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A physics teacher put a ball at the top of a ramp and let it roll down toward the floor. The class determined that the height of the ball could be represented by the equation h( t)=−16 t 2+4, where the height, h( t), is measured in feet from the ground and time, t , is measured in seconds.
a. What do you notice about the structure of the quadratic expression in this problem?
b. In the equation, explain what the 4 represents.
c. Explain how you would use the equation to determine the time it takes the ball to reach the floor.
d. Now consider the two solutions for t . Which one is reasonable? Does the final answer make sense based on this context? Explain.
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2. The length of a rectangle is 5∈. more than twice a number. The width is 4∈. less than the same number. The perimeter of the rectangle is 44∈¿. Sketch a diagram of this situation, and find the unknown number.
3. The length of a rectangle is 5∈. more than twice a number. The width is 4∈. less than the same number. If the
area of the rectangle is 15¿2, find the unknown number.
ExercisesSolve each equation. Some of them may have radicals in their solutions.