Math Problem Statement
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x =
4 + t , y = 2 + 1 5 t, where x and y are measured in centimeters. The temperature function satisfies Tx(3, 3) = 3 and Ty(3, 3) = 1. How fast is the temperature rising on the bug's path after 5 seconds? (Round your answer to two decimal places.)
Incorrect: Your answer is incorrect. °C/s
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Parametric Equations
Partial Derivatives
Chain Rule
Formulas
Parametric equations: x(t) = 4 + t, y(t) = 2 + 1/5 * t
Temperature rate change: dT/dt = (∂T/∂x) * (dx/dt) + (∂T/∂y) * (dy/dt)
Theorems
Multivariable Chain Rule
Suitable Grade Level
University Calculus (1st year)
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