1. a baseball is thrown into the air with an upward velocity of 25 ft/sec. it’s height (in feet) after t seconds can be modeled by the function h(t) = -16t^2 + 25t + 5. algebraically determine how long will it take the ball to reach its maximum height? what is the ball’s maximum height?

2. a company that sells digital cameras has found that their revenue can be remodeled by the equation r(p) = -5p^2 + 1230p, where p is the price of the camera in dollars. algebraically determine what price will maximize the revenue? what is the maximum revenue?

We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:

X-term:

Half of the x term:

After squaring:

Finally, the vertex of this function is:

So in this vertex we can find the answer to this problem:

The ball will reach its maximum height at

The ball maximum height is

Also we will use completing squares. We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:

X-term:

Half of the x term:

After squaring:

Finally, the vertex of this function is:

So in this vertex we can find the answer to this problem:

The price will maximize the revenue is

The maximum revenue is

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step-by-step explanation:

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see attached graph