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An implicit relationship between x and y is given by the equation x² + y² - 20x - 16y + 64 = 0. This is the equation of a circle. a) Find the center and the radius of the circle and draw this circle. b) Use implicit differentiation to find a formula for y'(x).

An implicit relationship between x and y is given by the equation x² + y² - 20x - 16y + 64 = 0. This is the equation of a circle. a) Find the center and the radius of the circle and draw this circle. b) Use implicit differentiation to find a formula for y'(x).

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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An implicit relationship between x and y is given by the equation x² + y² – 20x − 16y + 64 = 0. This is the equation of a circle. a) Find the center and the radius of the circle and draw this circle. b) Use implicit differentiation to find a formula for y'(x). Next, assume x = p (price) and y = q (demand). Hence the implicit equation is then given by p²+q²20p - 16q+64 = 0. c) Indicate on the drawing in a) which part of the graph can represent the demand function q(p). Find an explicit equation for q (p) and find its domain and range. d) e) Determine the price elasticity of demand when price is equal to 2 monetary units. f) Make the graph of the inverse demand function p(q) without making any additional calculations.
Transcribed Image Text:An implicit relationship between x and y is given by the equation x² + y² – 20x − 16y + 64 = 0. This is the equation of a circle. a) Find the center and the radius of the circle and draw this circle. b) Use implicit differentiation to find a formula for y'(x). Next, assume x = p (price) and y = q (demand). Hence the implicit equation is then given by p²+q²20p - 16q+64 = 0. c) Indicate on the drawing in a) which part of the graph can represent the demand function q(p). Find an explicit equation for q (p) and find its domain and range. d) e) Determine the price elasticity of demand when price is equal to 2 monetary units. f) Make the graph of the inverse demand function p(q) without making any additional calculations.
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