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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

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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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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