Suppose that z is a linear function of x and y with slope 2 in the x-direction and slope 3 in the y-direction. (a) a change of 0.5 in x and −0.1 in y produces what change in z?

Answer = 0.7

Solution -

Similar to linear functions of one variable, we have the Slopes - Intercept Formula for a linear function of two variables given by,

⇒ z  =  m₁x+m₂y+c

where

m₁ = slope in X direction = 2

m₂ = slope in Y direction = 3

c = c is the z-intercept of the plane defined by the equation.

Taking the derivatives of both sides

⇒ dz = m₁dx + m₂dy

dx = change in x = 0.5

dy = change in y = -0.1

Putting all the values in the equation

⇒ dz = 2×0.5 + 3(-0.1) = 0.7

Hence, change in z = 0.7

step-by-step explanation:

what grade level is this? need to know so i can look in my old textbooks!

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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step-by-step explanation: