Ivan's position on a Ferris wheel is represented by the graph below where x is time in seconds and y is his distance from the ground.
Which interpretations of the graph are true? Choose all that are correct.
A
The relationship between time and Ivan's position at 10.2 seconds to 12 seconds is nonlinear.
B
Ivan's position changes from increasing to decreasing at a little over 6 seconds.
C
The change in Ivan's position is linear from zero to 10.2 seconds.
D
Ivan's starting position is 2 feet off of the ground.
E
The Ferris wheel stops when Ivan is 10 feet from the ground.
A. The relationship between time and Ivan's position at 10.2 seconds to 12 seconds is nonlinear.
B. Ivan's position changes from increasing to decreasing at a little over 6 seconds.
D. Ivan's starting position is 2 feet off of the ground.
Interpretations A, B, and D are correct. The graph clearly shows that Ivan's position is changing non-linearly between 10.2 seconds to 12 seconds, his position changes from increasing to decreasing a little over 6 seconds, and his starting position is 2 feet off the ground. Interpretations C and E are not correct as the graph does not show a linear change in Ivan's position over time, and it does not provide any information on the duration or end of the Ferris wheel ride.
A. The relationship between time and Ivan's position at 10.2 seconds to 12 seconds is nonlinear. - True, as the graph shows a curved line during that time period.
B. Ivan's position changes from increasing to decreasing at a little over 6 seconds. - False, the graph does not show a clear change in direction at that specific time.
C. The change in Ivan's position is linear from zero to 10.2 seconds. - False, the graph shows a curved line, indicating a non-linear relationship.
D. Ivan's starting position is 2 feet off of the ground. - False, the graph does not provide information about the starting position.
E. The Ferris wheel stops when Ivan is 10 feet from the ground. - False, the graph does not show a clear stopping point at 10 feet.
To answer this question, let's analyze each statement:
A) The relationship between time and Ivan's position at 10.2 seconds to 12 seconds is nonlinear.
To determine if the relationship is nonlinear, we need to observe the shape of the graph between 10.2 seconds and 12 seconds. If the graph is not a straight line, then the relationship is nonlinear. Since we don't have access to the graph, we cannot determine if this statement is true or false.
B) Ivan's position changes from increasing to decreasing at a little over 6 seconds.
To check if Ivan's position changes from increasing to decreasing at a little over 6 seconds, we need to determine if there is a peak or maximum point in the graph around 6 seconds. If there is, then Ivan's position changes from increasing to decreasing. Since we don't have access to the graph, we cannot determine if this statement is true or false.
C) The change in Ivan's position is linear from zero to 10.2 seconds.
To determine if the change in Ivan's position is linear from zero to 10.2 seconds, we need to observe if the graph forms a straight line between these two points. If the graph is a straight line, then the change is linear. Since we don't have access to the graph, we cannot determine if this statement is true or false.
D) Ivan's starting position is 2 feet off the ground.
To determine Ivan's starting position, we need to observe the y-coordinate on the graph when x is equal to zero. If the y-coordinate is 2, then Ivan's starting position is 2 feet off the ground. Since we don't have access to the graph, we cannot determine if this statement is true or false.
E) The Ferris wheel stops when Ivan is 10 feet from the ground.
To determine if the Ferris wheel stops when Ivan is 10 feet from the ground, we need to observe if there is a point on the graph where the y-coordinate is equal to 10. If such a point exists, then the Ferris wheel stops at that point. Since we don't have access to the graph, we cannot determine if this statement is true or false.
Therefore, without access to the graph, we cannot determine which interpretations are true.
To determine which interpretations of the graph are true, let's analyze each statement:
A. The relationship between time and Ivan's position at 10.2 seconds to 12 seconds is nonlinear.
To verify this, we need to examine that specific time interval on the graph. Look for any curved or non-straight sections between 10.2 seconds and 12 seconds. If you observe a curved line, then the relationship is nonlinear. If the line is straight, then the relationship is linear. Based on the graph, you can determine whether this statement is true or false.
B. Ivan's position changes from increasing to decreasing at a little over 6 seconds.
To confirm this statement, identify the point on the graph that represents a shift from an upward trend to a downward trend. The change from increasing to decreasing can be observed at a certain time. Verify whether the change occurs at a little over 6 seconds by examining the graph.
C. The change in Ivan's position is linear from zero to 10.2 seconds.
To validate this statement, examine the graph from the starting point (time zero) up to 10.2 seconds. Check if the line is straight or follows a constant slope during that time interval. If the line is straight, then the change in Ivan's position is linear. If it is curved, then the change is nonlinear.
D. Ivan's starting position is 2 feet off of the ground.
To determine Ivan's starting position, locate the point on the y-axis (vertical axis) where the time value is zero. Check the corresponding height on the y-axis to find Ivan's starting position. If it is 2 feet off the ground, then this statement is true.
E. The Ferris wheel stops when Ivan is 10 feet from the ground.
To validate this statement, examine the portion of the graph where Ivan's position is 10 feet from the ground. Check if there is a horizontal line at that height, indicating that Ivan's position remains constant. If such a line exists, it suggests the Ferris wheel stops when Ivan is 10 feet from the ground.
By analyzing the graph according to the explanations provided, you can determine which interpretations are true and select the corresponding options.