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Answer:
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.
Step-by-step explanation:
The circumference (), in centimeters, and the surface area (
), in square centimeters, of a sphere are represented by following formulas:
(1)
(2)
Where is the radius of the sphere, in centimeters.
By applying (2) in (1), we derive this expression:
(3)
By definition of Total Differential, which is equivalent to definition of Linear Approximation in this case, we determine an expression for the maximum error in the calculated surface area (), in square centimeters:
(4)
Where:
- Measure circumference, in centimeters.
- Possible error in circumference, in centimeters.
If we know that and
, then the maximum error is:
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.
Answer:
The equation to represent the rate of receding water level is L = 34 .
Step-by-step explanation:
Given as :
The initial level of water in river = 34 feet
The rate of receding water level = 0.5 foot per day
Or, The rate of percentage of receding water level = 50 % per day
Let the level of water after d days = L
Now,
The level of water after d days = initial level of water × (
I.e L = 34 × (
∴ L = 34 ×
Hence The equation to represent the rate of receding water level is L = 34 . Answer
