Interpreting graphs of functions

Mathematics

2 answers:

Elena L [17]1 year ago

4 0

Answer:

non-linear
40
1/2

Step-by-step explanation:

This is a non-linear function specifically it is an oscillating function
The initial position of the weight occurs at t=0 and from the graph we see that at t=0, the weight position is 40 centimeters
The weight is said to reach equilibrium when its position is at 0 cm. From the graph we can see that the function first reaches 0 cm at t=0.5 seconds or at t= 1/2 second

horsena [70]1 year ago

3 0

Answer: non-linear 40 1/2 Step-by-step explanation: This is a non-linear function specifically it is an oscillating function The initial position of the weight occurs at t=0 and from the graph we see that at t=0, the weight position is 40 centimeters The weight is said to reach equilibrium when its position is at 0 cm. From the graph we can see that the function first reaches 0 cm at t=0.5 seconds or at t= 1/2 second

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The function h(t) = -16t2 + 48t + 28 models the height (in feet) of a ball where t is the time (in seconds).

Alex17521 [72]

Answer:

Step-by-step explanation:

<em>[using calculus] </em>When the function h(t) reaches its maximum value, its first derivative will be equal to zero (the first derivative represents velocity of the ball, which is instantaneously zero). We have $h'(t) = -32t + 48$ , which equals zero when $t = 3/2 = 1.5$ . The ball therefore reaches its maximum height when t = 1.5. To find the maximum height, we need to find h(1.5), which is 64 feet.

<em>[without calculus] </em>This is a quadratic function, so its maximum value will occur at its vertex. The formula for the x-coordinate of the vertex is -b/2a, so the maximum value occurs when t = -48/(2*16), which is 1.5. The maximum height is h(1.5), which is 64 feet.