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Pinocchio's nose length y (in inches) is dependent on his lie count s. Geppetto has modeled this phenomenon with the equation y = a', where a is a “magic" constant. (a) Use implicit differentiation to find the derivative of Pinocchio's nose length with respect to his lie count. Simplify your answer. (Hint: Use the fact that y = ev Iny.) (b) Pinocchio experiences "magical balance" when his nose length eguals the "magic" con-

Pinocchio's nose length y (in inches) is dependent on his lie count s. Geppetto has modeled this phenomenon with the equation y = a', where a is a “magic" constant. (a) Use implicit differentiation to find the derivative of Pinocchio's nose length with respect to his lie count. Simplify your answer. (Hint: Use the fact that y = ev Iny.) (b) Pinocchio experiences "magical balance" when his nose length eguals the "magic" con-

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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Please answer a and b and show full solution (in pictures). thanks

Pinocchio's nose length y (in inches) is dependent on his lie count s. Geppetto has modeled this phenomenon with the equation y = a°, where a is a "magic" constant. (a) Use implicit differentiation to find the derivative of Pinocchio's nose length with respect to his lie count. Simplify your answer. (Hint: Use the fact that y = evlIny.) (b) Pinocchio experiences "magical balance" when his nose length equals the "magic" con- stant. If he is experiencing "magical balance" right now, what is the rate of change of his nose length with respect to his lie count when it is 6 inches long?
Transcribed Image Text:Pinocchio's nose length y (in inches) is dependent on his lie count s. Geppetto has modeled this phenomenon with the equation y = a°, where a is a "magic" constant. (a) Use implicit differentiation to find the derivative of Pinocchio's nose length with respect to his lie count. Simplify your answer. (Hint: Use the fact that y = evlIny.) (b) Pinocchio experiences "magical balance" when his nose length equals the "magic" con- stant. If he is experiencing "magical balance" right now, what is the rate of change of his nose length with respect to his lie count when it is 6 inches long?
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