+93 Hey, I need help with some of the following problems:
1. 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?
(I think that may be answered before but I am still a bit confused)
2.Find the maximum value of f(x)=-4(x-1)^2+6.
(I'm getting (1,6) as vertex and idk why its wrong)
3. What is the maximum value of 4(x+7)(2-x) over all real numbers ?
(again not sure why im wrong)
+129899 1. 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?
We want to solve this
-4.9t^2 + 14t - 0.4 = 6 subtract 6 from both sides
-4.9t^2 + 14t - 6.4 = 0 multiply through by -10
49t^2 - 140t + 64 = 0 factor as
(7 t - 16) ( 7t - 4) = 0
Set each factor to 0 and solve for t and it will be at 6m at 4/7 sec and 16/7 sec
So....it will be a height of 6m (or above) for 16/7 - 4/7 = 12/ 7 seconds
+129899 2.Find the maximum value of f(x) = -4(x-1)^2+6.
The vertex is (1 , 6)
So....the max value is 6
You are correct....this graph proves it : https://www.desmos.com/calculator/ewjtfy8u96
+129899 3. What is the maximum value of 4(x+7)(2-x) over all real numbers ?
4 [ 2x + 14 - x^2 - 7x ] =
4 [ -x^2 - 5x + 14]
-4x^2 - 20x + 56
The x coordinate of the vertex = - (-20) / [ 2 * -4] = 20 / -8 = -5/2 = -2.5
So.....the max is
-4 (-5/2)^2 - 20 (-5/2) + 56 =
-4 ( 25/4) + 50 + 56 =
-25 + 50 + 56 =
81
Here's the graph : https://www.desmos.com/calculator/pzjfnx8ugd
