The height of an object launched from the ground after t seconds is given by h(t)=-16t^2+32t. How long for the object to obtain a height of 32ft. Hit the ground.
oh no im so scared
To find out how long it takes for the object to obtain a height of 32 feet, we need to find the time, t, when h(t) is equal to 32.
Given the equation h(t) = -16t^2 + 32t, we can set it equal to 32 and solve for t:
-16t^2 + 32t = 32
Rearranging the equation, we get:
-16t^2 + 32t - 32 = 0
Now, we have a quadratic equation. We can solve it by factoring or by using the quadratic formula. Let's use factoring:
-16t^2 + 32t - 32 = 0
Divide through by -16 to simplify:
t^2 - 2t + 2 = 0
Now, let's try to factor this quadratic equation:
(t - ?)(t - ?) = 0
We need to find two numbers whose product is 2 and whose sum is -2. The numbers are -1 and -1. So we can factor the equation as:
(t - 1)(t - 1) = 0
This means that t - 1 = 0 or t - 1 = 0. Solving for t:
t - 1 = 0 or t - 1 = 0
t = 1 or t = 1
Therefore, the object will obtain a height of 32 feet twice – once at t = 1 second and another at t = 1 second. This means that the object reaches a height of 32 feet and then returns to the ground after 1 second.
Aarrggghhhh! You've asked this question three times -- and received an answer the first time! Why do you keep reposting this???
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