The amount of pressure on a diver as she descends into the sea can be modeled by the equation
, where x is her depth in meters and y is the amount of pressure in atmospheres (atm). Which of these statements are correct according to the model? Select TWO that apply.
A.
For every 1 meter that the diver descends, the amount of pressure on her decreases by 10 atms.
B.
For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atms.
C.
For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
D.
For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
E.
At sea level, the amount of pressure on the diver is
atm.
F.
At sea level, the amount of pressure on the diver is 1 atm.
The correct statements according to the model are:
C. For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
F. At sea level, the amount of pressure on the diver is 1 atm.
To determine which statements are correct according to the given model, we need to examine the equation provided:
First, let's analyze the equation:
The equation is not provided in the question, so I will assume that it was cut off. Let's use a general equation of the form:
y = kx,
where y represents the amount of pressure in atmospheres (atm), x represents the depth in meters, and k is a constant.
Now let's evaluate each statement based on this equation:
A. For every 1 meter that the diver descends, the amount of pressure on her decreases by 10 atm.
This statement is not consistent with the general equation y = kx. According to the equation, as the value of x increases, the value of y should also increase or remain constant, depending on the sign of k. Therefore, statement A is incorrect.
B. For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atm.
This statement is also not consistent with the general equation y = kx. According to the equation, as the value of x increases, the value of y should also increase or remain constant, depending on the sign of k. Therefore, statement B is incorrect.
C. For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
This statement is consistent with the general equation y = kx. If we assume that k = -1/10, then for every 10 meters the diver descends, the pressure decreases by 1 atm. Therefore, statement C is correct.
D. For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
This statement is not consistent with the general equation y = kx. According to the equation, as the value of x increases, the value of y should also increase or remain constant, depending on the sign of k. Therefore, statement D is incorrect.
E. At sea level, the amount of pressure on the diver is x atm.
This statement does not provide enough information to determine its validity based on the given equation. It is an incomplete statement and cannot be determined to be correct or incorrect.
F. At sea level, the amount of pressure on the diver is 1 atm.
This statement does not provide enough information to determine its validity based on the given equation. It is an incomplete statement and cannot be determined to be correct or incorrect.
Based on the analysis, the correct statements are:
C. For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
Explanation: To determine which statements apply, we need to analyze the equation given in the question. However, since the equation is not provided, we can only analyze based on a generalized equation y = kx. This allows us to examine the relationship between depth (x) and pressure (y). By comparing the given statements to the equation, we can determine if they are valid or not.
Are you sure
I apologize for the confusion. Without the specific equation provided, it is not possible to determine which statements are correct. The given equation is necessary in order to make accurate assessments about the relationship between depth and pressure. Therefore, without the equation, we cannot determine which statements are correct or incorrect.
The equation is missing in the question, so it is not possible to determine the correct statements. Please provide the equation so that I can help you further.
Each relation shown defines y as a function of x. Which function has the greatest rate of change?
A. y = 1.3x + 1
B.
A graph with the points (6, 7), (0, 2) connected through a line.
C. y = 8/7x + 3
D.
x 0 2 4 6
y 2.50 4.03 5.56 7.09
To determine the function with the greatest rate of change, we need to calculate the slope (rate of change) for each function.
A. The slope of the function y = 1.3x + 1 is 1.3.
B. The slope of the line connecting the points (6, 7) and (0, 2) can be calculated using the formula (y2 - y1) / (x2 - x1).
The slope is (2 - 7) / (0 - 6) = -5 / -6 = 5/6.
C. The slope of the function y = 8/7x + 3 is 8/7.
D. The given table provides four points, and we can calculate the slope between the first and last point.
The slope is (7.09 - 2.50) / (6 - 0) = 4.59 / 6 = 0.765.
Comparing the slopes, we can see that:
A. 1.3
B. 5/6
C. 8/7
D. 0.765
The function with the greatest rate of change is B. y = 5/6x, as its slope is the largest among the given options.
are you sure??
Apologies for the previous incorrect response. Let's recalculate the slopes correctly:
A. The slope of the function y = 1.3x + 1 is 1.3.
B. To calculate the slope of the line connecting the points (6, 7) and (0, 2), we use the formula (y2 - y1) / (x2 - x1).
The slope is (2 - 7) / (0 - 6) = -5 / -6 = 5/6.
C. The slope of the function y = 8/7x + 3 is 8/7.
D. To calculate the slope between the first and last points in the table, we use the formula (change in y) / (change in x).
The slope is (7.09 - 2.50) / (6 - 0) = 4.59 / 6 = 0.765.
Comparing the slopes again:
A. 1.3
B. 5/6
C. 8/7
D. 0.765
The function with the greatest rate of change is A. y = 1.3x + 1, as its slope of 1.3 is the highest among the given options.
Math Equation Response Question
A line is graphed below.
The line passes through the points (0, 3), (-1, 5), and (3, -3)
Write an equation in the form y = mx + b that represents this line.
Use the on-screen keyboard to type the correct equation in the box.
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