تكلم مع الذكاء الاصطناعي
Deck 13: Section 10: Functions of Several Variables
ملء الشاشة (f)
سؤال
The material for constructing the base of an open box costs 1.5 times as much per unit area as the material for constructing the sides. For a fixed amount of money $150.00, find the dimensions of the box of largest volume that can be made.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find three positive numbers x, y, and z whose sum is 24 and product is a maximum.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
سؤال
Find the least squares regression line for the points shown in the graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The least squares regression line for the points shown in the graph is 
. Calculate S, the sum of the squared errors. 
A)
B)
C)
D)
E)
. Calculate S, the sum of the squared errors. A)
B)
C)
D)
E)
سؤال
Suppose an agronomist used four test plots to determine the relationship between the wheat yield y (in bushels per acre) and the amount of fertilizer x (in hundreds of pounds per acre). The results are shown in the table. Use the regression capabilities of a graphing utility to find the least squares regression line for the data. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Suppose a store manager wants to know the demand y for an energy bar as a function of price x. The daily sales for three different prices of the energy bar are shown in the table. Use the regression capabilities of a graphing utility to find the least squares regression line for the data. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the least squares regression line for the points 
. Round numerical values in your answer to two decimal places.
A)
B)
C)
D)
E)
. Round numerical values in your answer to two decimal places.A)
B)
C)
D)
E)
سؤال
Find the least squares regression line for the points 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
A company manufactures two types of sneakers: running shoes and basketball shoes. The total revenue from 
units of running shoes and 
units of basketball shoes is: 
, where 
and 
are in thousands of units. Find 
and 
so as to maximize the revenue.
A)
B)
C)
D)
E)
units of running shoes and units of basketball shoes is: , where and are in thousands of units. Find and so as to maximize the revenue.A)
B)
C)
D)
E)
سؤال
Suppose a corporation manufactures candles at two locations. The cost of producing 
units at location 1 is 
and the cost of producing 
units at location 2 is 
. The candles sell for $43 per unit. Find the quantity that should be produced at each location to maximize the profit 
.
A)
B)
C)
D)
E)
units at location 1 is and the cost of producing units at location 2 is . The candles sell for $43 per unit. Find the quantity that should be produced at each location to maximize the profit .A)
B)
C)
D)
E)
سؤال
Find three positive numbers x, y, and z whose sum is 30 and the sum of the squares is a minimum.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Suppose a store manager wants to know the demand y for an energy bar as a function of price x. The daily sales for three different prices of the energy bar are shown in the table. Determine the least squares regression line for the data using the regression capabilities of a graphing utility, and then use this model to estimate the demand when the price is $1.59. 
A) 202
B) 166
C) 190
D) 151
A) 202
B) 166
C) 190
D) 151
سؤال
Suppose a trough with trapezoidal cross sections is formed by turning up the edges of a 30-inch-wide sheet of aluminum (see figure). Find the cross section of maximum area. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 640 cubic feet. The cost of wall paint is $0.076 per square foot and the cost of ceiling paint is $0.19 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Find the room dimensions that result in a minimum cost for the paint. Round your answers to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the minimum distance from the point 
to the plane 
.
A)
B)
C)
D)
E)
to the plane .A)
B)
C)
D)
E)
سؤال
Suppose an agronomist used four test plots to determine the relationship between the wheat yield y (in bushels per acre) and the amount of fertilizer x (in hundreds of pounds per acre). The results are shown in the table. Determine the least squares regression line for the data using the regression capabilities of a graphing utility, and then use this model to estimate the yield for a fertilizer application of 160 pounds per acre. Round your answer to one decimal place. 
A) 37.3 bushels per acre
B) 39.7 bushels per acre
C) 35.6 bushels per acre
D) 38.4 bushels per acre
E) 39.3 bushels per acre
A) 37.3 bushels per acre
B) 39.7 bushels per acre
C) 35.6 bushels per acre
D) 38.4 bushels per acre
E) 39.3 bushels per acre
سؤال
Find the minimum distance from the point 
to the surface 
.
A)
B)
C)
D)
E)
to the surface .A)
B)
C)
D)
E)
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العب
ملء الشاشة (f)
Deck 13: Section 10: Functions of Several Variables
1
The material for constructing the base of an open box costs 1.5 times as much per unit area as the material for constructing the sides. For a fixed amount of money $150.00, find the dimensions of the box of largest volume that can be made.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Find three positive numbers x, y, and z whose sum is 24 and product is a maximum.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 360 cubic feet. The cost of wall paint is $0.054 per square foot and the cost of ceiling paint is $0.18 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Identify the room dimensions that result in a minimum cost for the paint and use these dimensions to find the minimum cost for the paint. Round your answer to the nearest cent.
A) $54.00
B) $8.64
C) $7.00
D) $19.44
E) $21.60
A) $54.00
B) $8.64
C) $7.00
D) $19.44
E) $21.60
$19.44
4
Find the least squares regression line for the points shown in the graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
The least squares regression line for the points shown in the graph is . Calculate S, the sum of the squared errors.
A)
B)
C)
D)
E)
. Calculate S, the sum of the squared errors. A)
B)
C)
D)
E)
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6
Suppose an agronomist used four test plots to determine the relationship between the wheat yield y (in bushels per acre) and the amount of fertilizer x (in hundreds of pounds per acre). The results are shown in the table. Use the regression capabilities of a graphing utility to find the least squares regression line for the data.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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فتح الحزمة
k this deck
7
Suppose a store manager wants to know the demand y for an energy bar as a function of price x. The daily sales for three different prices of the energy bar are shown in the table. Use the regression capabilities of a graphing utility to find the least squares regression line for the data.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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k this deck
8
Find the least squares regression line for the points . Round numerical values in your answer to two decimal places.
A)
B)
C)
D)
E)
. Round numerical values in your answer to two decimal places.A)
B)
C)
D)
E)
فتح الحزمة
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9
Find the least squares regression line for the points .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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10
A company manufactures two types of sneakers: running shoes and basketball shoes. The total revenue from units of running shoes and units of basketball shoes is: , where and are in thousands of units. Find and so as to maximize the revenue.
A)
B)
C)
D)
E)
units of running shoes and units of basketball shoes is: , where and are in thousands of units. Find and so as to maximize the revenue.A)
B)
C)
D)
E)
فتح الحزمة
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11
Suppose a corporation manufactures candles at two locations. The cost of producing units at location 1 is and the cost of producing units at location 2 is . The candles sell for $43 per unit. Find the quantity that should be produced at each location to maximize the profit .
A)
B)
C)
D)
E)
units at location 1 is and the cost of producing units at location 2 is . The candles sell for $43 per unit. Find the quantity that should be produced at each location to maximize the profit .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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12
Find three positive numbers x, y, and z whose sum is 30 and the sum of the squares is a minimum.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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13
Suppose a store manager wants to know the demand y for an energy bar as a function of price x. The daily sales for three different prices of the energy bar are shown in the table. Determine the least squares regression line for the data using the regression capabilities of a graphing utility, and then use this model to estimate the demand when the price is $1.59.
A) 202
B) 166
C) 190
D) 151
A) 202
B) 166
C) 190
D) 151
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افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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14
Suppose a trough with trapezoidal cross sections is formed by turning up the edges of a 30-inch-wide sheet of aluminum (see figure). Find the cross section of maximum area.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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15
Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 640 cubic feet. The cost of wall paint is $0.076 per square foot and the cost of ceiling paint is $0.19 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Find the room dimensions that result in a minimum cost for the paint. Round your answers to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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16
Find the minimum distance from the point to the plane .
A)
B)
C)
D)
E)
to the plane .A)
B)
C)
D)
E)
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افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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17
Suppose an agronomist used four test plots to determine the relationship between the wheat yield y (in bushels per acre) and the amount of fertilizer x (in hundreds of pounds per acre). The results are shown in the table. Determine the least squares regression line for the data using the regression capabilities of a graphing utility, and then use this model to estimate the yield for a fertilizer application of 160 pounds per acre. Round your answer to one decimal place.
A) 37.3 bushels per acre
B) 39.7 bushels per acre
C) 35.6 bushels per acre
D) 38.4 bushels per acre
E) 39.3 bushels per acre
A) 37.3 bushels per acre
B) 39.7 bushels per acre
C) 35.6 bushels per acre
D) 38.4 bushels per acre
E) 39.3 bushels per acre
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18
Find the minimum distance from the point to the surface .
A)
B)
C)
D)
E)
to the surface .A)
B)
C)
D)
E)
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