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Mathematics

1 answer:

liubo4ka [24]4 years ago

3 0

(A) Find the approximate length of the plank. Round to the nearest tenth of a foot.
Given that the distance of the ground is 3ft.
In order to get the length of the plank,
we can use the this one.

cos 49 = ground / plank
cos 49 = 3 / plank
plank = cos 49 / 3
plank = 0.10 ft

(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.

The remaining angle is equal to
angle = 180 - (90+49)
angle = 41

Finding the height.
tan 41 = height / ground
tan 41 = height / 3
height = tan 41 / 3
height = 0.05 ft.

(A) 0.10 feet
(B) 0.05 feet

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The dimensions of a closed rectangular box are measured as 60 centimeters, 50 centimeters, and 70 centimeters, with an error in

Studentka2010 [4]

Answer:

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 ( $A_{s}$ ), in square centimeters, is represented by the following formula:

$A_{s} = w\cdot l + (w + l)\cdot h$ (1)

Where:

$w$ - Width, in centimeters.

$l$ - Length, in centimeters.

$h$ - Height, in centimeters.

And the maximum error in calculating the surface area ( $\Delta A_{s}$ ), in square centimeters, is determined by the concept of total differentials, used in Multivariate Calculus:

$\Delta A_{s} = \left(l+h\right)\cdot \Delta w + \left(w+h\right)\cdot \Delta l + (w+l)\cdot \Delta h$ (2)

Where:

$\Delta w$ - Measurement error in width, in centimeters.

$\Delta l$ - Measurement error in length, in centimeters.

$\Delta h$ - Measurement error in height, in centimeters.

If we know that $\Delta w = \Delta h = \Delta l = 0.2\,cm$ , $w = 60\,cm$ , $l = 50\,cm$ and $h = 70\,cm$ , then the maximum error in calculating the surface area is: