Meteorologists 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

Question

Meteorologists 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
.
(b) Using the slope found in part (a) and the point
76, 564
, find a linear model that represents the minimum pressure of a hurricane,
y
, versus its maximum sustained wind speed,
x
.

Answer 1

To find the linear model that represents the minimum pressure of a hurricane (y) versus its maximum sustained wind speed (x), we need to use the slope found in part (a) and the point (76, 564).

The slope found in part (a) is the change in pressure (y) divided by the change in wind speed (x). Let's denote the slope as m.

m = (873 - 564) / (150 - 76) = 309 / 74 ≈ 4.1757

Using the point-slope form of a linear equation, we can write the linear model as:

y - 564 = 4.1757(x - 76)

Simplifying,

y - 564 = 4.1757x - 318.3052

Moving the constant term to the other side,

y = 4.1757x - 318.3052 + 564

y = 4.1757x + 245.6948

So, the linear model that represents the minimum pressure of a hurricane (y) versus its maximum sustained wind speed (x) is:

y = 4.1757x + 245.6948

Answer 2

To find a linear model that represents the relationship between the minimum pressure (y) and maximum sustained wind speed (x) of a hurricane, we need to determine the equation of a line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

We are given two data points:
Hurricane A: (150 knots, 873 mb)
Hurricane B: (76 knots, 564 mb)

First, let's find the slope (m) using the two data points. The slope is the change in y divided by the change in x:
m = (y2 - y1) / (x2 - x1)

Using Hurricane A as point 1 and Hurricane B as point 2:
m = (564 mb - 873 mb) / (76 knots - 150 knots)
= -309 mb / -74 knots
≈ 4.176 mb/knot

Now that we have the slope, we can substitute it into the equation y = mx + b and use one of the given points to solve for the y-intercept (b).

Using Hurricane B's values (76 knots, 564 mb):
564 = 4.176(76) + b

Simplifying the equation:
b = 564 - 4.176(76)
= 564 - 317.376
≈ 246.624

Now we have the slope (m) and the y-intercept (b), so we can write the linear model:
y = 4.176x + 246.624

Therefore, the linear model representing the minimum pressure (y) versus the maximum sustained wind speed (x) of a hurricane is:
y = 4.176x + 246.624

Answer 3

To find the linear model that represents the minimum pressure of a hurricane (y) versus its maximum sustained wind speed (x), we need to use the slope found in part (a) and the point (76, 564).

We know that the relationship between wind speed (x) and pressure (y) is approximately linear.

The slope (m) is the change in pressure divided by the change in wind speed:

m = (change in y) / (change in x)

Since we have two points, (150, 873) and (76, 564), we can calculate the change in y and change in x:

change in y = 873 - 564 = 309
change in x = 150 - 76 = 74

So, the slope is:

m = (309) / (74) = 4.1757 (approximated to four decimal places)

Now, we can use the point-slope form of a linear equation to find the linear model:

y - y1 = m(x - x1)

Using the point (76, 564), we have:

y - 564 = 4.1757(x - 76)

Expanding the equation:

y = 4.1757x - 314.3252 + 564

Simplifying the equation:

y = 4.1757x + 249.6748

Therefore, the linear model that represents the minimum pressure of a hurricane (y) versus its maximum sustained wind speed (x) is:

y = 4.1757x + 249.6748