Answer :
To determine how many seconds after diving Ana will hit the water, we need to find the time \( x \) when her height \( h(x) \) above the water is zero.
Given the equation modeling her height:
[tex]\[ h(x) = -5(x + 1)(x - 3) \][/tex]
we set \( h(x) \) to 0 and solve for \( x \):
[tex]\[ -5(x + 1)(x - 3) = 0 \][/tex]
Since the product of two factors is zero, at least one of the factors must be zero. Therefore, we set each factor to zero and solve for \( x \):
1. \( x + 1 = 0 \)
[tex]\[ x = -1 \][/tex]
2. \( x - 3 = 0 \)
[tex]\[ x = 3 \][/tex]
These calculations give us two potential solutions: \( x = -1 \) and \( x = 3 \).
However, in the context of this problem, \( x \) represents the time in seconds after Ana dives. Time cannot be negative, so we discard \( x = -1 \).
Thus, the valid solution is:
[tex]\[ x = 3 \][/tex]
Therefore, Ana will hit the water 3 seconds after diving.
[tex]\[ \boxed{3} \][/tex]
Given the equation modeling her height:
[tex]\[ h(x) = -5(x + 1)(x - 3) \][/tex]
we set \( h(x) \) to 0 and solve for \( x \):
[tex]\[ -5(x + 1)(x - 3) = 0 \][/tex]
Since the product of two factors is zero, at least one of the factors must be zero. Therefore, we set each factor to zero and solve for \( x \):
1. \( x + 1 = 0 \)
[tex]\[ x = -1 \][/tex]
2. \( x - 3 = 0 \)
[tex]\[ x = 3 \][/tex]
These calculations give us two potential solutions: \( x = -1 \) and \( x = 3 \).
However, in the context of this problem, \( x \) represents the time in seconds after Ana dives. Time cannot be negative, so we discard \( x = -1 \).
Thus, the valid solution is:
[tex]\[ x = 3 \][/tex]
Therefore, Ana will hit the water 3 seconds after diving.
[tex]\[ \boxed{3} \][/tex]
