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S_A_V [24]
3 years ago
12

The volume v of a cylinder is computed using the values 2.2 m for diameter and 6.8 m for height. use the linear approximation to

estimate the maximum error in v if each of these values has a possible error of at most 5% (use decimal notation. give your answer to three decimal places.)
Mathematics
1 answer:
geniusboy [140]3 years ago
4 0

A linear approximation to the error in volume can be written as

... ∆V = (∂V/∂d)·∆d + (∂V/∂h)·∆h

For V=(π/4)·d²·h, this is

... ∆V = 2·(π/4)·d·h·∆d + (π/4)·d²·∆h

Using ∆d = 0.05d and ∆h = 0.05h, this becomes

... ∆V = (π/4)·d²·h·(2·0.05 + 0.05) = 0.15·V

The nominal volume is

... V = (π/4)·d²·h = (π/4)·(2.2 m)²·(6.8 m) = 25.849 m³

Then the maximum error in volume is

... 0.15V = 0.15·25.849 m³ ≈ 3.877 m³

_____

Essentially, the error percentage is multiplied by the exponent of the associated variable. Then these products are added to get the maximum error percentage.

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Now we need to check for extraneous solutions:

√3(4) + 4 = 4

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8 0
2 years ago
​ Commemorative coins come in packs of 15, while coin holders come in packs of 25. What are the least numbers of packs you shoul
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2 years ago
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guajiro [1.7K]
The volume of the metal box if the box was completely solid (V1), is:
 
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 Then, the volumen of the no solid metal box is:
 
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 Therefore, the volume of metal needed to smelt the cubical metal box, is:
 
 V3=V1-V2
 V3=1728 inches³-216 inches³
 V3=1512 inches³
6 0
3 years ago
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