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 mL of mixture = concentration of acid 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 x + 50 = concentration of acid x + 17.5 x + 50 = 0.75 Let’s solve this graphically… 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. 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: 1 in. 0.75 in. 1.5 in. 1 in. x x 40 (a) Area as a function of x: (b) Minimize this function (graph!): Min. at Dimensions of about 7.042 in. by 10.059 in. yield a minimum area of about 70.833 square inches.

7. Page 256, #38 The diagram: x 1000 (a) Area as a function of x: (b) Minimize this function (graph!): Min. at With dimensions of approximately 35.623 ft x 35.623 ft, the plot of land has minimum area of about 1268.982 sq ft. 22 2 2 x  The pool is square!!!

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… 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. 2