a.
To find: the rates of change of the area.
a.
Answer to Problem 9E
The value of
Explanation of Solution
Given information:
All variables are differentiable function of
l = 12 cm, w = 5 cm.
Calculation :
To calculate the rate of change of the area,
Therefore,
Area of a rectangle dimension
l = length, w = width
Differentiate with respect to t .
Putting the value of
Hence, the value of
b.
To find: the rates of change of the perimeter.
b.
Answer to Problem 9E
The value of
Explanation of Solution
Given information:
All variables are differentiable function of
l = 12 cm, w = 5 cm.
Calculation :
To calculate the rate of change of the perimeter,
Therefore,
Perimeter of a rectangle dimension
l = length, w = width
Differentiate with respect to t .
Putting the value of
Hence, the value of
c.
To find: the rates of change of the length of a diagonal of a rectangle.
c.
Answer to Problem 9E
The value of
Explanation of Solution
Given information:
All variables are differentiable function of
l = 12 cm, w = 5 cm.
Calculation :
To calculate the rates of change of the length of a diagonal of a rectangle,
Therefore,
Length of a diagonal of the rectangle dimension
Differentiate with respect to t .
Putting the value of
Hence, the value of
d.
To find: the quantities that are increasing and that are decreasing.
d.
Answer to Problem 9E
The area is increasing because
The perimeter is not changing because
The length of the diagonal is decreasing because
Explanation of Solution
Given information:
l = 12 cm, w = 5 cm.
All variables are differentiable function of
Calculation :
To explain which of these quantities are increasing and which are decreasing.
Therefore,
We have calculated,
Since
Again, we have calculated
Since
Again, we have calculated
Since
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic
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