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A tiny ant walks on a stovetop. The temperature T(1, y) in °C of the stovetop at the position z cm east and y cm north from the corner of the stove is given by T(1, y) = 50 + y – (z – 5)? where 0

A tiny ant walks on a stovetop. The temperature T(1, y) in °C of the stovetop at the position z cm east and y cm north from the corner of the stove is given by T(1, y) = 50 + y – (z – 5)? where 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A tiny ant walks on a stovetop. The temperature T(r, y) in °C of the stovetop at the position z cm east and y cm north from the corner of the stove is given by T(1, y) = 50 + y – (x – 5)ª where 0 <z< 10 and 0 < y< 10. (a) If the ant is currently standing at the location (r, y) = (6, 5) and he starts taking a few tiny steps east, at what rate will his temperature change with respect to the distance he has travelled? number units (b) If the ant is currently standing at the location (a, y) = (6,5), in which direction should he step in order to cool doun as quickly as possible? Please state your answer as a unit vector. (c) If the ant is standing at the location (z, y) = (6, 5) and steps in the direction you found in part (b), at what rate would his temperature change, with respect to the distance he has travelled? Please explain your answer. number units
Transcribed Image Text:A tiny ant walks on a stovetop. The temperature T(r, y) in °C of the stovetop at the position z cm east and y cm north from the corner of the stove is given by T(1, y) = 50 + y – (x – 5)ª where 0 <z< 10 and 0 < y< 10. (a) If the ant is currently standing at the location (r, y) = (6, 5) and he starts taking a few tiny steps east, at what rate will his temperature change with respect to the distance he has travelled? number units (b) If the ant is currently standing at the location (a, y) = (6,5), in which direction should he step in order to cool doun as quickly as possible? Please state your answer as a unit vector. (c) If the ant is standing at the location (z, y) = (6, 5) and steps in the direction you found in part (b), at what rate would his temperature change, with respect to the distance he has travelled? Please explain your answer. number units
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