The dimensions of a closed rectangular box are measured as 60 centimeters, 50 centimeters, and 70 centimeters, with an error in each measurement of at most 0.2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.

The maximum error in calculating the surface area of the box is 72 square centimeters.

Step-by-step explanation:

From Geometry, the surface area of the closed rectangular box (), in square centimeters, is represented by the following formula:

(1)

Where:

- Width, in centimeters.

- Length, in centimeters.

- Height, in centimeters.

And the maximum error in calculating the surface area (), in square centimeters, is determined by the concept of total differentials, used in Multivariate Calculus:

(2)

Where:

- Measurement error in width, in centimeters.

- Measurement error in length, in centimeters.

- Measurement error in height, in centimeters.

If we know that , , and , then the maximum error in calculating the surface area is:

The maximum error in calculating the surface area of the box is 72 square centimeters.

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

the answer is: the length is 5/6 yards.

give me a or a 5 star rating if this is correct!

step-by-step explanation: