Answer:
A
Step-by-step explanation:
The position of an atom moving inside a cathode ray tube is given by the function:
Where f(t) is in meters and <em>t</em> is in seconds.
And we want to determine its instantaneous velocity at <em>t</em> = 2.5 seconds.
The velocity function is the derivative of the position function. Thus, find the derivative of the function:
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Then the instantaneous velocity at <em>t</em> = 2.5 will be:
Our answer is A.
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.