The height (in meters) of a shot cannonball follows a trajectory given by h(t)=-4.9t^2+14t-0.4 at time t (in seconds). For how many seconds is the height of the cannonball at least 6 meters?
Determine the set of all real x satisfying (x^2+3x-1)^2<9
Enter your answer in interval notation.
Expressing your answer in interval notation, find all values of x such that x(x-2)^2 * (x+1)<0.
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(1) Solving the inequality, the answer is 5 seconds.
(2) Solving the inequality, the answer is (-5,2).
(3) The answer is (0,inf).
+36916 h(t)=-4.9t^2+14t-0.4 substitute 6 in for h(t) and solve for t
you should get two VALUES for t the ball is above 6m for the time in between
6 = -4.9t^2+14t-.4
-4.9t^2 +14t- 6.4 =0 solve for t = 0.571429 and 2.28571 now you calc the time the ball is above 6m
+128475 Determine the set of all real x satisfying (x^2+3x-1)^2<9
Enter your answer in interval notation.
Take both roots and we have that
x^2 + 3x - 1 = 3 x^2 + 3x - 1 = - 3
x^2 + 3x - 4 = 0 x^2 + 3x + 2 = 0
(x + 4) (x - 1) = 0 (x + 2) ( x + 1) = 0
Setting each factor to 0 and solving for x gives the answers that x = { -4, - 2,- 1, 1 }
So....we have the possible answers
(-inf, -4) ( -4, -2) ( -2, -1) (-1, 1) or ( 1 inf )
Testing a point in each interval in the original inequality we see that the solution intervals are
(-4, -2) U (-1, 1)
