We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
66
3
avatar

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.

 

 

PLEASE HELP

THANK YOU

 Nov 3, 2019
 #1
avatar
0

(1) Solving the inequality, the answer is 5 seconds.

 

(2) Solving the inequality, the answer is (-5,2).

 

(3) The answer is (0,inf).

 Nov 3, 2019
 #2
avatar+19937 
+2

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

 Nov 3, 2019
 #3
avatar+105238 
+2

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)

 

cool cool cool

 Nov 3, 2019

13 Online Users

avatar
avatar
avatar