Section 1.6 SolvingEquations

3 5 1 2 m 3 m 3m m 10 2x x 1 x 5 x 5 pf solve q

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Unformatted text preview: e following rational equations. 3 5 1 −2 =. m + 3 m + 3m m 10 2x +x =1+ . x −5 x −5 pf Solve q = for p . p−f Rational Exponents Applications Outline Solving Polynomial Equations Solving Rational Equations Rational Exponents Rational Exponents Theorem (The Power Property) If a and b are a real numbers (or real-valued expressions) then √ nm a = b if and only if am = b n . To solve an equation involving rational exponents: Isolate a term with a rational exponent. Use the Power Property to eliminate the radical. Repeat if more rational exponents remain. When only integer exponents remain, solve the equation. Check for extraneous solutions! Applications Outline Solving Polynomial Equations Solving Rational Equations Rational Exponents Examples Example 2 √ Solve −2 4x − 1 = −10. √ √ Solve x + 7 − x = 1. 3 Solve −2x 3/4 + 47 = 7. 4 Solve x 2/3 − x 1/3 − 15 = 0. Hint: Use u -substitution. 1 Applications Outline Solving Polynomial Equations Solving Rational Equations Rational Exponents Applications An Application Example The gelatin capsules manufactured for cold and flu medications are shaped like a cylinder with a hemisphere on each end. The interior volume V of each capsule can be modeled by 4 V = πr 3 + πr 2h 3 where r is the radius of the capsule and h is the height of the cylindrical portion of the capsule. If h = 8 mm, what radius would give the capsule a volume that is numerically equivalent to 15π times this radius?...
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This note was uploaded on 02/10/2014 for the course MATH 1050 taught by Professor K.jplatt during the Spring '14 term at Snow College.

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