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6) The number of cars produced when x dollars is spent on labor and y dollars is spent on capital invested by a manufacturer can be modeled by the equation 30x3y3 = 360. (Both x and y are measured in thousands of dollars.) Find dx and evaluate at the point (27, 8). а. b. Interpret the result of a.

6) The number of cars produced when x dollars is spent on labor and y dollars is spent on capital invested by a manufacturer can be modeled by the equation 30x3y3 = 360. (Both x and y are measured in thousands of dollars.) Find dx and evaluate at the point (27, 8). а. b. Interpret the result of a.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcription: --- **6) The number of cars produced when x dollars is spent on labor and y dollars is spent on capital invested by a manufacturer can be modeled by the equation \(30x^{\frac{1}{3}}y^{\frac{2}{3}} = 360\). (Both x and y are measured in thousands of dollars.)** a. Find \(\frac{dy}{dx}\) and evaluate at the point (27, 8). b. Interpret the result of a. --- **7) Suppose that a particle moves along a straight line with velocity defined by \(v(t) = t^2 - 3t - 18\), where \(0 \leq t \leq 6\) (in meters per second). Find the displacement at time t and the total distance traveled up to \(t = 6\).** ---
Transcribed Image Text:Transcription: --- **6) The number of cars produced when x dollars is spent on labor and y dollars is spent on capital invested by a manufacturer can be modeled by the equation \(30x^{\frac{1}{3}}y^{\frac{2}{3}} = 360\). (Both x and y are measured in thousands of dollars.)** a. Find \(\frac{dy}{dx}\) and evaluate at the point (27, 8). b. Interpret the result of a. --- **7) Suppose that a particle moves along a straight line with velocity defined by \(v(t) = t^2 - 3t - 18\), where \(0 \leq t \leq 6\) (in meters per second). Find the displacement at time t and the total distance traveled up to \(t = 6\).** ---
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