(a) Describe a possible graph of the temperature, on an east-west line through D
ID: 3141757 • Letter: #
Question
(a) Describe a possible graph of the temperature, on an east-west line through Durango, Colorado, if the origin is at Durango, the positive x-axis corresponds to east of Durango, and the vertical z-axis is the temperature. For negative x within a few hundred miles of the origin, the sign of T(x) is while for positive x a few hundred miles from the origin, the sign of T(x) is We estimate that T(0) degrees Fahrenheit. (b) Describe a possible graph of the temperature, on a north-south line through Des Moines, lowa, if the origin is at Des Moines, the positive y-axis corresponds to north of Des Moines, and the vertical z-axis is the temperature. For negative y within a few hundred miles of the origin, the sign of T(y) is while for positive y a few hundred miles from the origin, the sign of T(y) is We estimate that T(0) degrees = degrees FahrenheitExplanation / Answer
Observe that the temperature increases if we move away from Durango and it decreases if we move towards Durango. So as we move along the X axis from west the function will be decreasing till Durango and then will start increasing from Durango as we move further to east.
So the slope of function T(x) = T'(x) is negative for negative x within few hundred miles and is positive for positive x.
The graph will more or less look like a V opened upwards and based at origin.
Durango is on 55 degrees contour. So T(0) = 55 degrees Fahrenheit.
If we move towards Des Moines from North temperature increases and it will keep increasing as we go further down south. Thus the Temperature function is increasing throughout. So irrespective of whether we are on positive side or negative side T'(y) has positive sign.
Des Moines is between 55 and 50 degree contours. But is more closer to 50 degrees contour. So T(0) ~ 53.5 degrees.
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