7) Solve each of the following equations: (a) 6x2 +x 25 10 (b) 4x3 + 8x2-12x = 0

Question

7) Solve each of the following equations: (a) 6x2 +x 25 10 (b) 4x3 + 8x2-12x = 0 8) Suppose that a small rocket is launched from ground level. Its height in meters t seconds after it is has been launched is given by h(t)--5t2 +100t (a) Evaluate and interpret h(4) (b) Solve and interpret h(t) - 180 (c) Solve and interpret h(t) -500 (d) When does the rocket hit the ground? 9) Let f(x)-2 (a) Evaluate f (7) (b) Solve f(x) = 2 (c) Using graph transformations, sketch the graph of f(x) (d) Label the asymptotes on your graph. (e) Give the domain and range of f(x) 10) Simplify each of the following rational expressions (b) 3268 4z2+12x

Explanation / Answer

1a) 6x^2 - x - 25 = 10

6x^2 -x - 35 = 0

( 3x + 7 ) ( 2x - 5) = 0

x = -7/3 , 5/2

b)  4x^3 + 8x^2 - 12x = 0

4x ( x^2 + 2x - 3 ) = 0

4x ( x+3) (x-1) = 0

x = 0 , -3 , 1

c) x^5 - 25x^3 + x^2 = 25

x^3 ( x^2 - 25 ) + 1 ( x^2 - 25 ) = 0

(x^3 + 1 ) ( x^2 - 25 ) = 0

x = cube root (-1 ) , x = + 5 , -5

d) x^4 + 25x^2 = x^3 + 25x

x^4 + 25x^2 - x^3 - 25 x = 0

x^4 - x^3 + 25x^2 - 25x = 0

x^3 ( x -1 ) + 25x ( x -1 ) = 0

( x^3 + 25x ) ( x- 1 ) = 0

x ( x^2 + 25 ) ( x-1 ) = 0

x = 0 , x = + 5i , x = -5i , x = 1

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