QuestionGiven $g(x, y, z)=0.07 x+0.02 y-0.09 z-0.01$ , complete: (a) $g$ changes by _ for 1 unit increase in $z$ . (b) $g$ changes by _ for 1 unit increase in $x$ . (c) $g$ increases by 0.02 for _ in _

Studdy Solution

STEP 1

Assumptions1. The function $g(x, y, z)$ is given by $g(x, y, z)=0.07 x+0.02 y-0.09 z-0.01$ . . We are asked to find the change in $g$ with respect to each variable $x$ , $y$ , and $z$ .

STEP 2

The coefficients of $x$ , $y$ , and $z$ in the function $g(x, y, z)$ represent the change in $g$ for every1 unit of increase in the respective variable.
(a) The coefficient of $z$ is $-0.09$ .

STEP 3

This means that for every1 unit of increase in $z$ , $g$ decreases by $0.09$ units.
The variable $g$ decreases by $0.09$ units for every1 unit of increase in $z$ .

STEP 4

(b) The coefficient of $x$ is $0.07$ .

STEP 5

This means that for every1 unit of increase in $x$ , $g$ increases by $0.07$ units.
The variable $g$ increases by $0.07$ units for every1 unit of increase in $x$ .

STEP 6

(c) We are given that the variable $g$ increases by $0.02$ units.

STEP 7

This increase corresponds to the coefficient of $y$ in the function $g(x, y, z)$ .
Therefore, $g$ increases by $0.02$ units for every1 unit of increase in $y$ .

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QuestionGiven $g(x, y, z)=0.07 x+0.02 y-0.09 z-0.01$ , complete: (a) $g$ changes by _ for 1 unit increase in $z$ . (b) $g$ changes by _ for 1 unit increase in $x$ . (c) $g$ increases by 0.02 for _ in _

Studdy Solution

STEP 1

Assumptions1. The function $g(x, y, z)$ is given by $g(x, y, z)=0.07 x+0.02 y-0.09 z-0.01$ . . We are asked to find the change in $g$ with respect to each variable $x$ , $y$ , and $z$ .

STEP 2

The coefficients of $x$ , $y$ , and $z$ in the function $g(x, y, z)$ represent the change in $g$ for every1 unit of increase in the respective variable.
(a) The coefficient of $z$ is $-0.09$ .

STEP 3

This means that for every1 unit of increase in $z$ , $g$ decreases by $0.09$ units.
The variable $g$ decreases by $0.09$ units for every1 unit of increase in $z$ .

STEP 4

(b) The coefficient of $x$ is $0.07$ .

STEP 5

This means that for every1 unit of increase in $x$ , $g$ increases by $0.07$ units.
The variable $g$ increases by $0.07$ units for every1 unit of increase in $x$ .

STEP 6

(c) We are given that the variable $g$ increases by $0.02$ units.

STEP 7

This increase corresponds to the coefficient of $y$ in the function $g(x, y, z)$ .
Therefore, $g$ increases by $0.02$ units for every1 unit of increase in $y$ .

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QuestionGiven g(x,y,z)=0.07x+0.02y−0.09z−0.01g(x, y, z)=0.07 x+0.02 y-0.09 z-0.01g(x,y,z)=0.07x+0.02y−0.09z−0.01, complete: (a) ggg changes by ___ for 1 unit increase in zzz. (b) ggg changes by ___ for 1 unit increase in xxx. (c) ggg increases by 0.02 for ___ in ___

Studdy Solution

STEP 1

Assumptions1. The function g(x,y,z)g(x, y, z)g(x,y,z) is given by g(x,y,z)=0.07x+0.02y−0.09z−0.01g(x, y, z)=0.07 x+0.02 y-0.09 z-0.01g(x,y,z)=0.07x+0.02y−0.09z−0.01. . We are asked to find the change in ggg with respect to each variable xxx, yyy, and zzz.

STEP 2

The coefficients of xxx, yyy, and zzz in the function g(x,y,z)g(x, y, z)g(x,y,z) represent the change in ggg for every1 unit of increase in the respective variable.(a) The coefficient of zzz is −0.09-0.09−0.09.

STEP 3

This means that for every1 unit of increase in zzz, ggg decreases by 0.090.090.09 units.The variable ggg decreases by 0.090.090.09 units for every1 unit of increase in zzz.

STEP 4

(b) The coefficient of xxx is 0.070.070.07.

STEP 5

This means that for every1 unit of increase in xxx, ggg increases by 0.070.070.07 units.The variable ggg increases by 0.070.070.07 units for every1 unit of increase in xxx.

STEP 6

(c) We are given that the variable ggg increases by 0.020.020.02 units.

STEP 7

This increase corresponds to the coefficient of yyy in the function g(x,y,z)g(x, y, z)g(x,y,z).Therefore, ggg increases by 0.020.020.02 units for every1 unit of increase in yyy.

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QuestionGiven $g(x, y, z)=0.07 x+0.02 y-0.09 z-0.01$ , complete: (a) $g$ changes by _ for 1 unit increase in $z$ . (b) $g$ changes by _ for 1 unit increase in $x$ . (c) $g$ increases by 0.02 for _ in _

Assumptions1. The function $g(x, y, z)$ is given by $g(x, y, z)=0.07 x+0.02 y-0.09 z-0.01$ . . We are asked to find the change in $g$ with respect to each variable $x$ , $y$ , and $z$ .

The coefficients of $x$ , $y$ , and $z$ in the function $g(x, y, z)$ represent the change in $g$ for every1 unit of increase in the respective variable.
(a) The coefficient of $z$ is $-0.09$ .

This means that for every1 unit of increase in $z$ , $g$ decreases by $0.09$ units.
The variable $g$ decreases by $0.09$ units for every1 unit of increase in $z$ .

(b) The coefficient of $x$ is $0.07$ .

This means that for every1 unit of increase in $x$ , $g$ increases by $0.07$ units.
The variable $g$ increases by $0.07$ units for every1 unit of increase in $x$ .

(c) We are given that the variable $g$ increases by $0.02$ units.

This increase corresponds to the coefficient of $y$ in the function $g(x, y, z)$ .
Therefore, $g$ increases by $0.02$ units for every1 unit of increase in $y$ .