The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A line

Question

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A linear model with ordered pairs at 0, 60 and 2, 80 and 3, 80 and 4, 20 and 6, 0 and 7, 0 and 8, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet. Part A: During what interval(s) of the domain is the water balloon’s height increasing? (2 points) Part B: During what interval(s) of the domain is the water balloon’s height staying the same? (2 points) Part C: During what interval(s) of the domain is the water balloon’s height decreasing the fastest? Use complete sentences to support your answer. (3 points) Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 10 seconds. Use complete sentences to support your answer. (3 points)

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Dulcie 5 years 2021-08-16T18:31:43+00:00 1 Answers 1164 views 1

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  1. Adela
    -1
    2021-08-16T18:33:24+00:00
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    Answer:

    The data for linear pair are;

    \begin{array}{ll}x&f(x)\\0&60\\2&80\\3&80\\4&20\\6&0\\7&0\\8&0\end{array}

    The domain are the values (input) on the x-axis which is the time

    The range are the values input on the y-axis which is the height reached by the balloon

    Part A

    The interval of the domain during which the water balloon height is increasing is 0 ≤ x ≤ 2

    Part B

    The intervals of the domain the water balloon’s height stays the same are;

    2 ≤ x ≤ 3 and 6 ≤ x ≤ 8

    Part C

    The water balloon height is decreasing at the following intervals;

    At the interval 3 ≤ x ≤ 4

    The rate of decrease = (20 ft. – 80 ft.)/(4 s – 3 s) = -20 ft./s.

    At the interval 4 ≤ x ≤ 6

    The rate of decrease = (0 ft. – 20 ft.)/(6 s – 4 s) = -10 ft./s

    Therefore, the interval of the domain that the balloon’s height is decreasing the fastest is 3 ≤ x ≤ 4

    Part D

    According to Newton’s law of motion, provided that the no additional force is applied to the the balloon, at 10 seconds, the height of the water balloon is 0 ft. given that the height of the balloon is constantly decreasing from 3 seconds after being thrown off the roof, reaching a height of 0ft. at 6 seconds and maintaining that height up until 8 seconds.

    By extending the graph further, the height of 0 ft. is obtained at 10 seconds after the balloon is thrown

    Step-by-step explanation:

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