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A heavy industrial plant located in the center of a small town emits particulate matter into the atmosphere. Suppose that the concentration of particulate matter (in parts per million) at a point d miles from the plant is given by C= 150 - 12d2. If the boundaries of the town form a rectangle 4 miles long and 8 miles wide, what is the average concentration of particulate matter throughout the city? Express C as a function of x and y, set up a double integral, and evaluate it The average concentration of particulate matter is parts per million.

A heavy industrial plant located in the center of a small town emits particulate matter into the atmosphere. Suppose that the concentration of particulate matter (in parts per million) at a point d miles from the plant is given by C= 150 - 12d2. If the boundaries of the town form a rectangle 4 miles long and 8 miles wide, what is the average concentration of particulate matter throughout the city? Express C as a function of x and y, set up a double integral, and evaluate it The average concentration of particulate matter is parts per million.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 1ECP: The ordered pairs below give the median sales prices y (in thousands of dollars) of new homes sold...
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A heavy industrial plant located in the center of a small town emits particulate matter into the atmosphere. Suppose that the concentration of particulate matter (in parts per million) at a point d miles from the plant is given by C = 150 - 12d2. If the boundaries of the town form a rectangle 4 miles long and 8 miles wide, what is the average concentration of particulate matter throughout the city? Express C as a function of x and y, set up a double integral, and evaluate it. The average concentration of particulate matter is parts per million.
Transcribed Image Text:A heavy industrial plant located in the center of a small town emits particulate matter into the atmosphere. Suppose that the concentration of particulate matter (in parts per million) at a point d miles from the plant is given by C = 150 - 12d2. If the boundaries of the town form a rectangle 4 miles long and 8 miles wide, what is the average concentration of particulate matter throughout the city? Express C as a function of x and y, set up a double integral, and evaluate it. The average concentration of particulate matter is parts per million.
Marketers for a drugstore chain chose two resort areas to test market a new sunscreen lotion. After a summer of varying the selling price and recording the monthly demand, the marketers arrived at the demand table (shown to the right), where y is the number of bottles of sunscreen purchased per month (in thousands) at x dollars per bottle. 5.0 5.5 6.0 6.5 7.0 y 2.1 1.7 1.6 1.3 1.1 (A) Use the method of least squares to find a demand equation. The demand equation is y = (Type an expression using x as the variable. Round to the nearest hundredth as needed.) (B) If each bottle of sunscreen costs the drugstore chain $4.50, how should the sunscreen be priced to achieve a maximum monthly profit? The price should be $ (Round to the nearest cent as needed.)
Transcribed Image Text:Marketers for a drugstore chain chose two resort areas to test market a new sunscreen lotion. After a summer of varying the selling price and recording the monthly demand, the marketers arrived at the demand table (shown to the right), where y is the number of bottles of sunscreen purchased per month (in thousands) at x dollars per bottle. 5.0 5.5 6.0 6.5 7.0 y 2.1 1.7 1.6 1.3 1.1 (A) Use the method of least squares to find a demand equation. The demand equation is y = (Type an expression using x as the variable. Round to the nearest hundredth as needed.) (B) If each bottle of sunscreen costs the drugstore chain $4.50, how should the sunscreen be priced to achieve a maximum monthly profit? The price should be $ (Round to the nearest cent as needed.)
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