eteorologists often measure the intensity of a tropical storm or hurricane by the maximum sustained wind speed and the minimum pressure. The relationship between these two quantities is approximately linear. Hurricane A had a maximum sustained wind speed of
150
knots and a minimum pressure of
873
mb
(millibars). Hurricane B had maximum sustained winds of
76
knots and a pressure of
564
mb
.
(a) Find the slope of the line between these two points. Round to one decimal place.
To find the slope of the line between these two points, we can use the formula:
slope = (change in y) / (change in x).
In this case, the y-values are the minimum pressure and the x-values are the maximum sustained wind speed.
The change in y is the difference between the minimum pressures of Hurricane A and Hurricane B:
change in y = 873 - 564 = 309 mb.
The change in x is the difference between the maximum sustained wind speeds of Hurricane A and Hurricane B:
change in x = 150 - 76 = 74 knots.
Therefore, the slope of the line between these two points is:
slope = (change in y) / (change in x) = 309 / 74 ≈ 4.2.
So, the slope of the line between these two points is approximately 4.2 (rounded to one decimal place).
To find the slope of the line between the two points, we can use the slope formula:
slope = (change in y)/(change in x)
In this case, the x-axis represents the maximum sustained wind speed and the y-axis represents the minimum pressure.
Let's assign:
(x1, y1) = (150 knots, 873 mb) for Hurricane A
(x2, y2) = (76 knots, 564 mb) for Hurricane B
Now, let's calculate the change in y and the change in x:
change in y = y2 - y1 = 564 mb - 873 mb = -309 mb
change in x = x2 - x1 = 76 knots - 150 knots = -74 knots
Next, we can substitute these values into the slope formula:
slope = (-309 mb)/(-74 knots)
Simplifying, we get:
slope ≈ 4.1757 mb/knot
Rounded to one decimal place, the slope of the line between the two points is approximately:
slope ≈ 4.2 mb/knot
To find the slope of the line between the two points, we can use the formula:
slope = (change in y) / (change in x)
In this case, the y-values represent the minimum pressure (in mb) and the x-values represent the maximum sustained wind speed (in knots).
Let's represent the maximum sustained wind speed as x and the minimum pressure as y.
For Hurricane A:
x1 = 150 knots
y1 = 873 mb
For Hurricane B:
x2 = 76 knots
y2 = 564 mb
Now, we can calculate the change in y and change in x:
change in y = y2 - y1 = 564 mb - 873 mb = -309 mb
change in x = x2 - x1 = 76 knots - 150 knots = -74 knots
Substituting the values into the slope formula:
slope = (-309 mb) / (-74 knots)
Now, let's calculate the slope:
slope = 309 mb / 74 knots = 4.1757
Rounding to one decimal place, the slope is approximately 4.2.