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Applications Involving Rational Equations

Applications Involving Rational Equations. Sec. 2.8b. Calculating Acid Mixtures. How much pure acid must be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid?. mL of pure acid. = concentration of acid. mL of mixture. mL of acid in 35% solution:.

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Applications Involving Rational Equations

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  1. Applications Involving Rational Equations Sec. 2.8b

  2. Calculating Acid Mixtures How much pure acid must be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid? mL of pure acid = concentration of acid mL of mixture mL of acid in 35% solution: (0.35)(50), or 17.5 mL of acid added: x mL of pure acid in resulting mixture: x + 17.5 mL of the resulting mixture: x + 50

  3. Calculating Acid Mixtures How much pure acid must be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid? x + 17.5 = concentration of acid x + 50 x + 17.5 Let’s solve this graphically… = 0.75 x + 50 Point of intersection: (80, 0.75) We need to add 80 mL of pure acid to the 35% acid solution to make a solution that is 75% acid

  4. Finding a Minimum Perimeter Find the dimensions of the rectangle with minimum perimeter if its area is 200 square meters. Find this least perimeter.

  5. Finding a Minimum Perimeter Find the dimensions of the rectangle with minimum perimeter if its area is 200 square meters. Find this least perimeter. Perimeter = 2(length) + 2(width) Let’s minimize this function!!! Calculator!!! Min. P of 56.569 meters at x = 14.142 meters Dimensions: 14.142 m by 14.142 m

  6. Page 256, #36 The diagram: (a) Area as a function of x: 1.5 in. (b) Minimize this function (graph!): 0.75 in. 40 Min. at 1 in. x Dimensions of about 7.042 in. by 10.059 in. yield a minimum area of about 70.833 square inches. x 1 in.

  7. Page 256, #38 The diagram: (a) Area as a function of x: 2 1000 2 2 x (b) Minimize this function (graph!): x Min. at 2  The pool is square!!! With dimensions of approximately 35.623 ft x 35.623 ft, the plot of land has minimum area of about 1268.982 sq ft.

  8. Designing a Juice Can Stewart Cannery will package tomato juice in 2-liter cylindrical cans. Find the radius and height of the cans if the cans have a surface area of 1000 square centimeters. S = surface area of can (square centimeters) r = radius of can (centimeters) h = height of can (centimeters) Note: 1 L = 1000 cubic centimeters

  9. Designing a Juice Can Stewart Cannery will package tomato juice in 2-liter cylindrical cans. Find the radius and height of the cans if the cans have a surface area of 1000 square centimeters.

  10. Designing a Juice Can Stewart Cannery will package tomato juice in 2-liter cylindrical cans. Find the radius and height of the cans if the cans have a surface area of 1000 square centimeters. Solve Graphically… r = 4.619 cm, or r = 9.655 cm Find the corresponding heights… 2 With a surface area of 1000 cm , the cans either have a radius of 4.619 cm and a height of 29.839 cm, or have a radius of 9.655 cm and a height of 6.829 cm.

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