Brainliest is given to whoever explains well and why your answer's the right 1.
1 answer:
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Answer:
- 1/2 of a second
Step-by-step explanation:
<u>Given function:</u>
- h(t) = -16t^2 +12t +8
<u>Finding the value of t when h(t) = 10 feet:</u>
- 10 = -16t^2 +12t +8
- -16t^2 +12t - 2 = 0
- 8t^2 - 6t + 1 = 0
- t = (6 ± √6²-8*4)/16 = (6 ± √4)/16 = (6 ± 2)/16
- t = 1/2
- t = 1/4
There are two solutions. 1/2 of a second would be the answer as the ball should go up and then down to go through the hoop.
Answer:
see details in graph and below
Step-by-step explanation:
There are many ways to generate the function.
We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.
1. f(x) has a local minimum at x = -3, and
2. a local maximum at x = 3
Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.
Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.
f'(x) = -x^2+9
will satisfy the above conditions.
Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.
Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0 so ok.
f(x) can then be obtained by integrating f'(x) :
f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3
A graph of f(x) is attached, and is found to satisfy all three conditions.
