Answer:
(a) 0.7
(b) 4.9
Step-by-step explanation:
If z is a linear function of x and y and the slopes in the x and y directions are 3 and 2, respectively, z can be written as:
[tex]z(x,y) = 3x+2y+c[/tex]
Where 'c' is a constant value.
(a) A change of 0.2 in x and 0.1 in y produces the following change in z:
[tex]\Delta z = 2\Delta x +3\Delta y\\\Delta z = 2*0.2+3*0.1\\\Delta z = 0.7[/tex]
(b) Applying the point x=7, y=4, z=5 to the general equation gives us the value of 'c':
[tex]5 = 3*7+2*4+c\\c= -24[/tex]
For x=7.1 and y=3.8, the value of z is:
[tex]z(7.1, 3.8) = 3*7.1+2*3.8-24\\z= 4.9[/tex]
