Suppose you are climbing a hill whose shape is given by the equation z = 1600 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 1464). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend?

you will start to ascend at the rate of 1.6

Step-by-step explanation:

Walking south, it's the negative part of a coordinate, so the unit vector at this point is; u = (0,-1)

We are told that the equation z = 1600 − 0.005x² − 0.01y²

Therefore, we have;

∇z = ((δ/δx)i + (δ/δx)j)(1600 − 0.005x² − 0.01y²)

This gives;

∇z = -0.005(2x)i - 0.01(2y)j

∇z = <-0.01x - 0.02y>

coordinates are (120, 80, 1464).

Thus;

∇z(120, 80, 1464) = <-0.01(120), - 0.02(80)> = <-1.20, -1.60>

D_uf = <-1.20, -1.60> × <0, - 1>

D_uf = 0 + 1.6

D_uf = 1.6

So, you will start to ascend at the rate of 1.6

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

add 5 subtract 1

step-by-step explanation: