8. The length L, width W, and height H of a box change with time. As a certain instant the dimensions are L = 1m and W = H = 2m, and L and W are increasing at a rate of 2 m/s while H is decreasing at a rate of 3 m/s. At that instant find the rates at which the following quantities are changing: a. the volume b. the surface area c. the length of the diagonal.
8. The length L, width W, and height H of a box change with time. As a certain instant the dimensions are L = 1m and W = H = 2m, and L and W are increasing at a rate of 2 m/s while H is decreasing at a rate of 3 m/s. At that instant find the rates at which the following quantities are changing: a. the volume b. the surface area c. the length of the diagonal.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve problem 8 with explanation please.
Transcribed Image Text:7. Show that the given function u(x, y, z) satisfies the 3-dimensional Laplace's partial differential equation
yux
д'и əzu
Əx² dy² Əz
+ =0 where:
u=
+
1
p²
8. The length L, width W, and height H of a box change with time. As a certain instant the dimensions are L = 1m
and W = H = 2m, and L and W are increasing at a rate of 2 m/s while H is decreasing at a rate of 3 m/s. At that
instant find the rates at which the following quantities are changing:
a. the volume
b. the surface area
c. the length of the diagonal.
1/1
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