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7.1 Assignment B even answers. 14. 24. 0 34. -4 16. 26. 2 36. 18. 28. 0 38. 20. 30. -10 40. 22. 32. 7.1 nth Roots and Rational Exponents Notes C. Example 5: Evaluating a Model with nth Roots
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7.1 Assignment B even answers 14. 24. 0 34. -4 16. 26. 2 36. 18. 28. 0 38. 20. 30. -10 40. 22. 32.
7.1 nth Roots and Rational ExponentsNotes C Example 5:Evaluating a Model with nth Roots The total mass M (in kilograms) of the magnetic sail is, in theory, given by the formula below where m is the mass (in kilograms) of the magnetic sail, f is the drag force (in newtons) of the spacecraft and d is the distance (in astronomical units) to the sun. Find the total mass of a spacecraft that can be sent to Mars using m = 5000kg, f = 4.52 N and d = 1.52 AU. M = 0.015m2 fd 4/3
Example 6:Solving an Equation Using an nth Root The Olympias is a reconstruction of a trieme, a type of Greek galley ship used over 2000 years ago. The power P (in kilowatts) needed to propel the Olympias at a desired speed s (in knots) can be modeled by this equation: P = 0.0289s3. A volunteer crew was able to generate a maximum power of about 10.5 kilowatts. What is their greatest speed?
7.2 Properties of Rational ExpressionsNotes A Property Example 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6.
Example 1:Using Properties of Rational Exponents • 5½. 5¼ • (8 ½. 5 1/3)2 • (24. 34) – ¼ • 7 7 1/3 (e) (12 1/3)2 4 1/3
Product property: Quotient property:
For a radical to be in simplest form, you must not only apply the properties of radicals, but also remove any perfect nth powers. Example 3:Writing Radicals in Simplest Form
7.1 Assignment C: pg. 405 #63-67 odd; pg. 404 #14-60 even; Standardized Test Practice 7.2 Assignment A: pg. 405 #62; pg. 411 #23-45 odd; Standardized Test Practice
OGT Practice Problems 1. Simplify: 42 – 3(5 + 6/2) (A) – 8 (B) -0.5 (C) 4 (D) 71.5 2. Subtract: (4.32 x 104) – (6.38 x 104) • - 1.07 x 105 (B) - 2.06 x 104 • - 2.06 x 100 (D) 2.06 x 100 3. Divide: 7 1/3 divided by 1 5/9 (A) 11 11/27 (B) 7 3/5 (C) 5 2/7 (D) 4 5/7 4. Divide: - 29.76 divided by 6.2 • 48 (B) 4.8 (C) - 4.8 (D) - 48