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Algebra
Pregunta

1. The height of water in the air \( t \) seconds ...

1. The height of water in the air \( t \) seconds after it is squirted from a fountain can be modeled by the function \( y = - 16 t ^ { 2 } + 64 t + 4 \) , where \( y \) is the vertical distance in meters and \( t \) is time in seconds. What is the maximum height that the water reaches? At what time does it reach its maximum height? A rock is thrown into the air. The path it follows is modelled by the equation 

\( y = - 4.9 t ^ { 2 } + 24.5 t + 20.5\) What is the max height that the rock reaches and what time does it reach its max height? 

\( Solution\) A. company's profit is modeled by this equation: 

\( p = - 2 x ^ { 2 } + 12000 x - 17900000\) where \( p \) is profit in \( \$ \) and \( x \) is the number of units sold. How many unit must be sold to maximize profit, and what is the max profit in dollars? 

Answer

1. \(y_{\max}= 4- \frac{64^{2}}{4(- 16)} = 68\)

\(t= - \frac{64}{2(- 16)} = 2\)

2. \(y_{\max}= 20.5- \frac{24.5^{2}}{4(- 4.9)} = 21.75\)

\(t= - \frac{24.5}{2(- 4.9)} = 2.5\)

3. \(p_{\max}= - 17900000- \frac{12000^{2}}{4(- 2)} = 100000\)

\(x= - \frac{12000}{2(- 2)} = 3000\)

Solución
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