The first three terms of a sequence are given. Round to the nearest thousandth (if
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We are given function: h(x)=-5(x-4)^2+180 for the height in meters, x seconds after the launch.
We need to find the time when it hit the ground.
The height of the object would be 0, when it hit the ground.
<em>So, we need to set the given function equal to 0 and solve for x.</em>
-5(x-4)^2+180 = 0.
Subtracting both sides by 180.
-5(x-4)^2+180-180 = 0-180.
-5(x-4)^2 = -180.
Dividing both sides by -5, we get
(x-4)^2 = 36.
Taking square root on both sides, we get
x-4 = + - 6
x-4 =6 and x-4 =-6
Adding 4 on both sides in both equations, we get
x-4+4 =6+4 and x-4+6 =-6+4
x=10 and x=-2.
<em>x represents time in seconds. So we can't take a negative value for time.</em>
<h3>Therefore, 10 seconds after being launched will the object hit the ground.</h3>