Rationalize the denominator of the given expression 6 Squar

Rationalize the denominator of the given expression. 6 - Squareroot 6/3 + 3 Squareroot 6 6 - Squareroot 6/3 + 3 Squareroot 6 = (Simplify your answer. Type an exact answer, using radical Let g (x) = 2x^2 - 1. (a) Find the average rate of change from -8 to 3. (b) Find an equation of the secant line containing (-8, g(-8)) and (3, g(3)). (a) The average rate of change from -8 to 3 is (Simplify your answer.) (b) An equation of the secant line containing (-8, g(-8)) and (3, g(3)) is. (Type your answer in slope-intercept form.) An accepted relationship between stopping distance, d in feet, and the speed of a car, in mph, is d(v) = 1.2v + 0.05v^2 on dry, level concrete. (a) How many feet will it take a car traveling 50 mph to stop on dry, level concrete? (b) If an accident occurs 250 feet ahead, what is the maximum speed at which one can travel to avoid being involved in the accident? (a) It will take ft to stop the car that is traveling at 50 mph. (Round up to the nearest foot as needed.) (b) The maximum speed is mph at which one can travel to avoid being involved in the accident. (Round down to the nearest mile per hour as needed.)

Solution

( 6 - sqrt 6 ) / ( 3 + 3 sqrt 6 )

( 6 - sqrt 6 ) / ( 3 + 3 sqrt 6 ) * ( 3 - 3 sqrt 6 ) / ( 3 - 3 sqrt 6 )

(18 - 18sqrt 6 - 3 sqrt 6 + 18 )/ ( 9 - 54 )

= ( 36 - 21 sqrt 6 ) / ( -45 )

= - ( 12 - 7 sqrt 6 ) / 15

= ( 7 sqrt 6 - 12 ) / 15