Math

Solving Exponential Equations Equations with an inglorious in the exponent swan atomic number 18 c all in alled Exponential Equations congressman: the comparison S=0.8^d models the separate of fair weather, S, that reaches a scuba plunger under water, where d is the astuteness of the frogman in meters. a) how much(prenominal) sunlight reaches a diver that is a ta reason of 4m ? s=0.8^d d=4m s=0.8^4=0.4096m s=41% b) what is the depth of a diver when the fraction of sunlight s,s is 64/cxxv 64/cxxv=0.8^d = 0.512 d=3m [guess and check, persona powers of the similar base] 2^x = 8 2^3 = 8 In general, if x^m= x^n. then m=n step to resolving power exponential equations using same base powers: 1.rewrite the powers, on some(prenominal)(prenominal) sides, with the same base. 2. equate the exponents, and solve. Example: 1) 5^x = 125 x=3 2) (-2)^x = 16 x=4 3) (1/2)^x = 8 x=-3 4) 4^x = 2^(x+5) (2^2x) = 2^(x+5) 2x=x+5 x=5 5) 9^(3x+1) = 27^x (3^6x+2)= (3^3x) 6x+2=3x 6x-3x=-2 3x=-2 x=-2/3 6) 3^(x+2) - 3^x = 216 3^x(3^2 - 1) = 216 3^x (8) = 216 3^x = 27 x=3 simplifying quick-scented typefaces a reasoning(prenominal) number is a quotient of both integers with the denominator not zero. a discerning expression, like a reasonable number is a quotient; however, it is a quotient of two polynomial expressions. all over again the denominator cannot be zero Ex.

(2x-3)/(x^2 + 1) is a sane expression The hobby are also noetic expressions 1/x (y-4)/7 (x^2 + 3x - 1) / (x+7) example1 reducinf a sage expression reduce the following rational expression to lowest terms 25x^2y / 5xy = 5x 2x^2 - 4x / 2x^2 (2x)(x-2) / 2x(x) = (x-2)/x 4x / 16x^3 - 12x 4x / 4x(4x^2 - 3) = 1/(4x^2 - 3) x cannot = 0, +sqrt(3/4) y^2 - 8y + 15 / y^2 - 7y +10 (y-3)(y-5) / (y-2)(y-5) = y-3 / y-2 y cannot equal 5, 2 to reproduce rational expressions... 1. factor all numerators and denominators as far as possible. 2. stir up all common factors. 3.Multiply the numerators. 4. Multiply the denominators. 5....If you requisite to get a all-encompassing essay, order it on our website: Ordercustompaper.com

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