Use these equations to find z / x and z / y for the following. x 3 + y 5 + z 5 =

Question

Use these equations to find z/x and z/y for the following.

x3 + y5 + z5 = 5xyz

10.–/0.9 pointsSCalc7 14.5.038.MI.My Notes

The radius of a right circular cone is increasing at a rate of 1.7 in/s while its height is decreasing at a rate of 2.3 in/s. At what rate is the volume of the cone changing when the radius is 106 in. and the height is 152 in.?
in3/s

11.–/1 pointsSCalc7 14.5.039.My Notes

The length , width w, and height h of a box change with time. At a certain instant the dimensions are = 5 m and

w = h = 2 m,

and and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 7 m/s. At that instant find the rates at which the following quantities are changing.

(a) The volume.
m3/s

(b) The surface area.
m2/s

(c) The length of a diagonal. (Round your answer to two decimal places.)
m/s

Explanation / Answer

9) z/x and z/y

x3 + y5 + z5 = 5xyz

partially differentiate with respect to x on both sides

derivative of xn=nxn-1

(uv)'=u'v+uv'

3x2 + 0 + 5z4z/x = 5y(1*z +   x* z/x)

3x2 +    5z4z/x = 5yz +   5yx z/x

5z4z/x - 5yx z/x = 5yz -3x2

z/x (5z4- 5yx )=5yz -3x2

z/x=(5yz -3x2)/(5z4- 5yx )

x3 + y5 + z5 = 5xyz

partially differentiate with respect to y on both sides

derivative of xn=nxn-1

(uv)'=u'v+uv'

0+ 5y4 + 5z4z/y = 5x(1*z +   y* z/y)

5y4 +    5z4z/y = 5xz +   5yx z/y

5z4z/y - 5yx z/y = 5xz -5y4

z/y (5z4- 5yx )= 5xz -5y4

z/y=(5xz -5y4)/(5z4- 5yx )

z/y=(xz -y4)/(z4- yx )

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