Chose the equation for a line that passes through (2,-3) and has a slope of m=-4 in point slope form. A y - 3 = -4(2-2) By - 2 =
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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.
Break the numbers under the radical into perfect squares: . Take the perfect squares out: you have two 2's, and 2 x's, on the outside of the radical with 2 and z leftover:
. Multiply everything together to get
.