unique line that intersects the graph at that point only. We apply his method to find an equation of the tangent line to the parabola at the point (2,4). See the figure.
First, we know that the equation of the tangent line must be in the form . Using the fact that the point is on the line, we can solve for b in terms of m and get the equation . Now we want to be the unique solution to the system
From this system, we get . By using the quadratic formula, we get
To obtain a unique solution for x, the two roots must be equal; in other words, the discriminant must be 0.
Complete the work to get m, and write an equation of the tangent line.
Graph each system of linear inequalities by hand. Verify your results using a graphing utility.
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