Equations with an unknown in the exponent rank atomic number 18 called Exponential Equations
Example: the equation S=0.8^d models the fraction of sunlight, S, that reaches a scuba diver under water, where d is the deepness of the diver in meters.
a) how much sunlight reaches a diver that is a ta depth 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 64/125
64/125=0.8^d = 0.512 d=3m
[guess and check, use powers of the same base]
2^x = 8
2^3 = 8
In general, if x^m= x^n. then m=n
step to solving exponential equations using same base powers: 1.rewrite the powers, on both 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 rational expression, like a rational number is a quotient; however, it is a quotient of two polynomial expressions. over again the denominator cannot be zero
Ex.
(2x-3)/(x^2 + 1) is a rational expression
The following are also rational expressions
1/x (y-4)/7 (x^2 + 3x - 1) / (x+7)
example1 reducinf a rational 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 multiply rational expressions...
1. factor all numerators and denominators as far as possible.
2. stir up any common factors.
3.Multiply the numerators.
4. Multiply the denominators.
5....If you want to get a full essay, order it on our website: Orderessay
If you want to get a full essay, wisit our page: write my essay .
No comments:
Post a Comment