Question

A projectile launches from the ground and follows a path represented by the equation y=−x2+5x . At the same time, a frisbee is thrown from a platform at a height of 9 feet and follows a straight path to the ground represented by the equation y=−x+9 . What inequalities represent the constraints on the system of equations that represents this situation and where are the viable solutions?Select the correct answers from the lists to complete the statements.(1 point)The time in seconds, y, and the height, in feet, are always going to be  values, therefore the viable solutions will be limited to the  quadrant.

Answer 1

To analyze the projectile and the frisbee, we need to consider the context of their movements in relation to their respective equations.

1. Identifying values:
   • The time \(x\) must be non-negative, meaning \(x \geq 0\).
   • The height \(y\) must also be non-negative, meaning \(y \geq 0\).

Since both heights cannot be negative (the scenario implies that they are measured above the ground), we have the constraints:

• \(x \geq 0\)
• \(y \geq 0\)

2. Quadrant identification: The feasible region for the problem will thus be limited to the first quadrant of the Cartesian plane, where both \(x\) (time) and \(y\) (height) are positive.

3. Conclusion: The complete statements are:

• The values for time in seconds, \(x\), and the height in feet, \(y\), are always going to be non-negative values; therefore, the viable solutions will be limited to the first quadrant.

So, the inequalities representing the constraints are:

• \(x \geq 0\)
• \(y \geq 0\)

And the viable solutions will indeed be limited to the first quadrant of the coordinate plane.